Spatial variation of the two-fold anisotropic superconducting gap in a monolayer of $\mathrm{FeS}{\mathrm{e}}_{0.5}\mathrm{T}{\mathrm{e}}_{0.5}$ on a topological insulator

We present a low temperature scanning tunneling spectroscopy (STS) study of the superconducting properties of monolayers of $\mathrm{FeS}{\mathrm{e}}_{0.5}\mathrm{T}{\mathrm{e}}_{0.5}$ grown on the three-dimensional (3D) topological insulator $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_{1.2}\mathrm{T}{\mathrm{e}}_{1.8}$. While the morphology and the overall transition temperature resembles those of similarly doped bulk crystals, we find a two-fold anisotropic $s$-wave gap function. The two-fold nature of the gap symmetry is evident from the Bogoliubov quasiparticle interference (QPI) pattern, which shows distinct $C_2$ symmetric scattering intensities. Spatially resolved spectroscopic data shows a strong inhomogeneity in the size and anisotropy strength of the energy gaps, which cannot be correlated merely to the local chemical disorder. Instead, we argue that the gap inhomogeneity emerges with a similar mechanism as in disordered superconductors. Our sample system provides an ideal platform to study unconventional superconductivity in close proximity to a topological insulator.

Figure 1

Growth and superconductivity of $\mathrm{FeS}{\mathrm{e}}_x\mathrm{T}{\mathrm{e}}_{1-x}$ on $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_{1.2}\mathrm{T}{\mathrm{e}}_{1.8}$. (a) The 3D view of a 300 nm × 300 nm constant-current STM topograph showing islands of $\mathrm{FeS}{\mathrm{e}}_x\mathrm{T}{\mathrm{e}}_{1-x}(V=-600\mathrm{mV},I_s=30\mathrm{pA})$. (b) Height profile along the line shown in (a). (c) Constant-current topograph acquired on the substrate $(V=-5.7\mathrm{mV},I_s=200\mathrm{pA})$. The image is a composition of the original and a Fourier filtered topograph to enhance the atomic resolution. (d) Constant-current topograph acquired on the single layer of $\mathrm{FeS}{\mathrm{e}}_x\mathrm{T}{\mathrm{e}}_{1-x}(x\sim 0.5,V=200\mathrm{mV},I_s=3\mathrm{nA})$. (e) Height profile along the blue line shown in (d). (f) Tunneling spectra acquired at $T=1.1\mathrm{K}$ along the black arrow shown in (d). Blue arrows show the positions of second coherence peaks originating from a large gap structure characteristic for Te-rich sites. (g) Temperature dependent and background corrected spectra along with anisotropic BCS fits. Here the fits are done on the positive side of the spectra. Spectra are shifted vertically for clarity. The degree of anisotropy used for all temperatures is $a=0.38$. (h) Temperature dependence of the superconducting energy gap $\left({\mathrm{\Delta }}_0\right)$ (red) and the Dynes broadening parameter ($\mathrm{\Gamma }$) (purple). The solid black curve represents the temperature evolution of the energy gap $\mathrm{\Delta }\left(T\right)$ expected within BCS theory.

Figure 2

Inhomogeneities of gap structure, gap size, and gap anisotropy. (a) Constant current STM topograph showing an area of a single layer of $\mathrm{FeS}{\mathrm{e}}_x\mathrm{T}{\mathrm{e}}_{1-x}$, where the spectroscopic data of this figure has been measured. (b)–(d) Tunneling conductance spectra (markers) acquired at $T=1.1\mathrm{K}$ at the three different locations on $\mathrm{FeS}{\mathrm{e}}_{0.5}\mathrm{T}{\mathrm{e}}_{0.5}$, indicated by correspondingly colored markers in (a), (e), and (f). The continuous black curves plotted along with the measured spectra represent fits using an anisotropic gap function (see text). Fit parameters: (b) ${\mathrm{\Delta }}_0=2.1\mathrm{meV},a=0.3,\mathrm{\Gamma }=0.14\mathrm{meV}$; (c) ${\mathrm{\Delta }}_{0L}=4.2\mathrm{meV},{\mathrm{\Delta }}_{0S}=2.25\mathrm{meV},a=0.28,\mathrm{\Gamma }=0.14\mathrm{meV},\sigma =0.15$; (d) ${\mathrm{\Delta }}_0=1.75\mathrm{meV},a=0.5,\mathrm{\Gamma }=0.14\mathrm{meV}$. (e) Spatial evolution of the superconducting gap over the area of (a) obtained by fitting each spectrum of a $60\times 60$ pixel spectroscopic field employing an anisotropic gap in the BCS density of states (BCS-DOS). The fitting procedure is applied only to the positive side of the spectra. (f) Corresponding anisotropy map obtained from the fits. (g) The 2D histogram of ${\mathrm{\Delta }}_0$ and topographic height plotted as intensity map.

Figure 3

Two-fold symmetry in quasiparticle interference analyzed by FT-STS (a) $Z$ map, obtained by taking the ratio of conductance maps over an area of $25\mathrm{nm}\times 25\mathrm{nm}$ at 1 mV and $-1\mathrm{mV}$. (b) Autocorrelation of (a). (c) Simplified schematic diagram of the unfolded BZ of the unit cell with a single Fe atom. The blue circle at Γ and the green circles at the Μ points represent the expected hole and electron pockets, respectively. (d)–(f) Fourier transforms of $Z$ maps at the various indicated bias values. Light green circles in (d) represent Bragg peaks due to Se/Te atoms, while white circles in each panel represent Bragg peaks due to Fe atoms. (g), (h) Dispersions of QPI vectors along Cuts 1 and 2 shown in (d), which represent the high symmetry directions along Fe-Fe bonds. The corresponding origins of the scattering intensities are indicated in (d).

Figure 4

(a) Constant current STM topograph acquired on a single layer of $\mathrm{FeS}{\mathrm{e}}_x\mathrm{T}{\mathrm{e}}_{1-x}(V=60\mathrm{mV};I_s=200\mathrm{pA})$. (b) Histogram of the $z$ values of the centers of atoms in (a). The black curve, which is the sum of the blue and pink Gaussian functions, has been fitted to the histogram. The blue and the pink curve correspondingly represent the Se and Te atoms, respectively. The composition of Se and Te calculated by using the area below the two curves is 48% and 52%, respectively, with an error of 6%.

Figure 5

(a) Constant current STM topograph acquired on a single layer of $\mathrm{FeS}{\mathrm{e}}_x\mathrm{T}{\mathrm{e}}_{1-x}(V=10\mathrm{mV};I_s=400\mathrm{pA})$. Numbers indicate the Te-rich sites where spectroscopic data was acquired. The raw spectra corresponding to these numbered positions are plotted in (b)–(e). All the spectra show two gap features with two coherence peaks that appear symmetrically around $E_{\mathrm{F}}$ at $(2.1\pm 0.5)\mathrm{mV}$ and $(4.5\pm 0.5)\mathrm{mV}$.

Figure 6

(a) Anisotropic gap function given by $\mathrm{\Delta }\left(\theta \right)={\mathrm{\Delta }}_0\left[1+a\left(cos2\theta -1\right)\right]$, where ${\mathrm{\Delta }}_0$ is the maximum value of the energy gap and $a$ represents the degree of gap anisotropy. In this case, ${\mathrm{\Delta }}_0=2.25\mathrm{meV}$ and $a=0.325$ was assumed. (b) Typical $dI/dV$ spectrum (red circles). The green curve represents a fit using the BCS-Dynes density of states: $N\left(E\right)=N_n\left(E_F\right)·\mathrm{Re}\left[\frac{E+i\mathrm{\Gamma }}{\sqrt{{\left(E+i\mathrm{\Gamma }\right)}^2-{\mathrm{\Delta }}^2}}\right]$, where $\mathrm{\Delta }=2.1\mathrm{meV}$ and $\mathrm{\Gamma }=0.14\mathrm{meV}$, whereas the black curve denotes the fit using the BCS-Dynes density of states $N\left(E\right)=N_n\left(E_F\right)·\mathrm{Re}\left[\frac{E+i\mathrm{\Gamma }}{\sqrt{{\left(E+i\mathrm{\Gamma }\right)}^2-\mathrm{\Delta }{\left(\theta \right)}^2}}\right]$ (black curve) [29] employing an anisotropic energy gap $\mathrm{\Delta }\left(\theta \right)$ shown in (a) with the Dynes broadening parameter $\mathrm{\Gamma }=0.14\mathrm{meV}$. (c) Anisotropic gap function for two gaps with ${\mathrm{\Delta }}_{0L}=4.5\mathrm{meV}, {\mathrm{\Delta }}_{0S}=2\mathrm{meV}$, and $a=0.3$, where the subscripts $L$ and $S$ stand for large and small gaps, respectively. (d) Typical $dI/dV$ spectrum (red circles) taken at a Te-rich site. The black curve plotted together with the data represents a fit using a two gap model based on the equation $G=\sigma G_L+\left(1-\sigma \right)G_S$ [38], where $G_L$($G_S$) are the differential conductances simulated using large (small) energy gaps ${\mathrm{\Delta }}_{0L}$ (${\mathrm{\Delta }}_{0S}$), $\sigma$ is the spectral weight due to the large gap, and $G$ is the resulting conductance. The used anisotropic energy gaps are shown in (c), while the other fit parameters are $\sigma =0.4$ and $\mathrm{\Gamma }=0.22\mathrm{meV}$. It should be noted that the choice of the anisotropic gap function is not unique. We get the same results if we replace the $cos2\theta$ term in the gap function by $cos4\theta$.

Figure 7

Tunneling conductance maps at various bias voltages, which are derived from the $dI/dV$ spectra taken on $60\times 60$ pixels over a $20\mathrm{nm}\times 20\mathrm{nm}$ area. The inhomogeneity in the spectra within the gap region is apparent from the maps.

Figure 8

(a) Tunneling spectra (markers) plotted along with the fits using the model with a single anisotropic gap function (lines). Fit procedure is applied on the positive side of the conductance spectra, as described in the text. (b) Superconducting energy gap $\left({\mathrm{\Delta }}_0\right)$ corresponding to the fits shown in (a). (c) The degree of anisotropy $a$, obtained from the corresponding fits shown in (a).

Figure 9

Lateral evolution of tunneling spectra over a 3.5 nm long line as a function of temperature. We observe that the spectra evolve smoothly, and at high temperature $(T=10\mathrm{K})$ the local superconducting correlations persist, as seen by the formation of blue patches related to the gap in $dI/dV$.

Figure 10

Tunneling conductance maps at various bias voltages, which are derived from the $dI/dV$ spectra taken on $512\times 512$ pixels over a $25\mathrm{nm}\times 25\mathrm{nm}$ area. The inhomogeneity in the superconducting properties is apparent from the maps at low bias voltages

Figure 11

(a) Spatial evolution of the superconducting energy gap [same data as in Fig. 2 of the main text]. (b) Corresponding conductance map at $V=1\mathrm{mV}$. (c) The 2D histogram of the superconducting energy gap ($▵$) and the corresponding conductance value $g$ at $V=1\mathrm{mV}$, plotted as intensity map. The negative slope here represents an anticorrelation between $▵$ and $g\left(\vec{r},V=1\mathrm{mV}\right).$

Figure 12

Fourier transforms of $Z$ maps at various bias values. Here each plot is obtained using fast Fourier transform analysis of $Z$ maps and then subtracting the central core to enhance the visibility of relevant q vectors. For further analysis of different quasiparticle structures, the data is symmetrized along a high symmetry axis, i.e., along Fe-Fe bonds, and low pass filtered to reduce the noise. The resulting data is presented in Fig. 3 of the main text.

Figure 13

The plots represent the data extracted from Ref. [19], where the authors calculated the orbital splitting energy as a function of the dominant scattering vector q, corresponding to symmetry breaking states, employing the joint density of states approach. Using their results, we estimate orbital splitting energies of 19.5 meV in our system, corresponding to the observed scattering vector ${\mathbf{q}}_2=0.18\pi /a_{\mathrm{Fe}-\mathrm{Fe}}$.