Encuesta y Componentes

3.1 Introduction 39 3.2 Background physics for

Sr2RuO4

41

3.3 Experimental methods 60 3.4 Results and discussions 67 3.5 Conclusions 90

Materials with strong electron-electron correlations are of par- ticular importance in the study of condensed matter physics as it is here where conventional theories are often seen to be violated and exotic phases such as superconductivity and magnetism emerge. The transition metal oxide Sr2RuO4 shares the same layered per- ovskite crystal structure as the parent compound of the prototypical high-Tc superconductor La2-xSrxCuO4 and attracted considerable

interest after superconductivity was also found here by Maenoet al. in 1994, albeit at much lower temperatures [77]. Since then the superconductivity has been established to be unconventional in nature, but many open questions remain regarding the microscopic origin of the superconductivity and the exact pairing symmetry. What is known is that the superconductivity condenses from a firmly established and well characterised Fermi liquid [6].

To better understand mysteries such as the order parameter symmetry of an unconventional superconductor it can be beneficial to venture into neighbouring phase space. Hydrostatic pressure is often used, but in Sr2RuO4 its effects are disappointing. It is known to suppress the superconducting transition temperature and at the same time reduce the quasiparticle mass enhancements [78]. What may prove to be of particular importance in Sr₂RuO₄ is the close proximity of one of its three conduction bands to a Van Hove singularity. This is a special point in the band structure where the group velocity of the quasiparticles goes to zero and the density of states diverges (in 2D systems). Tuning towards a Van Hove singu- larity is of interest not just in terms of superconductivity but also for the study of a more general problem. Strong quasiparticle renor- malization and quasiparticle-quasiparticle scattering can occur near such singularities in the density of states and it has been postulated that for the cuprate superconductors some of the unusual behaviour observed may be the consequence of a Van Hove singularity close to the Fermi level. For Sr₂RuO₄ the Fermi level can be made to traverse the Van Hove singularity by electron doping, heterovalent substitution of La3+ _{for Sr}2+ _{[79, 80], or by introducing biaxial} strain though lattice mismatch of epitaxially grown thin films [81].

40 The Physics of Sr₂RuO₄Approaching a Van Hove Singularity

These experiments provided useful information about the metallic properties, but the extreme sensitivity of the superconductivity of Sr2RuO4to disorder meant that no superconductivity could be observed in either study.

Applying uniaxial stress to bulk samples has also demonstrated the importance of the Van Hove singularity in Sr₂RuO₄[33]. An applied strain of ∼ −0.2 % was shown to cause an enhancement

of the superconducting critical temperature by∼40 %, which was

argued to be caused predominately by the increase in density of states as the Van Hove singularity is brought closer to the Fermi energy.

Uniaxial stress is particular well suited, at least in principle, for tuning towards Van Hove singularities compared to hydrostatic pressure or even biaxial stress. Under uniaxial stress a smaller volume change takes place so it is a lower-energy distortion, and crucially a circular Fermi surface becomes elliptical extending out towards the zone boundaries in two opposite directions. In com- parison, any distortions to the Fermi surface on a square lattice under biaxial stress must be four-fold symmetric. Without a sig- nificant volume change of the Fermi surface, the only way for the Fermi surface to get closer to the zone boundary is for four lobes to grow out in a cross shape, overall a much higher energy configuration than the two fold distortion under uniaxial stress. In terms of hopping integrals, uniaxial pressure directly affects the ratios of nearest-neighbour hoppings, whereas biaxial stress or hydrostatic pressure can only alter the balance between nearest- and next-nearest-neighbour hopping, which has a generally weaker effect.

As stressed earlier in this thesis, uniaxial stress has the benefits that it is both a clean and continuous tuning parameter. We are now in the situation where we can achieve much larger uniaxial stresses motivating a continuation and extension of the previous study. We extended the strain range all the way to−1 %, higher

than was thought possible for this rather brittle metal oxide. At a strain of−0.55 %, I observe a maximum inTc of∼3.5 K

after which Tc decreases again rapidly with higher strains. I have

also measured resistivity, magnetoresistance and Hall effect, all of which are consistent with the Fermi level traversing the Van Hove singularity, producing a Lifshitz transition. We observe signatures of quantum criticality as the transition is approached, thus provid- ing the unique opportunity to study a topological Lifshitz transition in a system which is exquisitely clean and with a continuous tuning parameter that introduces minimal disorder. We see that the den- sity of states changes in a very restricted part of the Brillouin zone due to the Van Hove singularity affect the temperature-dependent scattering of all the quasiparticles.