Nanoscale electronic inhomogeneity in ${\mathrm{FeSe}}_{0.4}{\mathrm{Te}}_{0.6}$ revealed through unsupervised machine learning

We report on an apparent low-energy nanoscale electronic inhomogeneity in ${\mathrm{FeSe}}_{0.4}{\mathrm{Te}}_{0.6}$ due to the distribution of selenium and tellurium atoms revealed through unsupervised machine learning. Through an unsupervised clustering algorithm, characteristic spectra of selenium- and tellurium-rich regions are identified. The inhomogeneity linked to these spectra can clearly be traced in the differential conductance and is detected both at energy scales of a few electron volts as well as within a few millielectronvolts of the Fermi energy. By comparison with angle-resolved photoemission spectroscopy, this inhomogeneity can be linked to an electronlike band just above the Fermi energy. It is directly correlated with the local distribution of selenium and tellurium. There is no clear correlation with the magnitude of the superconducting gap, however, the height of the coherence peaks shows a significant correlation with the intensity with which this band is detected, and hence with the local chemical composition.

Figure 1

(a) Topographic STM image (scale bar: 5 nm) and (b) cluster-averaged spectra, identified through the cluster algorithm described in the text for $\overline{\mathrm{\Delta }}=7.5$, representative of Se- and Te-rich regions. Apart from a difference in differential conductance at $-1\mathrm{V}$, the spectra exhibit a small shift in the minimum close to the Fermi energy. (c) Spatial map of the cluster number spectra have been assigned to.

Figure 2

Machine-learning algorithm applied to low-energy spectra. (a) Typical topography of ${\mathrm{FeSe}}_{0.4}{\mathrm{Te}}_{0.6}$ acquired simultaneously with a spectroscopic map taken in the normal state at $T=16\mathrm{K}$ (scale bar: 5 nm); the inset shows the covered area from a higher-resolution topography on the same lateral and height scale. (b) Cluster-averaged spectra for Te- and Se-rich regions, respectively [obtained using $\overline{\mathrm{\Delta }}=13$, identifying in total three clusters of spectra from the map shown in (a)]. (c) Spatial map of the two most abundant clusters (the third cluster has only a single occurrence, black pixel). Comparison with (a) shows that red regions tend to be Te rich, whereas blue regions are Se rich. (d) Same spectra as in (b), but after subtraction of a polynomial of second degree, so that the peak at $2.4\mathrm{mV}$ is more visible.

Figure 3

Properties of low-energy feature. (a) Correlation between the amplitude of the peak in $g_{\mathrm{N}}\left(V\right)$ and the ratio $z(V=13.5\mathrm{mV})=g\left(V\right)/g(-V)$, showing a clear anticorrelation $\left(C=-0.64\right)$. (b) Correlation between the peak in the normal-state differential conductance $g_{\mathrm{N}}\left(V\right)$ at $V=2.4\mathrm{mV}$ with the local apparent height as a proxy for the chemical composition. Larger heights correspond to tellurium-rich regions and lower heights to selenium-rich areas. An anticorrelation with a coefficient $C=-0.64$ is observed.

Figure 4

Relation of the normal-state low-energy spectral feature with superconductivity. (a) Correlation between the height of the coherence peak at positive energy and the peak in the normal-state differential conductance $g_{\mathrm{N}}\left(V\right)$ showing a correlation with $C=0.54$. (b) Tunneling spectra $g_{\mathrm{S}}\left(V\right)$ and $g_{\mathrm{N}}\left(V\right)$ acquired in the normal and superconducting state, respectively, showing the definition of $\mathrm{\Delta },g_{\mathrm{S}}\left(\mathrm{\Delta }\right)$ and $g_{\mathrm{S}}(-\mathrm{\Delta })$. (c) Correlation between the height of the coherence peak at positive energy and the local chemical composition, showing a correlation coefficient of $C=-0.67$. (d) 2D histogram between gap size as measured by the energy of the coherence peak at positive energy and the apparent height and (e) between the ratio of the amplitude of the coherence peaks at positive and negative energy with the apparent height, both showing no correlation $(C=-0.026$ and $C=-0.056$, respectively).