Figure 9.4:Topography measured on the ex-situ grown samples by using the JT-STM (U=1 V,I=250 pA).
40 nm 4.32 nm 0.00 1.00 1.50 2.00 2.50 3.00 3.50
built JT-STM, the protection layer2 had to be desorbed after the transfer to the UHV
system. Therefore, the samples were annealed at 460◦ for half an hour. A representa- tive surface is shown in Fig. 9.4.
Compared to Fig. 9.3a, some muck hills appear at various positions of the surface. It was not possible to get rid of them, even after further annealing of the samples for several hours. Note that the annealing temperature has to stay below 550◦C. This is the decomposition temperature of FeSe. If the sample temperature was higher than 550◦C, the sample would evaporate.
Note that on the clean parts of the layer, the superconducting properties where not affected by the impurities.
9.4 Seeking the Pairing Glue by Tunneling
Spectroscopy
The measurements that are presented within this section were performed with the JT- STM. The samples were the ex-situ ones from Shanghai as described above. Thereby, tunneling spectroscopy was performed on clean areas of the sample.
Figure 9.5:The dI/dU spectrum measured in the superconducting state (T=800 mK is shown in blue (R=50 mΩ, Umodrms =461 µV). The green spectrum was measured at T=62 K and thus in the normal state (R=97.2 mΩ, Umodrms =6.6 mV).
-40 -20 0 20 40 0.0 0.2 0.4 0.6 0.8 1.0 U(mV) dI /dU (arb .units )
2Note that for the transportation from Shanghai to Karlsruhe, the grown FeSe monolayers were cov- ered with a thick Se layer.
9 FeSe monolayer on SrTiO3
In Fig. 9.5, two representative dI/dU spectra are shown. The blue curve displays a spectrum, which was measured in the superconducting state at T=800 mK. The green one was measured in the normal state at T=62 K. Similar to the measurement on bulk FeSe, a V-/U-shape background conductance is clearly visible indicating the presence of significant inelastic tunneling contributions. In the spectrum measured in the su- perconducting state, the superconducting gap appears in the range of U=±11.5 mV. Another hump is weakly visible at ±7.5 mV. It becomes more apparent in Fig. 9.6b and Fig. 9.7b. It could be related to a second gap originating from a second electron band crossing the Fermi energy around the ¯M point. Alternatively, it could originate from an anisotropic gap function, for which a minimum and a maximum gap would exist. Around U=26.45 mV, a redistribution of spectral weight within the superconducting spectrum is clearly visible. At voltages slightly lower than U=26.45 mV, the dI/dU sig- nal drops below the one measured in the normal state. For voltages slightly larger than U=26.45 mV, the opposite is observed, i.e, a peak appears at 28 meV.
A slight asymmetry is visible in both spectra measured in the normal and super- conducting state. The spectrum measured in the normal state has a rather skewed U-shape and in the spectrum recorded in the superconducting state, the redistribution of the spectral weight is stronger for the positive voltage side. Similar observations are reported for several other superconductors, e.g., LiFeAs [216]. In Ref. [34], it is argued that such an asymmetric behavior could either originate from a non-constant (linear) normal state DOS or from a asymmetry in the inelastic tunneling matrix element. How- ever, we will not address this point within the present thesis. In the following, the focus will be on the origin of the feature at around U=26.45 mV.
With the superconducting gap being ∆=11.5 mV, a resonance mode is expected to occur at ωres = 1.3 · ∆ + ∆ =26.45 mV. This voltage is marked with a black line in
Fig. 9.6a/b and Fig. 9.7a/b. Within the same figures, ∆ is marked with a dashed line. A comparison between our experimental results in Fig. 9.6a/b with the calculations of P. Hlobil and J. Schmalian is shown in Fig. 9.6c/d, indicating similarities. As dis- cussed in Sec. 6.3, calculations were performed in the framework of an extension of the Eliashberg theory within the spin-fermion approach [11]. The theoretical calculations as well as the experimental results shown in Fig. 9.6 represent normalized spectra. The superconducting spectrum shown in Fig. 9.6a was normalized according to Eq. 8.3 by using the normally conducting spectrum which is shown in Fig. 9.5 (green spectrum). The d2I/dU2 spectrum shown in Fig. 9.6b was normalized to the measured d2I/dU2
spectrum which is shown in Fig. 9.7b. It was measured simultaneously to the dI/dU spectrum shown in Fig. 9.5 (green line) by using a second synchronized analog lock-in amplifier. As can be seen in Fig. 9.6c, strong inelastic contributions lead to a suppres- sion of the differential conductance. In Sec. 6.3, this suppression was explained by the opening of a spin gap in the picture of spin-fluctuation-mediated superconductivity. The corresponding spectrum is shown again in Fig. 9.7d. In the experimental data in Fig. 9.6a, a drop below unity can be observed as well. It occurs in a small voltage range slightly below the position of ∆ + ωres just like it is illustrated in Fig. 9.6c. A
small difference between the experimental and theoretical data is only visible for volt- ages slightly larger than ∆+ωres. At these voltages, a peak appears in the experimental
spectrum (Fig. 9.6a, which is more pronounced compared to the theoretical expectation
9.4 Seeking the Pairing Glue by Tunneling Spectroscopy 0 10 20 30 40 0.0 0.5 1.0 1.5 U (mV) norm. dI/dU(arb. unit s) 0 10 20 30 40 0 5 10 15 U (mV) norm. d²I/dU² (arb. unit s) strong inelastic contr. pure elastic 0 Δ Δ+ωres 0 1 Δ 2Δ 3Δ a - 6 - 4 - 2 0 2 4 6 Δ Δ+ωres
strong inelastic contr.
pure elastic
a)
b)
c)
d)
Δ+ωres Δ+ωres Δ ΔFigure 9.6:a) Normalized and symmetrized version of the superconducting spectrum dis- played in Fig. 9.5 (blue line). Dashed and solid line mark the position of the gap and the corre- sponding resonance mode, respectively. The corresponding d2I/dU2-spectrum is shown in b). The normalization of this spectrum was done by using the two spectra shown in Fig. 9.7b. The theoretical calculations of σ ˆ=dI/dUand dσ ˆ=d2I/dU2performed by P. Hlobil and J. Schmalian are shown in c) and d) and are taken from Ref. [11].
9 FeSe monolayer on SrTiO3
(see Fig. 9.6c).
Exactly the same can be observed for the corresponding experimental and theoretical d2I/dU2 spectra shown in Fig. 9.6b and Fig. 9.6d.
0 10 20 30 40 -200 -100 0 100 200 300 400 U(mV) d²I/dU² (arb. unit s) 0 10 20 30 40 50 0.0 0.5 1.0 1.5 2.0 2.5 3.0 U(mV) dI/dU (arb. units) 0 10 20 30 40 50 0.00 0.05 0.10 0.15 meV g2χ(ω) Eoff2νF Δ ωres 2Δ 3Δ ω g 2 χ (ω ) [a rb .u ni ts ] b)
a)
b)
c)
d)
sym. dI/dU norm. dI/dU Dynes fit Δ+ωres Δ Δ+ωres Δ Δ2 ( σ0 )inel
Figure 9.7:a) The symmetrized spectrum of Fig. 9.5 is shown in the superconducting state marked by the dark blue line. A modeled Dynes fit is depicted in black. Both spectra are compared to the normalized spectrum which is shown in Fig. 9.6a. The green line marks unity. b) The antisymmetrized d2I/dU2spectrum is shown in dark blue for the superconducting state and in green for the normal state. c) The deconvoluted intergrated spin spectrum is shown. It was calculated by P. Hlobil [34] using the experimental data shown in a). In d), the spin- fermion approach calculated within the integrated spin spectrum (done by P. Hlobil) is again displayed in the normal as well as in the superconducting state [11].
The presence of inelastic contributions to our experimental data becomes even more apparent in Fig. 9.7a. The symmetrized experimental dI/dU spectrum of Fig. 9.5 is shown in dark blue. A Dynes fit is shown in black and represents the purely elastic part to the differential tunneling conductance (without renormalization)3. This Dynes fit, as well as the symmetrized spectrum, are compared to the spectrum in cyan, which illustrates the normalized spectrum of Fig. 9.6a. For the latter, the energy dependence of the differential tunneling conductance is in good agreement with the Dynes fit at 3The same Dynes fit was already used in the PhD thesis of P. Hlobil [34] in order to deconvolute the
integrated spin spectrum that is shown in Fig. 9.7c.
9.4 Seeking the Pairing Glue by Tunneling Spectroscopy voltages outside the gap range. In the case of a constant normally conducting DOS (which means a constant dIel/dU) of FeSe, a conclusion similar to that of the exper-
iment on Pb/Si(111) could be drawn: The light-gray-shaded area between the dark blue line and cyan line represents the inelastic contributions to the dI/dU spectrum. However, in the case of FeSe as well as many other iron-based superconductors, the normally conducting DOS is possibly not a constant. Therefore, conclusions about elastic and inelastic contributions cannot be drawn easily.
Chap. 4 and Chap. 5 explained that, in the case of the strong-coupling superconduc- tor lead, a d2I/dU2spectrum measured in the normal state is proportional to a function
that approximately equals to the Eliashberg function4.
In Sec. 6.3, it was mentioned that the same principle holds for the spin-fermion ap- proach (in the case of a constant normally conducting DOS). In the case of the latter, the inelastic part of the second derivative of the tunneling current is proportional to the integrated spin spectrum χ times the squared coupling constant g (between electron- like quasiparticles and spin fluctuations) d2Iinel/dU2 ∝ g2χ
tun(ω). For the normal state,
this can easily be proved by comparing the d2I/dU2 ≈ d2Iinel/dU2spectrum measured
in the normal state (green line of Fig. 9.7b) to the calculated g2χ(ω) spectrum in the
normal state (blue curve in Fig. 9.7d). Both spectra show a broad overdamped particle- hole continuum. Nevertheless, due to the high measurement temperature in the case of the normally conducting spectrum, the energy resolution is rather low. The spec- tra shown in Fig. 9.5 and in Fig. 9.7b have an energy resolution of only 21.6 meV and 29.86 meV, respectively. Compared to the superconducting spectra having an energy resolution that is higher than 1 meV, a lot of details are lost. However, heating the sam- ples up to temperatures above Tcis the only way to enter the normal state. In contrast
to the system of thin Pb film on a Si(111) substrate (cf. Chap. 5), where the normal state could be accessed by applying a magnetic field of 1 T, in the case of FeSe as well as most of the iron-based superconductors, the magnetic field needed in order to sup- press superconductivity is in the range of 30 T, so it is not applicable in typical STM setups5. Therefore, the sample has to be heated above the critical temperature in order
to enter the normal state. For our monolayer FeSe/STO samples Tc, was about 55 K.
This is the reason why our normally conducting spectra were measured at 62 K. As mentioned in Sec. 6.3, the spin spectrum is strongly renormalized when enter- ing the superconducting state [11], as can be seen in Fig. 9.7d. This is in contrast to the phonon DOS in conventional phonon-mediated superconductors. Furthermore, in contrast to the normal state, the comparison between theory and experiment for g2χ(ω)
in the superconducting state is much more difficult. In order to gain information on the pairing glue (which should be somehow related to g2χ(ω)) in the superconducting
state of our experimental tunneling data, the integrated spin spectrum was deconvo- luted by P. Hlobil [34]. The result is shown in Fig. 9.7c. The deconvolution process 4This proportionality followed from the fact of a constant normally conducting DOS of Pb leading to a
vanishing d2Iel/dU2contribution in the normal state and therefore d2I/dU2≈ d2Iinel/dU2.
5In principle, normally conducting areas can be accessed by measuring at a vortex core in the Shub- nikov phase. In the case of entering the Shubnikov phase, much smaller magnetic field are needed. However, when measuring inside a vortex, tunneling spectroscopy data can be influenced by bound states likely to occur therein.
9 FeSe monolayer on SrTiO3
was based on the relationship of the inelastic part of the differential conductance σi
and g2χ(ω) according to Eq. 6.19. σ
i was obtained by subtracting the modeled Dynes
fit shown in Fig. 9.7a from the measured data (dark blue line in Fig. 9.7a). By using an iterative process [34], g2χ(ω) could finally be extracted. The shape of the obtained
g2χ(ω)-function in the superconducting state (orange line in Fig. 9.7c), strongly resem-
bles the (within the spin-fermion approach) calculated g2χ(ω), which is shown in red
in Fig. 9.7d. In both spectra, a spin gap opens below ωres. Compared to the inelastic
contribution to the tunneling spectra in the normal state (blue line in Fig. 9.7d) these contributions are completely suppressed within the energy range. At energies around ωres, a peak appears which dissipates to a broad particle-hole continuum at larger en-
ergies. This behavior is visible both in Fig. 9.7c and Fig. 9.7d.
On the whole, there is strong evidence for the feature at 26.45 mV in our experimen- tal data of the superconducting state to originate from a strong coupling of electrons to spin fluctuations. This feature appears at an energy, at which a spin-fluctuation res- onance mode is expected. The resonance mode was explained to occur as an elastic strong-coupling feature which results from the renormalization of the band structure due to the strong coupling between spin fluctuations and the electronic quasiparti- cles. The hump in the superconducting state of our experimental data develops due to significant inelastic contributions. The (inelastic) spin spectrum is strongly renormal- ized when entering the superconducting state. It overshadows the resonance mode for larger contributions and creates the observed hump.
Nevertheless, we have to admit that a spectrum as it was shown in Fig. 9.5, could not be measured at any place of the surface, but only on distinct sample positions. In fact, the surface of our single layer FeSe on STO was electronically rather inhomo- geneous. The appearance of the gap varies a lot. Within a literature research, clear differences in the appearance of the the superconducting gap could be found as well (cf. Ref. [13, 302, 325, 342]). Gap sizes of ∆=10 meV, ∆=15 meV or even a double gap with ∆1=10 meV and ∆2=20 meV are reported. The reason for the different reported
gap sizes is most likely the difference in growth and interface conditions. It would be interesting to clarify this point within further investigations. In the case of our sam- ple, the superconductivity turned out to be more homogeneous after further annealing cycles. Such annealing cycles were carried out for several hours. However, the above- mentioned muck hills did not vanish. Furthermore, the coverage slightly decreased after a long-term annealing process. A reason could be the annealing temperature which is close to the decomposition temperature. As a result, clean and rather homo- geneously superconducting FeSe areas with a size of ≈30×30 nm2could not be found.
This is a big drawback of our ex-situ grown samples, since such areas are needed in order to perform quasiparticle interference (QPI) measurements, as we will see in the following section. This was the reason why successful QPI measurements could only be performed on the in-situ grown samples at Shanghai Jiao-Tong University.