Graphene on rhodium from first principles: Tailoring electronic, structural and chemical properties

Graphene on rhodium from first principles:

Tailoring structural, electronic and chemical properties

Carlos Romero Muñiz

principles: Tailoring structural, electronic and chemical properties

Universidad Autónoma de Madrid Departamento de Física Teórica

de la Materia Condensada

Dissertation submitted to obtain the degree of Doctor en Física

Author: Carlos Romero Muñiz

Supervisors: Prof. Rubén Pérez Pérez / Dr. Pablo Pou Bell

Madrid, April 2017

En primer lugar quiero darles las gracias a mis directores de tesis, Rubén y Pablo, por estos años en los que hemos trabajado juntos. No solo agradezco lo que he aprendido de ellos y el tiempo que me han dedicado, que no ha sido poco, sino la conanza y la libertad que me han dado siempre. En este tiempo me he alegrado muchas veces de haber coincidido no solo con buenos investigadores sino con excelentes personas.

Mis agradecimientos se hacen extensibles a todos los miembros pasados y presentes del grupo de investigación con los que he coincidido. A Alberto, nuestra última incorporación. A Guilherme por su alegría y cercanía desde el primer momento. A María, que siempre tiene palabras buenas para todo todos.

A Krzysztof, por nuestras discusiones sobre costumbres europeas. A Ruth, por su simpatía y su ayuda cada vez que se la he pedido. A Milica, quien me explicó al principio de los tiempos muchas cosas de física computacional con una profesionalidad sorprendente y se lo agradezco de verdad porque nunca son fáciles los comienzos. A Diego, por la mudanza y sus ánimos. A Michael, por enriquecer mi vocabulario y por ayudarme en tantas tareas informáticas, en las que yo soy realmente nefasto. A Linda, por ser un ejemplo a seguir para mí por la actitud que muestra ante cualquier problema que le surge. Y por supuesto a Lucía, por su amistad, y porque es la compañera de trabajo que todo el mundo querría tener. Yo he tenido la suerte de comprobarlo durante estos años.

Siguiendo el orden lógico pasamos a mis compañeros del Departamento de Física Teórica de la Materia Condensada. Tanto los profesores como los otros estudiantes son responsables del buen ambiente de trabajo del que nos bene-

ciamos todos. Aunque no puedo nombraros a todos para no hacer todavía i

ii Agradecimientos

más larga la tesis, sí que me gustaría mencionar explícitamente a algunos de vosotros. A Carlos y Paloma, mis primigenios compañeros de despacho, que ya son eminentes doctores. A nuestro grupo de los almuerzos, (solo ellos saben lo bien que nos lo pasamos, los temas tan estrafalarios que tratamos y las discu- siones recurrentes que aparecen una y otra vez). A Miguel, porque no es fácil coincidir de manera totalmente involuntaria en el colegio, en la facultad, en el departamento y en el piso, bueno, en el piso quizá no haya sido de forma tan involuntaria... Y por último a Rocío, que aunque solo lleve dos años siendo mi compañera de despacho, hemos compartido ya muchas cosas (incluyendo a las vetustas plantas del departamento). Gracias por escucharme siempre y por ayudarme en todo, desde los temas más complicados hasta en la elección de colores para las grácas.

Nuestros queridos colaboradores experimentales, Chema y Ana, se merecen una mención muy especial, ya que prácticamente todo el trabajo de la tesis es producto de nuestro trabajo en equipo. Han sido compañeros de trabajo excep- cionales y con los que todo se ha hecho más fácil. Incluidas las interminables tardes de correcciones que hemos tenido Ana y yo muchas veces, y de las que todavía, intuyo, quedan algunas.

Una parte de la tesis se ha desarrollado en Japón por lo que agradezco la calurosa acogida de Miyazaki-san y Nakata-san en el NIMS. En todo momento me trataron estupendamente y me llevaron a toda clase de eventos interesantes, incluyendo, entre muchos otros, una jornada de sumo memorable y un almuerzo en un restaurante de anguilas. Le agradezco también, junto a Abe-san, la ayuda en los trámites burocráticos, que si aquí son complicados en Japón... Por supuesto a los otros miembros del grupo CONQUEST, Tsumuraya-san, Tamura- san, mi amigo Lin y todos los demás. Aunque a veces he sentido allí la soledad más extrema siempre recordaré mis estancias en Japón como periodos realmente felices.

Sería injusto que me olvidara de Victorino, quien me introdujo en el mundo de la investigación. Aparte de por sus acertados consejos de índole variada le doy las gracias sinceramente por la honradez con la que me ha tratado desde el primer momento.

Dejando atrás el plano profesional, todo el mundo sabe que las familias sufren en mayor o menor medida ciertos daños colaterales de las tesis debido al alto grado de dedicación que normalmente requiere la investigación. Además, en mi caso hay añadir que la tesis era en otra ciudad. Yo tengo mucho que agradecerles, a mis padres, que desde siempre estuvieron muy preocupados por mi educación. Aunque mi caso era un poco especial no dejaron de apoyarme nunca y esta tesis en gran parte es el resultado de ese esfuerzo. En particular a mi padre le agradezco que haya tratado de mejorar, en la medida de lo posible, que no era fácil, la redacción de este texto. También agradezco la ayuda que en estos años he recibido de mis tres hermanos: Guillermo, Ignacio y Álvaro, en especial de Ignacio con quien he discutido bastantes cosas de química en general y relacionadas con esta tesis en particular. No me olvido tampoco de mi abuela, quien todavía sigue cuidando de mis hermanos y de mí, ni de los que ya no están, especialmente de mis abuelos y de mi tía María del Mar, quienes seguro se hubieran alegrado en este momento.

Por último, le dedico esta tesis a la persona más importante de mi vida, a mi mujer, Gema. Por desgracia, aunque no estamos juntos el tiempo que deberíamos no pasa ningún día sin que me acuerde de ella y valore la suerte que he tenido de que desde hace años seamos una familia. Sin ella no habría sido capaz de superar los contratiempos que han ido surgiendo o los días en los que parece que nada funciona. Por todo esto, por apoyarme siempre y por ser todo para mí le doy las gracias. Cada vez queda menos para que estemos juntos por

n.

Madrid, 25 de abril de 2017¹

1Esta tesis se ha podido llevar a cabo gracias a una beca de doctorado de la Universidad Autónoma de Madrid (FPI-UAM) y a una beca de la Fundación Universia.

Abstract 1

1 Graphene on metals 11

1.1 Introduction . . . 11

1.2 Basic properties of graphene . . . 14

1.3 Graphene-metal interfaces . . . 18

1.3.1 Moiré patterns . . . 19

1.3.2 Weakly coupled systems . . . 23

1.3.3 Strongly coupled systems . . . 26

1.4 Surface modication strategies . . . 29

1.4.1 Deposition of clusters and molecules . . . 30

1.4.2 Intercalation . . . 33

1.4.3 Heteroatom doping . . . 36

1.5 Outlook and scope of this thesis . . . 39

2 Atomistic modeling with Density Functional Theory 43 2.1 General considerations on electronic structure calculations . . . . 43

2.2 The foundations of Density Functional Theory . . . 47

2.2.1 The Hohenberg-Kohn theorems . . . 48

2.2.2 The Kohn-Sham self-consistent equations . . . 50

2.3 The exchange and correlation functional . . . 53

2.3.1 Local Density Approximation . . . 54

2.3.2 Generalized Gradient Approximation . . . 56

2.3.3 Hybrid and semi-empirical functionals . . . 59 v

vi CONTENTS

2.4 The treatment of dispersion interactions . . . 61

2.4.1 Semi-empirical corrections . . . 62

2.4.2 Non-local functionals . . . 64

2.5 Practical aspects of modern calculations . . . 66

2.5.1 Periodic Boundary Conditions and reciprocal space . . . 67

2.5.2 Pseudopotentials . . . 69

2.5.3 Ecient minimization algorithms and ionic relaxations . . 74

2.6 Basis sets for wave functions . . . 78

2.6.1 Plane waves . . . 79

2.6.2 Localized orbitals . . . 80

2.7 Commercial packages and simulation strategies . . . 85

3 Synthesis and characterization of graphene 91 3.1 Introduction . . . 91

3.2 Synthesis and production . . . 93

3.2.1 Mechanical exfoliation . . . 94

3.2.2 Liquid phase chemical methods . . . 95

3.2.3 Graphitization of silicon carbide . . . 96

3.2.4 Segregation . . . 97

3.2.5 Chemical Vapor Deposition (CVD) . . . 98

3.3 Brief survey on characterization techniques . . . 99

3.3.1 X-ray/Ultraviolet Photoemission Spectroscopy (XPS/UPS) 99 3.3.2 Angle Resolved Photoemission Spectroscopy (ARPES) . 101 3.3.3 Auger Electron Spectroscopy (AES) . . . 102

3.3.4 Raman Spectroscopy . . . 103

3.3.5 Low Energy Electron Diraction (LEED) . . . 104

3.3.6 Scanning Tunneling Microscopy (STM) . . . 106

3.3.7 Atomic Force Microscopy (AFM) . . . 108

3.3.8 Transmission Electron Microscopy (TEM) . . . 110

3.4 Modeling scanning tunneling microscopy experiments . . . 111

3.4.1 Bardeen Theory and the Terso-Hamann approximation . 112 3.4.2 Non-Equilibrium Green's Function formalism . . . 116

4 Graphene grown on rhodium 123

4.1 Introduction . . . 123

4.2 Experimental evidences . . . 127

4.2.1 Revealing multiple moiré patterns . . . 128

4.2.2 STM apparent corrugation and system size dependence . 134 4.3 Computational details and simulation cells . . . 136

4.4 Simulations results . . . 139

4.4.1 Atomic structures of moiré patterns . . . 140

4.4.2 STM simulations: Apparent corrugation vs. topography . 143 4.4.3 Energetic interplay between deformation and binding . . 148

4.5 Conclusions . . . 154

5 Oxygen intercalation on the graphene-rhodium interface 157 5.1 Introduction . . . 157

5.2 Methods and experimental evidences . . . 160

5.2.1 Graphene growth and oxygen intercalation . . . 160

5.2.2 Evolution of intercalation observed by STM . . . 163

5.2.3 Computational details . . . 167

5.3 Step-by-step decoupling of the graphene layer . . . 169

5.3.1 Atomic structures for dierent coverage . . . 169

5.3.2 Electronic decoupling . . . 171

5.4 Intercalation mechanisms at atomic-scale . . . 175

5.4.1 Oxygen penetration through graphene point defects . . . 176

5.4.2 Oxygen penetration through microetching points . . . 180

5.4.3 Binding and diusion on the low coverage limit . . . 181

5.4.4 Collective diusion for higher coverage . . . 185

5.5 Substrate-induced enhancement of the graphene chemical reactivity188 5.5.1 Molecular oxygen dissociation on graphene . . . 188

5.5.2 Adsorption and diusion of atomic oxygen . . . 193

5.6 Conclusions . . . 197

6 N-doped graphene on metals 199 6.1 Introduction . . . 199

viii CONTENTS

6.2 Substitutional N-doping on free-standing graphene . . . 203

6.3 N-doping on Pt(111) as weakly interacting system . . . 205

6.3.1 Ion bombardment and experimental results . . . 205

6.3.2 Computational details . . . 207

6.3.3 Characterization of nitrogen defects . . . 208

6.4 N-doping on Rh(111) as strongly interacting system . . . 214

6.4.1 Experimental characterization by STM . . . 214

6.4.2 Electronic properties of substitutional nitrogen defects . . 217

6.5 Combining N-doping and oxygen intercalation in G/Rh(111) . . 219

6.6 Oxygen-decorated free-standing N-doped graphene . . . 225

6.6.1 Adsorption of a single oxygen atom . . . 226

6.6.2 Cooperative eects on multiple-atom adsorption . . . 229

6.7 Conclusions . . . 233

7 High-accuracy simulations in large systems using CONQUEST 235 7.1 Introduction . . . 235

7.2 The CONQUEST scheme . . . 240

7.2.1 Standard localized orbitals . . . 240

7.2.2 Contracted multi-site basis set . . . 242

7.3 Computational methods and basis sets . . . 244

7.3.1 Systems and simulation cells . . . 244

7.3.2 Computational details . . . 247

7.4 CONQUEST vs. VASP comparison . . . 249

7.4.1 Atomic structures and energetics . . . 249

7.4.2 Electronic properties . . . 255

7.5 Large-scale simulations in cells containing thousands of atoms . . 258

7.6 Conclusions . . . 260

General conclusions 263

Publication list 271

Bibliography 272

After more than ten years of intense research on graphene, its potential appli- cations in electronic devices are not as encouraging as expected. Nevertheless, such a huge scientic production has led to interesting applications on surface modication, catalysis, coating technology, etc. Most of these applications have a common feature: the interaction with the supporting substrate is taken into account as a key parameter to tune the properties of graphene. For instance, it was pointed out that the proper selection of a metallic substrate could be used to tailor the electronic properties of the graphene monolayer with dierent doping levels. Similarly, corrugations and adsorption distances clearly depend on the interaction strength. In addition, there are other methods which allow further modications like the intercalation of dierent species in the space con-

ned between graphene and the metallic substrate, the deposition of molecules and clusters on the graphene, and the incorporation of dierent substitutional dopants on the graphene lattice like boron or nitrogen.

Despite all this recent progress, many aspects of these modication tech- niques are still under development and most of the details remain unknown, es- pecially those concerning the atomistic mechanisms involved in these processes.

The work presented on this thesis tries to widen our knowledge in this respect.

By means of rst principles simulations, we analyze recent scanning tunneling microscopy (STM) experiments in which one, or more, modication techniques have been carried out on a graphene-metal system. Since the substrate is not any more a mere support for the graphene monolayer, we make a particular emphasis on the graphene-metal interactions as well as the inuence of external agents like dopants or intercalants.

1

2 Abstract

In this thesis, we use graphene grown on Rh(111) as a reference system to study dierent graphene modication techniques. Consequently, as a rst step we fully characterize this graphene-metal interface. Since Rh(111) is regarded as a strongly interacting system, graphene adopts a rippled structure with a corrugation as large as ∼ 1 Å and remarkable dierences on the adsorption distances. The electronic properties of graphene on this system are completely dierent from those displayed by a free-standing layer. Challenging the common assumption for strongly interacting graphene-metal systems, we demonstrate the formation of dierent rotational domains leading to multiple moiré patterns with a wide distribution of surface periodicities. A strong correlation between the STM apparent corrugation and the lattice parameter of the moiré unit cell is found. We also analyze the subtle energy balance among strain, corrugation and binding that drives the formation of the dierent moiré patterns in all graphene- metal systems. Apart from the role played by purely geometric arguments on these structures, we conclude that the corrugation adopted by the graphene layer is also responsible for the selection of the nal stable congurations.

After the complete characterization of graphene grown on Rh(111), we fo- cus on the possibility of tailoring the degree of coupling with the substrate by controlling the amount of intercalants at the interface. The electronic and structural properties of the graphene monolayer can be tuned, ranging from a highly-coupled state to a quasi-free-standing at state after the formation of an ordered oxygen network at the interface. We study the electronic and structural decoupling of the graphene layer produced by oxygen intercalation including some intermediate steps for low oxygen coverage. We demonstrate that the attening and electronic properties depend on the local distribution of intercalants. Furthermore, we unveil the atomistic mechanism for the intercala- tion process. Our comprehensive study explores the possible penetration paths to the interface, discarding the access through point defects in this system.

We have also studied diusion phenomena taking place on the space conned between the graphene layer and the metallic substrate, that is recently known as chemistry under-cover. Additionally, we have investigated the interaction of the oxygen molecule with the rippled structure adopted by the graphene on

Rh(111). We clearly demonstrate that G/Rh(111) exhibits areas with distinctive chemical behavior according to the local coupling with the substrate. We nd areas whose properties resemble free-standing graphene, but also, more reac- tive regions in which, surprisingly, some chemical reactions like the dissociation of molecular oxygen become feasible. This local enhancement of the chemi- cal reactivity represents a dierent way to induce catalytic activity on the inert graphene layer. Therefore, our results show that the graphene-metal interaction is a new versatile and powerful handle to tailor the graphene chemical properties and to expand the possible applications to sensing and catalytic devices.

The nitrogen doping of graphene as a modication technique is also treated in detail for metal-supported systems. For this task, we use Pt(111) as an ideal weakly interacting system and, again, Rh(111) as a highly-coupled system. Re- cent experiments based on low energy ion implantation show that it is possible to obtain purely-substitutional N-doped graphene with a highly tunable dopant concentration, both on Pt(111) and Rh(111). We unveil the STM ngerprints of substitutional defects on both substrates by means of rst principles simu- lations, providing additional information about the electronic properties of the system. While in Pt(111) all defects are equivalent due to the atness of the physisorbed graphene, in the Rh(111) case, the chemical modulations induced in the graphene structure produce a remarkable variation of the electronic prop- erties of nitrogen defects. In a second step, we show that N-doping can be used in combination with oxygen intercalation. As a result, the interaction with the substrate can be controlled by the amount of intercalated oxygen atoms in the interface, while the doping level can be adjusted by the concentration of nitrogen dopants. After oxygen intercalation, the N-doped graphene layer decouples from the substrate preserving the incorporated nitrogen atoms which display a subtle dependence of the contrast in STM images with respect to the bias voltage.

First principles calculations conrm all the experimental features and reveal that this evolution of the STM contrast arises from the asymmetrical behavior of the electronic properties of defects at both sides of the Dirac cone. Therefore, the combination of doping and intercalation represents a novel strategy to tailor properties of graphene and other 2D materials.

4 Abstract

The results presented so far on this thesis are a good example of the useful- ness of theoretical simulations based on Density Functional Theory. However, this highly accurate quantum description of the system is usually not feasible for large systems containing more than 1000 atoms. For this reason, an important number of interesting systems fall outside the range of applicability of these calculations. Thus, there is a pressing need for new methodologies in which the electronic and structural properties of graphene-based complex systems can be calculated with high precision. A last part of this thesis is devoted to this kind of methodological improvements. For this task, we have collaborated with the developers of CONQUEST, an order (N) code based on a highly optimized basis set of numerical localized pseudoatomic orbitals. In particular, we explore a re- cently developed approach to project a large basis set onto a minimal-size one, and show that we keep the accuracy level in non-trivial systems but saving in computational time and memory requirements. We have characterized the per- formance of the method using the G/Rh(111) system and considering dierent concentrations of intercalated atomic oxygen. This system represents a tough test due to the pronounced variations on its electronic properties according to the oxygen coverage. The excellent agreement with state-of-the-art plane-wave calculations paves the way for the study of graphene-metal systems with more than 3000 atoms.

In summary, in this thesis we use the graphene grown on Rh(111) as an archetypical strongly interacting system, which had been less studied than other similar systems. First, we carry out a full characterization of the system. Then we analyze dierent procedures like oxygen intercalation and nitrogen doping to further modify graphene properties. We pay special attention to the under- standing of these processes at the atomic-scale and to the enhanced tunability oered by the simultaneous application of both modication techniques. Finally, we focus on methodological aspects of Density Functional Theory calculations, pursuing the simulation of very large systems containing more than 1000 atoms but keeping the high accuracy of plane-wave calculations.

Después de más de diez años de intensa investigación en grafeno, sus poten- ciales aplicaciones en dispositivos electrónicos no son tan alentadoras como se pronosticaba. Sin embargo, esta enorme producción cientíca ha dado lugar a interesantes aplicaciones en modicación supercial, catálisis, tecnología de re- cubrimientos, etc. La mayoría de estas aplicaciones presentan una característica común: la interacción con el sustrato es tenida en cuenta como un parámetro fundamental a la hora de modular las propiedades de la lámina de grafeno. Por ejemplo, la selección adecuada de un determinado sustrato inuye en el nivel de dopaje del grafeno y afecta drásticamente a sus propiedades electrónicas.

Análogamente, las corrugaciones y las distancias de adsorción de la lámina tam- bién dependen de la fuerza de la interacción con el sustrato. Además, existen distintos métodos que permiten diseñar con más precisión las propiedades nales del grafeno, como la intercalación de diferentes especies en el espacio connado entre el grafeno y el sustrato metálico, la deposición de moléculas y clústers sobre del grafeno, o la incorporación de diferentes dopantes sustitucionales en la red del grafeno, como pueden ser el boro o el nitrógeno.

Sin embargo, pese a todos los avances recientes, muchos aspectos de es- tas técnicas de modicación están todavía en fases tempranas de desarrollo y muchos detalles sobre los procesos involucrados resultan aún desconocidos, especialmente aquellos relacionados con los mecanismos atómicos. El trabajo presentado en esta tesis trata de aumentar nuestro conocimiento en estos as- pectos. Por medio de simulaciones de primeros principios, analizamos recientes experimentos de microscopía de efecto túnel (STM), en los cuales una o varias de estas técnicas de modicación se llevan a cabo en alguna interfase grafeno-

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6 Resumen

metal. Como consideramos que el sustrato ya no es un mero soporte para el grafeno, prestamos especial atención a las interacciones entre éste y el sustrato, así como a las inuencias de agentes externos como dopantes o especies inter- caladas.

En esta tesis usamos grafeno crecido sobre Rh(111) como sistema de referen- cia para estudiar distintas técnicas de modicación. En primer lugar, empezamos por hacer una caracterización completa de esta interfase donde el grafeno adopta una estructura ondulada con corrugaciones de hasta 1 Å que dan lugar a varia- ciones considerables en la distancia de adsorción. Por estas razones, el grafeno crecido en Rh(111) es considerado como un sistema altamente acoplado y por ello las propiedades electrónicas del grafeno en esta interfase son bien distintas de las del grafeno aislado. En nuestro estudio, desaando la visión imperante de los sistemas fuertemente acoplados, demostramos la existencia de diferentes do- minios rotacionales que dan lugar a distintos patrones de moiré con una amplia distribución de periodicidades superciales. Además encontramos una fuerte correlación entre la corrugación experimental del STM y el parámetro de red de la celda unidad del patrón de moiré. También analizamos el sutil balance energético existente entre las contribuciones de deformación, corrugación e in- teracción. Por tanto concluimos, que la corrugación adquirida por el grafeno en este sistema es también responsable, junto con factores puramente geométricos, de la existencia de los distintos dominios rotacionales,

Tras la caracterización del grafeno crecido en Rh(111) nos centramos en estudiar la posibilidad de modicar el grado de acoplamiento con el sustrato mediante la intercalación de oxígeno atómico en la interfase. Variando la can- tidad de átomos intercalados, las propiedades estructurales y electrónicas del grafeno evolucionan desde un estado inicial altamente acoplado hasta un estado prácticamente análogo al del grafeno aislado cuando una red ordenada de áto- mos de oxígeno se ha formado en la interfase. En nuestro estudio prestamos especial atención a ciertos estados intermedios del desacoplamiento para valores bajos de recubrimiento de oxígeno, que no habían sido observados con anteri- oridad. Lo que nos permite concluir que el desacoplamiento y las propiedades electrónicas dependen de la distribución local de los átomos intercalados. De

forma adicional, proponemos un mecanismo de intercalación a escala atómica para el proceso, donde estudiamos distintas posibilidades de penetración a la interfase, descartando los defectos puntuales como posibles vías de entrada y posteriormente los procesos de difusión en la interfase, lo que actualmente se conoce como chemistry under-cover. Otra parte interesante del trabajo es la referida a la adsorción y disociación de la molécula de oxígeno sobre el grafeno crecido sobre rodio, donde se demuestra que hay distintas regiones con compor- tamientos químicos muy distintos. Sorprendentemente, vemos cómo las regiones más alejadas del metal presentan un comportamiento similar a las del grafeno aislado, mientras que las zonas más cercanas, donde el grado de hibridación con el sustrato es mayor, presentan una mayor reactividad química, permitiendo in- cluso la disociación catalítica de la molécula de oxígeno, como ocurre en algunos metales nobles. Este aumento local de la reactividad química en el grafeno, que es considerado inerte químicamente, representa una nueva ruta alternativa para inducir nuevas funcionalidades químicas al grafeno, abriendo la puerta a nuevas aplicaciones en sensores o dispositivos catalíticos.

Otra parte importante de la tesis está dedicada a investigar cómo afecta a las propiedades del grafeno el dopado con nitrógeno en distintos sustratos metáli- cos. Para ello se estudia tanto un ejemplo de sustrato fuertemente acoplado, el Rh(111), como un sistema arquetípico de los débilmente interaccionantes, el Pt(111). Experimentos recientes basados en bombardeo iónico han permitido obtener grafeno dopado con nitrógeno sustuticional soportado sobre distintos metales con una concentración controlable. Usando cálculos de primeros princip- ios estudiamos tanto las características de los experimentos como las propiedades electrónicas de dichos defectos, concluyendo que mientras en el Pt(111) todos los dopantes son equivalentes debido a la planicidad de la lámina, en el caso del Rh(111) las fuertes modulaciones químicas y estructurales inducidas en la lámina hacen que las propiedades de los defectos varíen acusadamente según la zona. En una segunda parte del estudio proponemos que la técnica del dopado se aplique conjuntamente con la de intercalación estudiada anteriormente. De esta forma el nivel de dopaje electrónico se puede controlar mediante la con- centración de átomos de nitrógeno y la interacción con el sustrato de forma

8 Resumen

independiente, mediante la cantidad de átomos de oxígeno intercalados en la in- terfase. El resultado nal, si se completa el desacoplo por intercalación, es una lámina plana sisorbida al sustrato en la que los defectos de nitrógeno muestran una dependencia signicativa de contraste en los experimentos de STM respecto al voltaje aplicado. Nuestros cálculos de primeros principios revelan que esa de- pendencia es el resultado de una fuerte asimetría de las propiedades electrónicas de los defectos y sus primeros átomos vecinos a ambos lados del cono de Dirac del grafeno. A raíz de este estudio concluimos que la combinación simultánea de varias técnicas de modicación del grafeno es una estrategia novedosa útil para el diseño de las propiedades nales tanto de este material como de otros materiales bidimensionales similares.

Como se ha podido ver los resultados presentados en esta tesis están basados mayoritariamente en cálculos cuánticos de Teoría del Funcional de la Densidad, gracias a los cuales se puede conseguir una descripción precisa de los sistemas estudiados a escala atómica. Sin embargo, estos cálculos no suelen ser aplicables a sistemas cuya celda unidad contenga más de 1000 átomos. Por esta razón muchos sistemas interesantes quedan fuera del rango de aplicabilidad de esta técnica y por eso existe una imperiosa necesidad de encontrar nuevas técnicas que permitan simular sistemas más grandes. Por ello, la última parte de la tesis está dedicada a este tipo de mejoras metodológicas en colaboración con los de- sarrolladores del código CONQUEST, un código de orden N basado en orbitales pseudoatómicos numéricos altamente optimizados. En particular, investigamos un nuevo esquema que permite la proyección de una base con muchos elementos en una base mínima sin pérdidas perceptibles de precisión, incluso en sistemas complejos. Esta nueva herramienta, además de ahorrar tiempo de computación, rebaja considerablemente las necesidades de memoria durante el cálculo. Hemos probado este nuevo código en cálculos de grafeno crecido en rodio, con y sin intercalación de oxígeno. Como se ha comentado anteriormente este sistema representa un reto desde el punto de vista de la simulación debido a la gran variabilidad en sus propiedades electrónicas. El buen acuerdo entre los resulta- dos obtenidos con este código y los cálculos anteriores con otros métodos más establecidos acreditan su uso en términos de precisión con la ventaja de que se

pueden simular sistemas con más de 3000 átomos.

En resumen, en esta tesis se estudia a fondo el grafeno crecido sobre Rh(111), que es un caso arquetípico de sistema fuertemente acoplado y que con anteri- oridad había sido mucho menos estudiado que otros sistemas similares. Aparte analizamos diferentes procedimientos, como la intercalación de oxígeno o el dopado con nitrógeno, para modicar las propiedades del grafeno, prestando es- pecial atención a la comprensión de los procesos involucrados a escala atómica y a la aplicación simultánea de varias de estas técnicas. Finalmente, también estudiamos aspectos metodológico de la Teoría del Funcional de la Densidad con el objetivo de simular sistemas con más de 1000 átomos pero manteniendo la precisión obtenida en cálculos de ondas planas.

1 | Graphene on metals

1.1 Introduction

Historically, only two crystalline allotropes of carbon, diamond and graphite,

together with other amorphous forms like coal or charcoal were known at standard conditions. It is well-known that the dierent chemical hybridizations of carbon atoms confer to graphite and diamond completely dierent chemical and physical properties despite being constituted by exactly the same kind of atoms. This scenario abruptly changed in the mid 80's when new synthetic al- lotropic forms of carbon were obtained. First, the fullerenes at Rice University (USA) [1], and some years later, the nanotubes at NEC Corporation in Tsukuba (Japan) [2]. These discoveries represented real breakthroughs with plenty of potential applications due to the awesome mechanical and electronic proper- ties found in these new allotropic forms [3]. However, an even more shocking carbon allotrope appeared at the beginning of the 21st century. In 2004, the isolation of a stable single graphite layer was reported for the rst time by K. S.

Novoselov and coworkers [4]. They took advantage of the exfoliation capacity of graphite to extract, by mechanical means, a single layer of graphite, known as graphene. Previously, theoretical scientists had speculated about the hypo- thetical properties of isolated graphite layers [5] but their real existence was seriously questioned, or even discarded, by some researches. These concerns were not only restricted to graphene but to any two-dimensional material [6].

This discouraging panorama contributed to enhance the promotion and diusion of the unexpected discovery of graphene, making it one of the milestones in the material science of the 21st century and creating a new paradigm in condensed

11

12 1.1. Introduction

matter physics [7].

From the very beginning, the scientic community became aware of the un- precedented properties of such a peculiar low-dimensional material. Moreover, the existence of a purely two-dimensional material was enthusiastically welcomed by the theoretical community because it served to conrm in a real system sev- eral phenomena and exotic properties only studied in toy-models. Among them:

(i) the existence of massless conduction electrons near the Fermi level [8] lead- ing to extremely high electron mobilities [4,9]; (ii) the achievement of ballistic conduction for low enough electron-phonon scattering rates [10, 11]; (iii) the unconventional integer quantum hall eect [12,13]; which (iv) provided direct evidence of theoretically predicted Berry's phase of massless Dirac fermions, even at room temperature [14]; or (v) the Klein paradox [15] where the al- most massless electrons display a perfect transmission through high and wide potential barriers. During the following years of graphene's early life additional outstanding properties were found. It possesses the highest thermal conductivity ever measured (∼ 5 × 10³ W m⁻¹ K⁻¹) [16], excellent optical properties [17], it is the strongest material ever tested [18] with an intrinsic tensile strength of 130 GPa and a Young's modulus of 1 TPa, much stier than any other bulk material.¹ Therefore, graphene was suggested to to be used as a reinforcement in composites [19], as a possible substitute for silicon in electronic devices [20]

and many other emerging applications [21].

If fullerenes and nanotubes had already meant a true revolution in ba- sic chemistry, the signicance of the discovery of graphene was incomparably broader. According to the citation statistics on scientic journals,² in less than

fteen years graphene research is one of the most studied topics in terms of scientic production even in comparison with other much older research top-

1For a comparison, the tensile strength of a standard structural steel is around 500 MPa and the values for structural metals are in the range of 200 − 2500 MPa. For a broader comparison see for example M. F. Ashby and D. R. H. Jones: Engineering Materials vol. 1 Butterworth-Heinemann 2nd Edition (1996) pp. 86 and 87.

2This conclusions is extracted after a word search on the ISI Web of Knowledge, comparing the results obtained for the word graphene appearing in the title with other words like

superconductor or ferroelectric.

ics. The rich variety of its dierent outstanding properties has been able to attract the attention of many research groups from very dierent disciplines and elds, including crystal growth, organic chemistry, spectroscopy, thin lms, membrane science and technology, electrochemistry, catalysis, electronics, device physics, theoretical and mathematical physics, optoelectronics, photonics, and many others. Additionally, just after the isolation of graphene it was pointed out the possibility of obtaining other two-dimensional materials [22] based mainly on transition metal dichalcogenides (i.e. MoS2, WS2, MoSe2, etc.) or boron nitride whose layered structures resemble the graphite-like arrangement. Since then a large amount of research has been devoted to the isolation of new two- dimensional materials constituting a new research area which presently includes a great variety of materials beyond graphene [23]. Such a host of excellent at- tributes discovered in the graphene brought to the research community an atmo- sphere of excitement and optimism regarding potential applications of graphene in a near future [24, 25]. As a consequence, K. S. Novoselov and A. K. Geim were awarded the Physics Nobel Prize in 2010, only six years after the rst graphene synthesis had taken place.

However, in spite of the intense research on graphene and related two- dimensional materials for over a decade, the scientic community has been forced to lower its initial expectations about the feasibility of graphene's technological applications at an industrial scale [26]. Especially those applications in electronic devices are not as encouraging as expected. Nonetheless, such a huge scientic production has still led to other interesting applications on surface modica- tion, catalysis, coating technology, etc. For example, new directions point out towards applications in which the interactions between graphene and the sub- strate where it is grown play a crucial role. In this way the substrate, instead being a mere support, is used to tailor graphene properties as desired. This new approach drastically diers from traditional approaches where an ideal free- standing isolated graphene monolayer is considered. In this thesis we will show several examples of these new trends on the graphene grown on Rh(111). This includes, among others, the study of dierent rotational domains with distinc- tive properties, the tuning of the substrate interaction via oxygen intercalation

14 1.2. Basic properties of graphene

at the interface, the enhancement of the chemical reactivity on some areas, the nitrogen doping, etc.

In this chapter we will briey review the basic properties of graphene. Then we will focus on the graphene-metal interfaces with special emphasis in the role of the substrate interaction which constitutes the main research topic of this thesis. Finally, we will describe the dierent available techniques of tuning the structural and electronic properties of graphene like molecule deposition, atomic intercalation on the interface or heteroatom doping.

1.2 Basic properties of graphene

Graphene was the rst purely two-dimensional crystal isolated and it is entirely constituted by carbon atoms. Its crystalline structure is closely related to the bulk graphite whose planar structure consists in the successive stacking of weakly bonded carbon layers. In each individual layer, the carbon atoms are arranged in a honeycomb lattice with hexagonal symmetry and with a constant bond length of d = 1.42 Å between rst neighbors as shown in Fig. 1.1. It is worth noting that the honeycomb lattice is constituted by two dierent sets or sublattices with hexagonal symmetry whose inequivalent atoms are alternately distributed on the plane. Therefore, each carbon atom has three nearest neighbors of the second sublattice, constituting a diatomic basis for the crystal structure. As a result, graphene lattice must be described with an hexagonal primitive cell containing two atoms with a reticular parameter of b0 = √

3d ' 2.46 Å, as it is also shown in Fig. 1.1. This crystal structure gives rise to another hexagonal lattice on the reciprocal space. The reciprocal cell or rst Brillouin zone (BZ) is rotated 30^◦ with respect to the real-space cell and its lattice parameter is 4π/3d as illustrated in Fig. 1.2. According to this geometry the BZ of the graphene lattice presents several relevant high symmetry points characteristic of the hexagonal lattice. The Γ point is located at the geometrical center of the BZ, M is the midpoint of the edge delimited by the inequivalent points K and K⁰. According to the hexagonal symmetry a reasonable path to show dierent properties within the unit cell containing all inequivalent points would be Γ → M → K → Γ.

Figure 1.1: Schematic top and side views of the graphene structure showing its typical two-dimensional honeycomb arrangement. The primitive cell and some characteristic distances are shown together with the shape of the hybrid sp²and p_z orbitals involved in the chemical bond.

The planar geometry of graphene is originated by the sp² hybridization of carbon atoms where three electrons belonging to the hybrid orbitals give rise to three dierent in-plane σ-bonds forming 120^◦, while the remaining valence elec- tron contained in the out-of-plane pz orbital is able to freely move through the overlapped π-bonds parallel to the basal plane. This strong anisotropy between the in-plane directions and the normal directions is responsible for the awesome properties of graphene. While strong in-plane σ-bonds lead to extreme mechan- ical properties, i.e. high stiness and strength, out-of-plane π-bands account for the awesome electronic properties. In graphite the inter-layer interactions arise from the spatial extension of pz orbitals leading to an inter-layer separation of 3.35 Å. The out-of-plane overlap of dierent π-bonds makes these electrons to be completely delocalized in the π system which allows the electrical conduc- tivity of graphite along the directions contained in the plane. In the case of graphene, the inter-layer distance of graphite is considered as the thickness of the atomically thin layer and it also displays a high in-plane conductivity. We

16 1.2. Basic properties of graphene

Figure 1.2: Main features of the electronic structure of graphene. Band struc- ture following the high symmetry path Γ → M → K → Γ as indicated in the scheme of the rst Brillouin zone. The corresponding density of states is presented together with the band structure. Note the singular linear dispersion in K near the Fermi level, both in the π bands and in the DOS leading to the well-known Dirac cones depicted in the three-dimensional scheme. These calculations have been carried out using the VASP package.

will see in a moment how most of its notable electronic properties arise from these electronic π bands.

If we look at the band structure along this path presented in Fig. 1.2 we will observe the surprising linear behavior of the π bands (highlighted in red and blue) in the K point at the Fermi level, where they meet exactly at one point.

Since π^∗ and π bands represent the conduction and valence bands respectively, this implies that graphene behaves as a zero-gap semiconductor or semimetal.

In contrast with the archetypical case of silicon and other semiconductors, in which a parabolic dispersion relation near the gap is found, this is not the case in graphene. Instead, a linear dependence of the energy with respect to the wave vector in the vicinity of K is obtained, which clearly resembles the relativistic particle described long ago by the Dirac equation [27]. As it is shown in Fig.

1.2, there are a total of six K points in the rst Brillouin zone but only two of them are independent, K and K⁰, while the rest are equivalent by symmetry.

Around each of these points in the reciprocal space the energy of the electrons adopts a cone-like shape called Dirac cone, as illustrated in the colored scheme of Fig. 1.2. As a consequence of this unusual feature of the band structure, at low energies, even neglecting the true spin, the electrons can be described by an equation that is formally equivalent to the massless Dirac equation. Hence, the electrons and holes are called Dirac fermions. In this context, the spin of a particle may be used to dene a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. Although other three-dimensional crystals, such as HgTe and α-Sn (grey tin) are known to be gapless semiconductors, what makes graphene unique is not the gapless state itself but the very special, chiral nature of the electron states, as well as the high degree of electron-hole symmetry. In this region the electron mobility is nearly independent of temperature between 10 K and 100 K, which implies that the dominant scattering mechanism is defect scattering, instead of the usual phonon scattering. The absence of these phenomena leads to extremely high mobilities of ∼ 2×10⁵cm² V⁻¹ s⁻¹at a carrier density of 10¹²cm⁻²[10,28]. As it is also shown in Fig. 1.2, the density of states also displays the linear dispersion near the Fermi energy and it vanishes at exactly EF as a consequence of the zero-gap of the band structure. From energy values far enough from the Fermi level, the linear dispersion disappears giving rise to the so-called van Hove singularities [29] located around ±1 eV. They are essentially non-smooth points where the density of states is not dierentiable and they correspond to critical points of the BZ.

As we will see along this chapter, this extremely peculiar electronic structure described by the Dirac cones in the free-standing graphene is highly sensitive to the presence of many extrinsic agents like defects, adsorbates, dopants, the interaction with the substrate, etc. Therefore, it would be possible to modify the electronic properties, including the complete destruction of the Dirac cones, a gap opening or energy shifts of the Dirac cones, etc. In this latter case, following the classical analogy of semiconductors, we can distinguish between n-doped and p-doped graphene where electrons of the π system are added or withdrawn respectively. These alterations of the electronic properties, far from

18 1.3. Graphene-metal interfaces

being a drawback, constitute a unique opportunity to tailor electronic properties of graphene for a great variety of dierent applications. Along this thesis, we will describe dierent techniques to modify the electronic properties of graphene.

1.3 Graphene-metal interfaces

The aim of this section is to give an overview as comprehensive as possible about the dierent gaphene-metal interfaces and their main characteristics.

Graphene is often grown on metallic surfaces by CVD or controlled segrega- tion (See Sec. 3.2 for more details and a brief introduction to graphene syn- thesis). Therefore, the study of the particular features of each interface and how the substrate aects to the graphene properties has become an important topic among the grahene research community [3032]. Although for some pur- poses the metallic substrate is regarded as a mere support to make possible the growth of graphene, from the very beginning some pioneering works drew attention to the possibility of tuning the structural and electronic properties of graphene via substrate interactions. For instance, in 2008, G. Giovannetti et al.

[33] used rst principles calculations to show how the metallic substrates alter the electronic properties of graphene by shifting the Fermi level with respect to the Dirac cone of pristine graphene. The modication of the work function according to the dierent metallic substrate has important implications on de- vice physics. Subsequently it was shown that according to the strength of the graphene-metal interactions two clearly dierent groups of substrates can be distinguished, weakly-coupled and strongly-coupled systems. While in the rst group the original electronic properties of graphene prevail in the presence of the metallic substrate except for rigid shifts of the Dirac cone, in the second group a total destruction of the linear dispersion in the band structure is ob- served [3032]. This distinction is also patent on the structural properties. By means of synchrotron-radiation-based XPS measurements A. B. Preobrajenski et al. [34] showed that the strength of the substrate interactions varies a lot depending on the dierent metal. The variable degree of interfacial orbital hy- bridization between graphene and metal states of the substrate gives rise to a a gradual change in the morphology of the graphene layer, from nearly at to

strongly corrugated. In this way, strongly interacting substrates, like Ru(0001), Re(0001) and Rh(111), interact with the graphene layer leading to chemisorbed states. As we will see in this section, they present average adsorption distances of ∼ 2 Å and the graphene adopts a rippled conguration (with corrugations larger than 1 Å) due to the formation of C-metal chemical bonds. Conversely, in weakly interacting systems, like Pt(111), Cu(111) or Ag(111), the corrugation of the layer is minimal and its atness is conserved in the presence of the metal- lic substrate. More details about the properties of each system will be provided along this section.

After this kind of seminal works a great eort was put on the understand- ing of microscopic properties of graphene-metal interfaces at atomic level. All the results collected in this thesis are directly or indirectly focused on increas- ing our knowledge on this subject. More precisely we will extensively deal with the graphene grown on the (111) surface of rhodium and dierent techniques to modify its properties. In this section, we will present the main features of graphene grown on the available transition metal substrates. First, we will focus on the purely geometrical aspects of the interface related to the relative orien- tations of the graphene lattice with respect to the substrate. These possible orientations give rise to dierent rotational domains or moiré patterns charac- teristic of each system. Then, we will analyze the chemical interactions between the graphene layer and the metallic substrate, making special emphasis on their implications in the graphene properties which are clearly dependent on the sub- strate type.

1.3.1 Moiré patterns

The rst consideration to take into account when studying the graphene-metal interface is purely geometric. The hexagonal lattice of graphene described in Sec. 1.2 is the same of those presented by the (111) and (0001) surfaces of FCC and HCP metals respectively. In most of the transition metal substrates there is an evident discrepancy between their lattice parameters and the one of the graphene lattice, except for the cases of Ni(111) and Co(0001). As we will comment later in these cases the dierence between lattice parameters is so small

20 1.3. Graphene-metal interfaces

Figure 1.3: An example of the construction of a moiré pattern formed by the superposition of two dierent reconstructions in a graphene layer and a Rh(111) substrate as indicated in Wood's and matrix notations.

that they are able to adopt commensurate structures in 1 × 1 cells. However, in the vast majority of substrates the mismatch between lattice parameters leads to more complex super-structures called moiré patterns. In a more general sense moiré patterns refer to large scale interference patterns produced by a ruled pattern with transparent gaps when it is overlaid on another similar, but not identical, pattern. Mathematically described from very ancient times they have many physical implications in a broad range of phenomena related to wave interference. Additionally, they have been regularly employed in dierent kinds of artwork. However, in this context of surface science, we regard a moiré pattern as the superposition of two dierent lattices, for instance the graphene and the metallic surface, that with a proper relative orientation gives rise to a common periodicity. As it is shown in Fig. 1.3, despite being separately dierent, a joint periodicity dened by a larger unit cell appears after the appropriate rotation of one of the lattices.

The non-primitive unit cell which denes the common periodicity is given in terms of its Bravais vectors RM 1 and RM 2. By construction we should be able to express them, at the same time, as a linear combination of primitive cell

vectors either of the graphene (bG1, bG2) :

R^(G)_{M 1} = m^G₁₁bG1+ m^G₁₂bG2 (1.1) R^(G)_{M 2} = m^G₂₁bG1+ m^G₂₂bG2, (1.2) or the substrate (bT M 1, bT M 2).

R^{(T M )}_{M 1} = m^{T M}₁₁ bT M 1+ m^{T M}₁₂ bT M 2 (1.3) R^{(T M )}_{M 2} = m^{T M}₂₁ bT M 1+ m^{T M}₂₂ bT M 2. (1.4) Where m^G_ij and m^{T M}_ij are in total eight integer elements of the two 2 × 2 matrices which dene the reconstruction needed to create the moiré pattern in each lattice. Due to the absence of exact commensuration, the supercell given by the combination of graphene primitive vectors is going to be slightly dierent from the one obtained with the substrate counterparts. For this reason we have distinguished between the two pairs of vectors (RM 1, R_{M 2}) in each case.

Although this matrix notation is very ecient and precise to describe a moiré superlattice, it might be relatively cumbersome because it does not provide an immediate picture of the structure. Therefore, Wood's notation is often used instead. In this alternative notation the new cell is given by a more compact expression of the type (N1× N₂) − Rθ.According to Eq. (1.1) N1= R^(G)_{M 1}/b_G1 and N2 = R^(G)_{M 2}/b_G2 indicate the lengths of the new Bravais vectors and θ =

∠R^(G)_{M 1}b_G1 is the rotation angle of the new cell with respect to the primitive one. The only additional piece of information required to unambiguously dene a moiré pattern is the rotational angle needed to match both supercells, that is

∠R^(G)_{M 1}R^{(T M )}_{M 1} .

The generation of moiré patterns by the superposition of two dierent lat- tices has already been studied for arbitrary geometries [35]. In the case of graphene grown on transition metal surfaces additional symmetries simplify the problem, that is the same lattice with hexagonal symmetry. The hexagonal lattice implies that bG1 = b_G2 = b_G and ∠bG1b_G2 = 60^o or 120^o, and the same for the substrate. The observed moiré patterns of graphene on metallic substrates are often isotropically scaled so R_{M 1}^{(T M )}= R^{(T M )}_{M 2} = L_{T M} and equiv- alently R^(G)_{M 1} = R^(G)_{M 2} = LG or N1 = N2 in Wood's notation. Notice that the

22 1.3. Graphene-metal interfaces

condition LG = LT M should be ideally fullled but there is always a certain mist between the two lattices. Assuming that the substrate atoms keep xed at their crystallographic positions, graphene must stretch or compress in order to reach the common periodicity. In this case, according to the classical denition of strain in elasticity, we have:

ε = LT M − L_G

L_G , (1.5)

or alternatively another quantity dened as the mismatch in which the graphene lattice parameter is taken as a reference. That is:

∆_m= L_{T M} − L_G

b_G . (1.6)

Both quantities are closely connected by εLG = ∆mbG. Since the hexagonal symmetry is therefore conserved in the moiré super-structure only two elements of the reconstruction matrices are independent. Assuming ∠bG1b_G2 = 120^o the matrix elements for the graphene and the substrate become

m^G = m n

−n m − n

!

and m^{T M} = p q

−q p − q

!

. (1.7)

Under these circumstances, in the limit of very low strains (ε → 0) it is straight- forward to see that Eq. (1.5) leads to following diophantine equation:

b²_G(m²+ n²− mn) ' b²_{T M}(p²+ q²− pq), (1.8) which is a condition to be fullled by any moiré super-structure as it was already pointed out by P. Zeller and S. Günther [36]. In order to illustrate all these parameters we can use the example suggested in Fig. 1.3. Taking into account the lattice constants of graphene (2.4595 Å) and Rh(111) (2.687 Å) we can calculate LG=√

43 × 2.4595 = 16.128 . . . Å and LT M = 6 × 2.687 = 16.122 Å. Since they are slightly dierent we use Eqs. (1.5) and (1.6) to calculate the values of strain and mismatch. For this particular case we have ε ' −0.04%

and ∆m' −0.24%.

Some eort has been put to rationalize the rules governing the existence of these moiré patterns in the graphene-metal interfaces [3538]. Although it

seems that a minimum strain condition such as Eq. (1.8) is always fullled a complete description including the purely geometrical aspects of the lattices and also the chemical interactions with the graphene it is still missing. At this point we must remember that, apart from the geometrical considerations addressed here, the clear division between strongly and weakly-coupled systems mentioned before will have a prominent role in the formation of dierent moiré patterns than remains unclear. A lot of work must be done in order to elucidate why in strongly interacting systems a single preferential moiré pattern is systematically observed while weakly interacting systems usually display multi-domain structures as we will see in the following subsections. Additionally, there is not a clear explanation about why only a minimal fraction of the possible moiré patterns deduced from Eq. (1.8) has been found.

1.3.2 Weakly coupled systems

As we have just seen the absence of true chemical bonds between graphene and the metallic substrate in weakly interacting systems leads to a physisorbed state governed by dispersion interactions. Unlike strongly interacting systems, in these cases the graphene layer remains almost at, with corrugations ranging from almost zero to 0.4 Å and adsorption distances of ∼ 3.3 Å, very close to the graphite inter-layer distance. This is regarded as a ngerprint of the weak adsorption, mainly governed by van der Waals interactions. One system of this kind is the Pt(111) in which graphene can be grown by CVD [39]. One of its most distinctive characteristics is the appearance of many rotational domains or moiré patterns which have been described [37,39,40]. The graphene adsorption distance is ∼ 3.35 Å with a corrugation less than 0.025 Å in smaller size moiré patterns [41] while larger domains may present a higher corrugation [40]. In Fig.

1.4 several moiré patterns are characterized by STM experiments showing the dierent unit cells and proles to indicate the electronic apparent corrugation of graphene [40]. Despite the weak interaction between graphene and the platinum substrate the apparent corrugation revealed by STM measurements is much larger than the geometrical corrugation obtained with rst principles simulations.

Other systems with a similar behavior include substrates like Au(111) [42,43],

24 1.3. Graphene-metal interfaces

Figure 1.4: Atomic resolution STM images (Vs= −0.4V and It= 0.2nA) of six rotational domains of graphene grown on Pt(111) showing the dierent moiré supercells depicted in green. In Wood's notation with respect to the primitive graphene cell: (a) 2 × 2, (b) 3 × 3, (b) 4 × 4, (d) (√

37 ×√

37)-R21^o, (e) (√

61 ×√

61)-R26^o and (f) (√ 67 ×√

67)-R12^o.The relative orientation of the graphene with respect to the substrate is indicated by a yellow arrow in each case. The height proles along the green dashed lines in each image are plotted in (g) and (h). See text for details. All information extracted from [40].

Ag(111) [44] or Cu(111) [45]. In this kind of systems it is quite evident that the appearance of multiple rotational domains is a natural consequence of the weak interaction with the substrate. The low values of the adsorption energies (for instance, an upper limit would be ∼ 50 meV per C atom for iridium [46]) allow the graphene layer to have enough freedom to rotate adopting several favorable congurations without existing a clear preferential conguration.

Another typical feature of the weakly interacting systems is that the elec- tronic properties of the graphene layer remain unaltered by the presence of the substrate, except for a shift in the Dirac cone due to the charge transfer. This charge transfer, produced by the dierence in work functions between the free- standing graphene and the metallic substrate, changes the carrier concentration conferring a certain doping which may have either p or n character depending on the metal [33,47]. Furthermore, it has been recently shown that the graphene-

Figure 1.5: A complete LEED study of the graphene grown on Ir(111) by S.

K. Hämäläinen et al. [49] showing the main structural features. In (a) the unit cell (size ∼ 24.5 Å) consisting in the aligned 10 × 10 reconstruction of graphene superposed with a 9 × 9 reconstruction on Ir(111). The graphene corrugation is around 40 pm as it is shown in the color map and (b). The notation of TOP, HCP and FCC refers to the relative orientation of the graphene layer with respect the metallic lattice. See main text for details. Other relevant characteristics are the almost unaltered metallic surface, the adsorption distances of 3.39 Å and the detailed modulation of the layer showed in (c).

metal interaction of weakly interacting systems is a subtle interplay between the dierent decay lengths of the graphene Dirac π states and the metal surface state, giving rise to a tunable transparency of the graphene in STM experiments [48].

Other metals like Ir(111) or Pd(111) also belong to this class of weakly in- teracting systems but they start to shown some intermediate characteristics in the crossover region between high and low grahene-metal coupling. Graphene can be grown on Ir(111) by low pressure CVD [50] and it has been fully char- acterized by means of a great variety of experimental techniques, such as STM [50,51], XPS [46] ARPES [52], LEED [49,51], AFM [53], etc. The interaction between graphene and Ir(111) is basically weak as deduced from its adsorption distance ∼ 3.40 Å [46,49] and from its electronic structure [54]. Nevertheless, some features dier from other weakly interacting systems. Although there are

26 1.3. Graphene-metal interfaces

several rotational domains with very low corrugation [38], it seems that there is one preferential orientation (i.e. 10 × 10 graphene reconstruction on top and aligned with a 9 × 9 reconstruction on the iridium surface). This moiré pat- tern, illustrated in Fig. 1.5 has a geometrical corrugation of ∼ 0.4 Å [38,49], much larger than any other rotational domain. Besides, the electronic properties of carbon atoms in the low areas of the moiré pattern clearly start to deviate from the ideal properties of free-standing graphene [54]. The case of Pd(111) is somehow a similar intermediate system regarding graphene-metal interactions.

Despite not being as studied as Ir(111), it can be grown by CVD [55,56] and sev- eral rotational domains appear displaying slightly dierent properties and STM apparent corrugations of ∼ 0.3 − 0.4 Å. In this case it is not clear if there is or not a preferential orientation because the literature on this system is very scarce.

However, what makes this systems another limiting case is that the electronic properties of graphene grown on Pd(111) are signicantly distorted with respect to those of pristine graphene. Since a small gap seems to be opened in the band structure of this system a semiconducting behavior has been suggested [55].

1.3.3 Strongly coupled systems

As we have already mentioned, there are metallic substrates which strongly inter- act with the graphene layer with closer adsorption distances ∼ 2.2 Å, revealing the formation of C-metal chemical bonds. In this group we must distinguish between two dierent groups of substrates. A rst group is constituted by those substrates where the dierence between the lattice parameter of the substrate diers less than 2% with respect to the graphene lattice parameter. In these cases, like Ni(111) [57] and Co(0001) [58], the agreement between both lattices is close enough to lead to several commensurate structures. Despite the strong interaction, the small 1 × 1 periodicity on these systems does not let to reach a highly corrugated conguration on the graphene layer, similarly to the case of weakly interacting systems. In Ni(111) one sublattice of the graphene is located at top sites with respect to the uppermost metallic layer and the second sublat- tice is located in the three-fold hollow fcc sites. This is by a slight margin the most energetically favorable conguration although several more simultaneously

Figure 1.6: (a) The detailed top and side views of the graphene grown on Ru(0001) obtained after rst principles calculations is shown. The unit cell used consists of a 11 × 11 graphene cell superposed on a 10 × 10 Ru(0001) cell with a side of 27.3 Å. Notice the high graphene corrugation of ∼ 1.2 Å and the low adsorption distance of ∼ 2.2 Å as a proof of the strong graphene-metal interaction. Conversely, the metallic surface remains practically unaltered. In (b) a STM image (Vs= −1.0V) of the graphene-metal interface is shown with a prole also exhibiting a high corrugation [62].

coexist [59, 60]. A similar behavior has been observed for Co(0001) [58]. It is worth noting that the growth of graphene on Ni(111) may be more complex than in other similar metals due to the natural tendency to form carbides [57]. How- ever, it has been extensively studied compared to other metallic substrates for dierent reasons, mainly related to its magnetic properties. For a comprehensive review on this substrate see [61] and references therein.

The second group of strongly interacting substrates are constituted by metal- lic substrates like Ru(0001), Re(0001) or Rh(111). Each of them presents a single preferential rotational domain or moiré pattern. In all of them the strong

28 1.3. Graphene-metal interfaces

interaction with the substrate leads to a chemisorbed state with an average ad- sorption distance of ∼ 2 Å. In these cases the graphene layer adopts a rippled conguration with corrugations larger than 1 Å due to the formation of C-metal chemical bonds in some areas of the moiré pattern. The most studied case of this group is the Ru(0001) substrate. Graphene can be grown on Ru(0001) ei- ther by controlled segregation [63,64] or by CVD [65]. From the very beginning the strong interaction with the substrate was noted as well as the rippled cong- uration adopted by the graphene and its distinctive aligned periodicity. Further

rst principles calculations conrmed the great corrugation of ∼ 1.5 Å [66,67]

achieved by this system. More recently, it was shown that the dispersion forces on this system play a crucial role reducing the corrugation to ∼ 1.2 Å, closer to the apparent corrugation of observed in STM experiments [62,68]. However, there still is a largely debated controversy about the correct assignment of the global periodicity in this system. On the one hand, the common assumption is an unit cell of c. 30 Å but there are discrepancies among several proposals for the graphene reconstruction 12 × 12 (29.5 Å) [63] or 11 × 11 (27.0 Å) [65]. In Fig. 1.6 the detailed structure of one unit cell of this moiré pattern is shown together with an experimental STM image and the corresponding prole also exhibiting a large corrugation. On the other hand, it was pointed out that the real periodicity of this system is constituted by a much larger cell of 25 × 25 in graphene formed by four non-equivalent subunits [69, 70]. In any case all reports roughly agree in the high corrugation values and the short adsorption distances of ∼ 2.2 Å. Finally, unlike in the previously discussed weakly interact- ing systems, the electronic properties of the graphene layer grown on Ru(0001) are completely dierent from those of pristine graphene as a result of the strong hybridization of the carbon atoms with the substrate [68,71].

The other strongly coupled systems like Re(0001) and Rh(111) have sim- ilar features to the ones explained for Ru(0001). For instance, in the case of Re(0001) grown by CVD [72] the minimal C-metal distances are within the in- terval 2.1 − 2.4 Å and the corrugation is as large as 1.6 Å showing a periodicity of 10 × 10 with respect to the graphene unit cell. At present not much infor- mation is available about the graphene grown on Rh(111). Precisely, the study