Nanoscale electronic inhomogeneity in FeSe 0.4 Te 0.6 revealed through unsupervised machine learning
aa r X i v : . [ c ond - m a t . s t r- e l ] F e b Nanoscale electronic inhomogeneity in FeSe . Te . revealed through unsupervisedmachine learning P. Wahl, ∗ U. R. Singh, † V. Tsurkan,
3, 4 and A. Loidl SUPA, School of Physics and Astronomy, University of St. Andrews,North Haugh, St. Andrews, Fife, KY16 9SS, United Kingdom Max-Planck-Institut f¨ur Festk¨orperforschung, Heisenbergstr. 1, D-70569 Stuttgart, Germany Center for Electronic Correlations and Magnetism, Experimental Physics V,University of Augsburg, D-86159 Augsburg, Germany Institute of Applied Physics, 5 Academiei str., Chisinau, MD 2028, Moldova (Dated: February 25, 2020)We report on an apparent low-energy nanoscale electronic inhomogeneity in FeSe . Te . due tothe 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 thedifferential conductance and is detected both at energy scales of a few electron volts as well as withina few millielectronvolts of the Fermi energy. By comparison with ARPES, this inhomogeneity canbe linked to an electron-like band just above the Fermi energy. It is directly correlated with thelocal distribution of selenium and tellurium. There is no clear correlation with the magnitude of thesuperconducting gap, however the height of the coherence peaks shows significant correlation withthe intensity with which this band is detected, and hence with the local chemical composition. PACS numbers: 74.55.+v, 74.70.Xa, 74.81.-g
The 11 iron-chalcogenide superconductors have thesimplest crystal structure of the iron-based superconduc-tors, consisting of planar iron layers with chalcogenide(Se, Te) anions above and below. The crystal structureprovides a well-defined and non-polar cleavage plane be-tween the chalcogenide layers. LEED and STM stud-ies show no indication for a surface reconstruction[1, 2].Previous studies of the local density of states in thismaterial by scanning tunneling microscopy have eitherconcentrated on the superconducting state[3–5] or notdetected any electronic inhomogeneity in the energyrange investigated [6]. Interest in the superconductiv-ity in FeSe − x Te x has recently had a renaissance drivenlargely by the existence of topologically non-trivial sur-face states[7] and the detection of zero bias anomaliesin vortex cores[7, 8]. In particular for the interpretationof the latter, one of the big outstanding puzzles is whynot all vortex cores exhibit zero bias anomalies, as wouldbe expected for a topologically protected state, but onlysome. This hints to some influence of the chemical in-homogeneity in the material that has hitherto not beenaccounted for in analyzing the experiments.To investigate the electronic inhomogeneity in the nor-mal state electronic structure, we have carried out STMmeasurements on a single crystal of FeSe − x Te x with x = 0 .
61 (determined by EDX measurement) and witha superconducting transition temperature T C ≈
14 K[9].We have used a home-built low temperature STM whichallows for in-situ sample transfer and cleavage[10]. Sam-ple cleaving was performed at temperatures around 20 K.Spectroscopic maps in which differential tunneling con-ductance d I/ d V is measured as a function of bias voltage V and position r have been acquired in the temperature range from 2 K to 16 K through a lock-in amplifier witha modulation of 600 µ V RMS . The differential conduc-tance in the normal state and superconducting state arereferred to g N ( V ) and g S ( V ), respectively. Bias voltagesare applied to the sample, with the tip at virtual ground.Tunneling spectra are acquired with open feedback loop.Here, we employ an unsupervised machine learningapproach through a cluster analysis of the tunnelingspectra measured on FeSe . Te . . The algorithm is avariant of a k -means clustering algorithm (or Lloyd’salgorithm). It uses a similarity analysis of spectra tocategorize them, aiming to minimize the metrics definedthrough ∆( g ( x , V ) , g ( y , V )) = P i | g ( x , V i ) − g ( y , V i ) | ofspectra g ( x , V ) defined on a discrete lattice with voltages V i . The algorithm compares individual spectra in eachidentified cluster to the average spectra of the cluster,and assigns them to the cluster with minimal difference.This process is performed iteratively until the clustersremain static in successive iterations. Apart from thedifferential conductance data g ( x , V ), the only inputparameter is the threshold ∆ above which spectra areconsidered different by the algorithm and a new clusteris created. The main difference to the k -means algorithmis that here, the number of clusters is not predeter-mined, but depends on the threshold ∆. Higher values of∆ thus lead to a larger number of clusters and vice-versa.We have applied the machine learning algorithm totwo data sets to investigate spatial inhomogeneitiesin the normal state differential conductance g N ( V ) toextract information about the normal state electronicstructure of FeSe . Te . . The first covers a bias voltagerange of + / −
1V and the second energies in the vicinity (a)(c) (b) O cc u r en c e s ( % ) Cluster
Cluster -1 0 10510 d I/ d V ( a . u . ) Bias (V)
FIG. 1: (a) topographic STM image (scale bar: 5nm) and(b) cluster-averaged spectra, identified through the clusteralgorithm described in the text for ∆ = 7 .
5, representative ofSe- and Te-rich regions. Apart from a difference in differentialconductance at − of the Fermi energy, between − ± ± −
1V (if the tip is stabilized at +1V), while above − . − .
4V may be due to the energy of d z -derived bands, which occur at different energies inFeTe compared to FeSe[1].Having demonstrated that the algorithm can extractmeaningful information from spectroscopic maps, wehave applied the same algorithm to investigate the lowenergy density of states in the vicinity of the Fermi en-ergy in the normal state of FeSe . Te . , to understandthe relation between the local chemical composition andthe electronic states in an energy range that is relevantfor superconductivity. Fig. 2(a) shows the topographicimage of a differential conductance map acquired in thenormal state of FeSe . Te . at a temperature T = 16K, ( )b( )d( )a( )c 40-40 Height (pm) Cluster -20 -10 0 102030405060 d I/ d V ( a . u . ) Bias (mV) -20 -10 0 10 20-20246810 d I/ d V ( a . u . ) Bias (mV)
FIG. 2: Machine learning algorithm applied to low energyspectra. (a) Typical topography of FeSe . Te . acquired si-multaneously with a spectroscopic map taken in the normalstate at T = 16K (scale bar: 5nm), inset shows the coveredarea from a higher resolution topography on the same lateraland height scale, (b) Cluster-averaged spectra for Te- and Se-rich regions, respectively (obtained using ∆ = 13, identifyingin total three clusters of spectra from the map shown in (a)).(c) Spatial map of the two most abundant clusters (the thirdcluster has only a single occurence, black pixel). Comparisonwith (a) shows that red regions tend to be Te-rich, whereasblue regions are Se-rich. (d) Same spectra as in (b), but aftersubtraction of a polynomial of second degree, so that the peakat 2 . i.e. above the superconducting transition temperature of T c ∼ z ( 1 3 . 5 m V ) P ea k i n g N ( V ) ( a . u . ) O cc u r en c e s -40 -20 0 20 400102030 Te richHeight (pm) P ea k i n g N ( V ) ( a . u . ) O cc u r en c e s Se rich (b)(a) () () (13.5mV)
FIG. 3: Properties of low energy feature. (a) Correlationbetween the amplitude of the peak in g N ( V ) and the ratio z ( V = 13 . g ( V ) /g ( − V ), showing a clear anticorrela-tion ( C = − . g N ( V ) at V = 2 . C = − .
64 is observed.
We find that not only do the normal state spectra varydue to the presence or absence of the peak at 2 . − . z ( V ) = g ( V ) /g ( − V ) for V = 13 . C = − .
64. We note that this ishigher than would be expected if the local compositionwould change the electronic states in the iron chalco-genide layer, because that should only yield a correlationcoefficient of C = 0 .
5, given that the composition of onlythe top half the chalcogenide layer is observed, while theone of the bottom half is expected to be random. It canbe argued that the correlation coefficient should be evenlower if one assumes that it is the four nearest neigh-bour chalcogen atoms below the iron layer that need tobe considered. The question arises how this low energy electronic in-homogeneity affects superconductivity, and what the ori-gin of the peak close to the Fermi energy is. To inves-tigate this, we can either compare a spectroscopic mapobtained in the normal state with one measured in thesame location in the superconducting state. The analysisof a combination of two such maps is shown in fig. 4(a),showing the correlation of the height of the coherencepeak with the height of the peak in the normal state tun-neling conductance. The histogram reveals again a clearcorrelation, with a correlation coefficient of about 0 .
5. Ifwe use the topographic height as proxy for the heightof the peak in the normal state conductance, we findan even higher correlation of − .
67 (compare fig. 4(b)).For comparison, no correlation is found between the sizeof the superconducting gap and the topographic height(fig. 4(c)), consistent with previous reports[13], or the ra-tio in the height of the coherence peaks at positive andnegative bias voltage (fig. 4(d)). d I/ d V ( a . u . ) -10 0 10Bias (mV) -40 -20 0 20 401.01.52.02.5 Te richHeight (pm) g S ( D ) / g S ( - D ) Se rich -40 -20 0 20 4023
Height (pm) G ap s i z e D (m e V ) peak in g N ( V ) ( a .u .) g S ( D ) ( a .u .) O cc u r en c e s (a) (e)(d) ( ) D g S ( ) D g S ( ) -D g S (V) g N (V) ( m e V ) () / (-) (b) -40 -20 0 20 40020406080100 Height (pm) g S ( D ) ( a .u .) Se rich Te rich (c) () ( a . u . )() ( a . u . ) FIG. 4: Relation of the normal state low energy spectralfeature with superconductivity. (a) Correlation between theheight of the coherence peak at positive energy and the peakin the normal state differential conductance, g N ( V ), showinga correlation with C = 0 .
54. (b) Tunneling spectra g S ( V ) and g N ( V ) acquired in the normal and superconducting state, re-spectively, showing the definition of ∆, g S (∆) and g S ( − ∆).(c) Correlation between the height of the coherence peak atpositive energy and the local chemical composition, showinga correlation coefficient of C = − .
67. (d) 2D histogram be-tween gap size as measured by the energy of the coherencepeak at positive energy and the apparent height and (e) be-tween the ratio of the amplitude of the coherence peaks atpositive and negative energy with the apparent height, bothshowing no correlation ( C = − .
026 and C = − . Our analysis of the peak in the differential conduc-tance spectra at 2 . . Te . shows that there is indeeda flat band just above the Fermi energy that could beresponsible for the feature we observe.[14] Due to theheavy character of this band, one can expect an increasein density of states, as detected in our spectra. We notethat a similar peak is observed in the normal state ofLiFeAs, at an energy of − . Te . exhibit zero energystates[8].The variation of the normal state differential conduc-tance has potential implications for the interpretationof measurements of the critical current in JosephsonSTM, as recently reported in [18]. The very narrowenergy interval around zero bias in which we observevariations of the tunneling matrix element in the normalstate suggests that an extrapolation of the normal stateresistance from outside the energy scale of the super-conducting gap to estimate the normal state resistanceof the junction R N is difficult and subject to spatialvariations. Our data indicate a strong correlation ofthe height of the coherence peak as well as the peak in the normal state differential conductance with thetopographic height (see figs. 3(b) and 4(b)), suggestingthat the same effect may contribute to spatial variationsof the critical current.Our results show how unsupervised machine learningcan be used to identify trends in spectroscopic STM datathat would otherwise be difficult to discern. In our case,it has helped us to identify the characteristic tunnelingspectra of Selenium- and Tellurium-rich regions in theiron chalcogenide superconductor FeSe . Te . , and hasuncovered a new spectroscopic feature associated withthe local chemical composition that leads to an inhomo-geneity in the appearance of the superconducting gap. ∗ Electronic address: [email protected] † Present address: Center for Hybrid Nanostructures(CHyN), Universit¨at Hamburg, Luruper Chaussee 149,22761, Hamburg, Germany[1] A. Tamai, A. Y. Ganin, E. Rozbicki, J. Bacsa,W. Meevasana, P. D. C. King, M. Caffio, R. Schaub,S. Margadonna, K. Prassides, et al., Physical Review Let-ters , 097002 (2010).[2] F. Massee, S. de Jong, Y. Huang, J. Kaas, E. vanHeumen, J. B. Goedkoop, and M. S. Golden, PhysicalReview B , 140507 (2009).[3] T. Hanaguri, S. Niitaka, K. Kuroki, and H. Takagi, Sci-ence , 474 (2010).[4] F. Massee, P. O. Sprau, Y.-L. Wang, J. C. S. Davis,G. Ghigo, G. D. Gu, and W.-K. Kwok, Science Advances , e1500033 (2015).[5] U. R. Singh, S. C. White, S. Schmaus, V. Tsurkan,A. Loidl, J. Deisenhofer, and P. Wahl, Science Advances , e1500206 (2015).[6] X. He, G. Li, J. Zhang, A. B. Karki, R. Jin, B. C. Sales,A. S. Sefat, M. A. McGuire, D. Mandrus, and E. W.Plummer, Physical Review B , 220502 (2011).[7] P. Zhang, K. Yaji, T. Hashimoto, Y. Ota, T. Kondo,K. Okazaki, Z. Wang, J. Wen, G. D. Gu, H. Ding, et al.,Science , 182 (2018).[8] D. Wang, L. Kong, P. Fan, H. Chen, S. Zhu, W. Liu,L. Cao, Y. Sun, S. Du, J. Schneeloch, et al., Science ,333 (2018).[9] V. Tsurkan, J. Deisenhofer, A. Gnther, C. Kant,M. Klemm, H.-A. Krug von Nidda, F. Schrettle, andA. Loidl, The European Physical Journal B , 289(2011).[10] S. C. White, U. R. Singh, and P. Wahl, Review of Scien-tific Instruments , 113708 (2011).[11] R. Aluru, H. Zhou, A. Essig, J.-P. Reid, V. Tsurkan,A. Loidl, J. Deisenhofer, and P. Wahl, Phys. Rev. Mate-rials , 084805 (2019).[12] T. Machida, Y. Sun, S. Pyon, S. Takeda, Y. Kohsaka,T. Hanaguri, T. Sasagawa, and T. Tamegai, Nat. Mater. , 811 (2019).[13] U. R. Singh, S. C. White, S. Schmaus, V. Tsurkan,A. Loidl, J. Deisenhofer, and P. Wahl, Physical ReviewB , 155124 (2013). [14] K. Okazaki, Y. Ito, Y. Ota, Y. Kotani, T. Shimo-jima, T. Kiss, S. Watanabe, C.-T. Chen, S. Niitaka,T. Hanaguri, et al., Scientific Reports , 04109 (2014).[15] S. Chi, R. Aluru, S. Grothe, A. Kreisel, U. R. Singh,B. M. Andersen, W. N. Hardy, R. Liang, D. A. Bonn,S. A. Burke, et al., Nature Communications , 15996(2017). [16] A. V. Chubukov, I. Eremin, and D. V. Efremov, PhysicalReview B , 174516 (2016).[17] O. Fischer, M. Kugler, I. Maggio-Aprile, C. Berthod, andC. Renner, Reviews of Modern Physics , 353 (2007).[18] D. Cho, K. M. Bastiaans, D. Chatzopoulos, G. D. Gu,and M. P. Allan, Nature571