Lifted electron pocket and reversed orbital occupancy imbalance in FeSe
Soonsang Huh, Jeongjin Seo, Beomseo Kim, Soohyun Cho, Jongkeun Jung, Sunghun Kim, Yoonyoung Koh, Changil Kwon, Junsung Kim, Wonshik Kyung, J.D.Denlinger, Younghak Kim, Boknam Chae, Namdong Kim, Yeongkwan Kim, Changyoung Kim
LLifted electron pocket and reversed orbital occupancy im-balance in FeSe
S. S. Huh , , J. J. Seo , B. S. Kim , , S. H. Cho , , J. K. Jung , , S. Kim , Y. Y. Koh , C. I. Kwon , ,Jun Sung Kim , , W. S. Kyung , J. D. Denlinger , Y. H. Kim , B. N. Chae , N. D. Kim , Y. K.Kim , ∗ , C. Kim , , ∗ Department of Physics and Astronomy, Seoul National University (SNU), Seoul 08826, Republicof Korea Center for Correlated Electron Systems, Institute for Basic Science (IBS), Seoul 08826, Republicof Korea Institute of Physics and Applied Physics, Yonsei University, Seoul 03722, Korea Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141,Republic of Korea Department of Physics, Pohang University of Science and Technology, Pohang 37673, Republicof Korea Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science (IBS), Po-hang 37673, Republic of Korea Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Pohang Accelerator Laboratory, Pohang University of Science and Technology, Pohang 37673,Republic of Korea a r X i v : . [ c ond - m a t . s up r- c on ] M a r he FeSe nematic phase has been the focus of recent research on iron based supercon-ductors (IBSs) due to its unique properties. A number of electronic structure studies wereperformed to find the origin of the phase. However, such attempts came out with conflictingresults and caused additional controversies. Here, we report results from angle resolved pho-toemission and X-ray absorption spectroscopy studies on FeSe with detwinning by a piezostack. We have fully resolved band dispersions with orbital characters near the Brillouinzone corner which reveals absence of a Fermi pocket at the Y point in the 1Fe Brillouin zone.In addition, the occupation imbalance between d xz and d yz orbitals is found to be opposite tothat of iron pnictides, which is consistent with the identified band characters. These resultssettle down controversial issues in the FeSe nematic phase and shed light on the origin ofnematic phases in IBSs. Nematic phase is a state with a broken rotational symmetry but with an intact translationalsymmetry. It has attracted renewed attention with a notion that it may provide an important clueto the mystery of unconventional superconductivity . Its region almost coincides with that of thesuperconducting region in the phase diagram for both cuprates and iron based superconductors(IBS) , implying its possible connection to the superconductivity. Finding the origin of nematicphases thus has been considered to be one of the most important goals in the research on unconven-tional superconductivity, especially for IBSs where studies on nematic phases were first initiated.Recently, the nematic phase in FeSe has attracted attention due to its distinct propertiesfrom those of pnictide nematic phases. The most peculiar aspect is the absence of long range2agnetic order which always coexists with orbital order in pnictide nematic phases
4, 5 . Further-more, it was revealed that resistivity anisotropy for FeSe has the opposite sign compared to thatof iron pnictides ; resistivity along the longer a -axis is smaller than that along the shorter b -axisfor iron pnictides while it is the other way around for FeSe. These two observations promptedthe conjecture that the nematic phase in FeSe may be different from that of iron pnictides. There-fore, understanding the FeSe nematic phase may provide insight on universal understanding of thenematic phase in IBS. More importantly, considering the recent discovery of orbital selective cor-relation and superconductivity in FeSe in STM studies
7, 8 , superconductivity mechanism could beaddressed by understanding the origin of the nematic phase because the nematic phase is widelybelieved to induce orbital selectivity.In this regard, a number of angle resolved photoemission spectroscopy (ARPES) experimentshave been performed to investigate the electronic structure of FeSe . However, interpretationsfrom different experiments vary and caused more controversies on the origin of the nematic phasein FeSe. Various conflicting scenarios were proposed as the origin of the nematic phase basedon ARPES results such as simple ferro-orbital ordering , d-wave orbital order , unidirectionalnematic bond order and reversal sign ordering . Probable cause of such controversies is thelack of full and accurate electronic structure information which may be obtained only from fullydetwinned single crystals. Therefore, the issue may be resolved only with full electronic structureinformation. Only then, the origin of the nematic phase in FeSe may be addressed.Here, we present results of electronic structure studies by AREPS and X-ray linear dichro-3sm (XLD) on fully detwinned FeSe in its nematic phase. Full detwinning was obtained by usinga piezo stack based strain device, the first attempt to use such device in ARPES and XLD exper-iments (See Figs. 1A and 1B). Difficulty in using mechanical strain methods such as uncertaintyof strain direction from ’accident detwin’ by anisotropic shrink of epoxy has been overcome byusing piezo bias on/off which provides strain on/off. As a result, we could investigate detailed banddispersions with full orbital characters (with ARPES) as well as the orbital occupancy imbalancebetween d xz and d yz orbitals (by XLD). Our ARPES results show that there are orbital dependentband shift and hybridization that lead to only one Fermi surface pocket in 1Fe BZ scheme, whichmay explain why there is no long-range magnetism. Furthermore, XLD reveals an unexpectedreversed occupation imbalance between d xz and d yz orbital ( n xz < n yz ) which naturally explainsthe opposite resistivity anisotropy. These results resolve controversial issues on the nematic phaseof FeSe and may shed light on the driving instability of nematic phases in IBS. ResultsElectronic structures of twinned and detwinned FeSe.
The key issue in the study of the FeSeelectronic structure is if, in addition to an elliptical pocket, there is another large pocket whichmainly consists of the d xy orbital around the Brillouin zone (BZ) corner. Therefore, we first focuson the overall Fermi surface topology. Fermi surface maps from twin and single domains (Figure1c) indeed show clear differences, and may provide answers to the issue. For the twin domaincase (left), two perpendicularly crossing elliptical pockets are observed at zone corner X/Y points.However, Fermi surfaces from a single domain sample (right) consists only of a single elliptical4ocket at each zone corner. Note that, if there is a large pocket of d xy orbital character, it shouldbe visible in our data as the experimental geometry allows the transition from the d xy initial state.Based on this experimental observation as well as the full band dispersion characterization alongwith its temperature dependence (discussed below), we conclude that there is only one ellipticalpocket at zone corners as illustrated in Figure 1d. It immediately implies that, one of two pocketsin the normal state should disappear across the nematic phase transition. That is, the pocket at theY point in 1Fe BZ scheme shown in Figure 1e should disappear while the pocket at the X pointremains. Dispersions and orbital characters of bands.
To proceed with the discussion on how and why thepocket at the Y point in 1Fe BZ disappears, band dispersions as well as orbital characters shouldbe fully identified first. Figures 2a and 2b show overall band dispersions along the Γ -X and Γ -Ydirections from a single domain sample in the normal and nematic states. Starting from isotropicnormal state band dispersions, highly anisotropic band dispersions develop in the nematic phase.Especially, the band dispersions around the zone corner are dramatically renormalized and becomethose of two merged Dirac cones (possibly with small gaps at band crossing points) (see Figure 2b).The Γ -X ( k x -direction) data shows a sizable electron band and two split hole bands, while a tinyelectron band near E F and two closely located hole bands at a higher binding energy are seen in thecut along the Γ -Y ( k y -direction). These observed dispersions are consistent with previous results . In order to understand the band structure more concretely, polarization dependent experiment isrequired to provide exact orbital characterization. The results of orbital characterization of bands5re shown in Figures. 2c-2j. In particular, orbital characters of bands near the zone corner arenewly interpreted. Along the k x -direction, the large electron band consists mainly of d xy orbitalwhile the two upper and lower hole bands have d yz and d xy characters. Along the ( k y -direction,the tiny electron band consists d yz orbital and hole bands have d xz and d xy characters (see Figures2e and 2i). As for the zone center, the polarization dependence yields orbital characters of the holebands that are consistent with previous results (See Figures 2f and 2j) .The resulting full orbital characters of the bands are schematically summarized in Figures 2kand 2l. The result reveals two unique features of the FeSe electronic structure in the nematic phase.First of all, there is a reversal behavior in the relative energy positions of d xz and d yz hole bands.The d xz hole band at Y point is located below the d yz hole band at the X point (zone corners) whilethe d xz hole band is placed above the d yz band at the zone center. The other and more importantfeature is the reduced number of electron bands at X and Y points. In the normal state, there aretwo electron bands at both X and Y points - the common d xy electron band and d xz ( d yz ) electronband for the X (Y) point. On the other hand, only one electron band exists at each point in thenematic phase: d xy ( d yz ) at the X (Y) point. Other two electron bands - d xz and d xy at X and Ypoints, respectively - are not observed in any experimental geometry, i.e. polarization. Therefore,it is reasonable to speculate that those two bands do not exist below E F , and that they should bepushed above E F across the nematic phase transition. Temperature evolution of electronic structure.
The temperature evolution of electronic structure6cross the nematic phase transition clearly shows that what we speculated is indeed the case. Fig-ure 3a shows temperature dependence of band dispersion along k x -direction at the Y point, withoverlaid momentum distribution curves taken at 5meV above E F . In the normal state, d xz electronband crosses E F and peak positions in the curve have finite momentum values (indicated with redarrows). As the temperature decreases, peak positions for the d xz electron band shift towards theY point. This indicates that the d xz electron band shifts upward and is finally pushed above E F .Meanwhile, the d yz ( d xz ) hole band around the X (Y) point shifts upward (downward) as the tem-perature decreases, as seen in temperature dependent spectra at X and Y points (Figures. 3b and3c). The splitting at a low temperature is about 60 meV and remains finite above the nematic phasetransition temperature, possibly due to the applied strain (Figure 3c). It is noteworthy that the twohole bands do not cross E F and remain under E F after the shift.Now we are ready to discuss how the electron pocket at Y disappears in 1Fe BZ, that is, howthe number of electron bands is reduced across the nematic phase transition. We argue that theobserved electronic structure evolution can be explained within the picture of orbital dependentband shift (or splitting) and hybridization. Let us look at the case for the zone corner in 1Fe BZscheme. Starting from symmetric bands in the normal state (Figure 3d left), the d yz ( d xz ) bandshifts upward (downward) as the temperature goes down below T S (Figure 3d middle), which wecall nematic band shift. Then, the orbital dependent hybridization comes in. For the d yz band case,there is only weak mixing with d xy and thus the overall dispersion remains intact. The d xz band,on the other hand, strongly hybridizes with d xy band, pushing the hole band down below E F whilelifting both d xz and d xy electron bands above E F (Figure 3d right). This, results in vanishing7lectron pocket at Y in the 1Fe BZ scheme. Reversed orbital occupancy imbalance.
A surprising implication of the above interpretation isthat d xz orbital should be less occupied than d yz , opposite to the iron pnictide case and also to theprediction of ferro-orbital order scenario . At the zone center, the energy position of the d xz bandis higher than that of d yz , and thus d xz state is less occupied. Disappearance of the d xz electronband at the zone corner also leads to less occupied d xz orbital ( d xz and d yz hole bands at the zonecorner are irrelevant as both of them are fully occupied). In order to obtain direct informationon such anomalous orbital occupancy, we performed XLD measurements on detwinned samples.XLD measurement, a local probe for orbital selective density of states, can provide direct proof ofthe imbalance in the orbital occupancy
14, 16 .Figure 4a shows the experimental geometry with two light polarizations, parallel and perpen-dicular to the strain direction. Fe L -edge absorption spectra from detwinned FeSe taken with thetwo light polarizations at 10 K are plotted in Figure 4b. With the given experimental geometry, thelinear dichroism or XLD shown with the black solid line in Figure 4b should reflect the imbalancein d xz and d yz orbital occupancy. A complication is that not only the orbital occupation imbal-ance but also the orthorhombic structural distortion is known to contribute to the XLD signal .It was previously shown that the two contributions can be separated by considering their distinctbehaviors in the temperature dependence . A close inspection of the temperature dependent XLDdata in Figure 4c reveals that XLD signal starts to appear below T S and monotonically increases8s the temperature decreases down to 10 K. Such monotonic increase of XLD can be more clearlyvisualized by plotting the integrated XLD (see the figure caption for the definition) as a functionof temperature (Figure 4d). If the XLD contains only the structure contribution, it should imme-diately saturate below T S as the structure contribution should follow the orthorhombicity of thecrystal (see the overlaid diffraction data) . Therefore, the non saturating increase far below T S indicates that XLD does contain contribution from orbital imbalance. An important point to noteis that the orbital contribution is positive. Positive XLD from orbital means that d xz orbital is lessoccupied ( n xz < n yz ), contrary to the case of simple ferro-orbital order scenario and to the ironpnictide case ( n xz > n yz ) (Figure 4e). Discussion
As our interpretation of the electronic structure evolution across the nematic phase transitionin FeSe is confirmed by observation of the reversed orbital occupancy imbalance, its implicationmay be discussed. First of all, the sign reversal in the hole band splitting and the reduced number ofelectron bands in our interpretation do not support the unidirectional nematic bond order scenariowhich requires absence of hole band splitting . On the other hand, d-wave form splitting andsign reversal order scenario are partially consistent with our result when the hole band splittingis considered. From these results, we learn that the evolution of electron band dispersions as wellas the role of the d xy band are taken into account to obtain a fully consistent picture, that is to say,full understanding of the nematic phase. 9ith the concrete understanding of the electronic structure, the unique properties of FeSe ne-matic phase - absence of magnetism and opposite resistivity anisotropy - can also be understood.The absence of the magnetism can be explained for both weak and strong coupling pictures. Inthe weak coupling picture, a weak Fermi surface nesting condition stemming from opposite or-bital characters of Fermi surface pockets could explain the absence of magnetism; the inter-orbitalnesting between Fermi surfaces at the zone center (mostly d xz with small contribution from d yz )and corner (mostly d yz ), which is considered to be the source of the magnetism in the weak cou-pling picture, is mostly suppressed due to the opposite orbital characters. In the strong couplingpicture, the absence of the magnetism could be explained within an orbital weight redistributionscheme
18, 19 . A strong hybridization between d xy and d xz tends to open a gap near the E F , resultingin suppression of the d xy and d xz orbital weight. Since the magnetic moment dominantly comesfrom the d xy orbital
20, 21 , the reduced d xy orbital weight should weaken the magnetic instability.Meanwhile, the opposite resistivity anisotropy can be easily explained within the observed reversedorbital occupancy imbalance if we simply follow the argument that orbital occupation imbalancecharacterizes the resistivity anisotropy
22, 23 .Another important implication of our work is that it provides a new perspective on the originof the nematic phase. It has been believed that the nematic band shift and the occupancy imbalancebetween d xz and d yz orbitals are equivalent. Therefore, they represent a single phenomenon of theferro-orbital order stemming from symmetry breaking at the atomic level. Our observation ofthe reversed orbital occupancy imbalance, an occupancy imbalance opposite to the nematic bandshift, clearly shows that they are not equivalent. Furthermore, their opposite behaviors strongly10uggest that the nematic band shift is neither a manifestation of nor generated by the developmentof occupancy imbalance. The occupancy imbalance should rather be a by-product of the nematicband shift as well as the role of d xy orbital discussed above. In short, our results indicate thatthe ferro-orbital order is unlikely the driving instability of the nematic phase in IBSs. Instead, theinstability responsible for the system independent nematic band shift should be the true driver ofthe nematic phase. It could be an instability with a spin origin or still an orbital origin but in adifferent form. In any case, our findings provide crucial information on the nematic phase originissue by eliminating the ferro-orbital order from the candidate list. It should further shed light onthe origin of the nematic phase in IBSs. MethodsExperiments
XAS experiments were performed at the beam line 2A of the Pohang Light Source and spectrawere recorded in the TEY mode. All spectra were normalized by the incident photon flux intensitymeasured from a gold mesh and calibrated with respect to L absorption peak of Fe O alloylocated in front of the analysis chamber. ARPES measurements were carried out at the Beamline4.0.3 of the Advanced Light Source. Linearly polarized light with the photon energy of 56 eVwas used. All crystals were cleaved in situ in a pressure better than 9 × − Torr for XAS and4 × − Torr for ARPES experiments. Samples were detwinned using uniaxial strain which isapplied along the tetragonal [110] direction. The best quality data used in the figures were obtainedfrom accidentally detwinned domain. 11 eferences
1. Fernandes, R. M., Chubukov, A. V. & Schmalian, J. What drives nematic order in iron-basedsuperconductors?
Nat. Phys. , 97-104 (2014).2. Daou, R. et al . Broken rotational symmetry in the pseudogap phase of a high T c superconductor. Nature , 519-522 (2010).3. Kasahara, S. et al . Electronic nematicity above the structural and superconducting transition inBaFe (As − x P x ) . Nature , 382-385 (2012).4. Medvedev, S. et al . Electronic and magnetic phase diagram of β Fe . with superconductivityat 36.7 K under pressure. Nat. Mater , 630-663 (2009).5. Baek, S. H. et al . Orbital-driven nematicity in FeSe. Nat. Mater , 210-214 (2015).6. Tanatar, M. A. et al . Origin of the Resistivity Anisotropy in the Nematic Phase of FeSe. Phys.Rev. Lett. , 127001 (2016).7. Sprau, P. O. et al . Discovery of orbital-selective Cooper pairing in FeSe.
Science , 75-80(2017).8. Kostin, A. et al . Imaging orbital-selective quasiparticles in the Hunds metal state of FeSe.
Nat.Mater , 896-874 (2018). 12. Shimojima, T. et al . Lifting of xz / yz orbital degeneracy at the structural transition in detwinnedFeSe. Phys. Rev. B. , 121111 (2014).10. Zhang, P. et al . Observation of two distinct d xz / d yz band splittings in FeSe. Phys. Rev. B. ,214503 (2016).11. Watson, M. D. et al . Evidence for unidirectional nematic bond ordering in FeSe. Phys. Rev. B. , 201107 (2016).12. Suzuki, Y. et al . Momentum-dependent sign inversion of orbital order in superconductingFeSe. Phys. Rev. B. , 205117 (2015).13. Watson, M. D. et al . Electronic anisotropies revealed by detwinned angle-resolved photoemis-sion spectroscopy measurements of FeSe. New J. Phys. , 103021 (2017).14. Kim, Y. K. et al . Existence of orbital order and its fluctuation in superconductingBa(Fe − x Co x ) As single crystals revealed by x-ray absorption spectroscopy. Phys. Rev. Lett. , 217001 (2013).15. Lee, C. -C., Yin, W. -G. & Ku, W. Ferro-Orbital Order and Strong Magnetic Anisotropy in theParent Compounds of Iron-Pnictide Superconductors.
Phys. Rev. Lett. , 267001 (2009).16. Chen, C.-C. et al .Orbital order and spontaneous orthorhombicity in iron pnictides.
Phys. Rev.B. , 100504 (2010).17. Margadonna, S. et al . Crystal structure of the new FeSe − x superconductor. Chem. Commun. , 5607-5609 (2008). 138. Mazin, I. I., Singh, D. J., Johannes, M. D. & Du, M. H. Unconventional superconductivitywith a sign reversal in the order parameter of LaFeAsO − x F x . Phys. Rev. Lett. , 057003(2008).19. Dong, J. et al . Competing orders and spin-density-wave instability in La(O − x F x )FeAs. Euro.Phys. Lett. , 27006 (2008).20. Yin, Z. P. & Pickett, W. E. et al .Crystal symmetry and magnetic order in iron pnictides: Atight-binding Wannier function analysis. Phys. Rev. B. , 174534 (2010).21. Oh, H., Moon, J., Shin, D., Moon, C.-Y. & Choi, H. J. Prog. Brief review on iron-basedsuperconductors: are there clues for unconventional superconductivity? Prog. Supercond. ,65-84 (2011).22. LV, W. & Phillips, P. et al . Orbitally and magnetically induced anisotropy in iron-based super-conductors. Phys. Rev. B. , 174512 (2011).23. Liang, S., Alvarez, G., en, C., Moreo, A. & Dagotto, E. et al . Anisotropy of Electrical Trans-port in Pnictide Superconductors Studied Using Monte Carlo Simulations of the Spin-FermionModel. Phys. Rev. Lett. , 047001 (2012).
Acknowledgements
This work was supported by the Institute for Basic Science in Korea (Grant No.IBS-R009-G2). The work at Pohang University of Science and Technology (POSTECH) was supported byIBS (no. IBS-R014-D1) and the NRF through the SRC (No. 2018R1A5A6075964) and the Max Planck-POSTECH Center (No. 2016K1A4A4A01922028). The Advanced Light Source is supported by the Officeof Basic Energy Sciences of the US DOE under Contract No. DE-AC02-05CH11231. uthor Contributions C.I.K. and J.S.K. grew the crystals; S.S.H., J.J.S., B.S.K., S.H.C., J.K.J., and S.K.performed ARPES measurements with the support from J.D.D. and W.S.K.; S.S.H., J.J.S., B.S.K., Y.Y.K.,performed XAS measurements with the support from Y.H.K.; S.S.H. analyzed the ARPES and XAS data;S.S.H., Y.K.K. and C.K. wrote the paper; Y.K.K. and C.K. are responsible for project direction and planning.
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Competing financial interests
The authors declare no competing financial interests. b Twin
100 μm 100 μm
Detwina P i e z o S t r a i n S a m p l e Twin Detwin
XX/YX/Y
Г (Z) Y -1.0 -0.5 0.0 0.5 1.0-1.0-0.50.00.51.0 d Y Г X T>T S Г YX e M o m en t u m ( Å - ) Momentum (Å -1 ) T Electronic structures of pristine and surface electron doped FeSe. ( a ) Schematicdrawing of the piezo sample holder for strain experiments. ( b ) Optical images of twinned anddetwinned FeSe single crystal, taken with a polarized microscope. Both images were taken at atemperature below T S . ( c ) Corresponding Fermi surface maps. X and Y points are defined by thestrain direction of the piezo. Schematic Fermi surface maps in the ( d ) 2Fe BZ and ( e ) 1Fe BZ.16 < T S Y X -1.2 -0.8 -0.4 0.0 0.4 0.8 1.2Y X -0.20-0.100.00 T > T S k (Å -1 ) E - E F ( e V ) a b -1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 k (Å -1 ) c e -0.15-0.10-0.050.000.05 1.41.21.0 -0.20.00.2 X d d xy d yz d xz Y X Г strain d xy d yz d xz E - E F ( e V ) k y ( Å - ) k x (Å -1 ) k x (Å -1 ) k y (Å -1 )h i f X - Z - X -0.15-0.10-0.050.000.05 0.2-0.2 k x (Å -1 ) Y -0.20.00.2 1.41.21.0 -0.15-0.10-0.050.000.05 1.41.21.0 0.2-0.2 g YX Г s t r a i n j Y - Z - Y -0.15-0.10-0.050.000.05 0.2-0.2 k y (Å -1 )k y (Å -1 ) k x ( Å - ) E - E F ( e V ) k y (Å -1 ) k x (Å -1 ) k Y X Г Y X Г l Г (Z) XY T > T S Г (Z) XY E F T < T S E F Figure 2: Dispersions and orbital characters of bands via polarization dependent ARPES. ( a )-( b ) 3D Schematic band dispersions and high symmetry cuts along the Y-Z-X direction aboveand below T S . All the data were taken with s -polarized 56 eV light. ( c ) Schematic Fermi surfaceswith orbital characters in the nematic state in the 2Fe BZ scheme. ( d ) Fermi surface map aroundthe X point. ( e ) High symmetry cuts along the k x - and k y -directions near the X point. The cutdirections are shown in ( d ). The overlaid dashed lines are band dispersions with color coded orbitalcharacters. ( f ) High symmetry cut along the X-Z-X direction near the zone center. ( g )-( j ) Similarmeasurements but with the sample rotated by 90 degree (light polarization along a -direction).Fermi surface map and high symmetry cuts are now shown for the Y point. ( k )-( l ) SchematicFermi surfaces and band dispersions with orbital characters along the Y-Z-X direction above andbelow T S . 17 S pe c t r a l I n t en s i t y ( a . u . ) -0.08-0.06-0.04-0.020.00 1006020 Temperature (K) d xz d yz yz 30 K50 K70 K80 K90 K100 K120 K130 K-0.1 E-E F (eV)X -0.1 0.0d xz 30 K50 K70 K80 K90 K100 K120 K130 K Y E F normal state nematic band shift hybridization with d xy b cd d xy d yz d xz k x (Å -1 ) -0.15-0.10-0.050.000.05 140 K E - E F ( e V ) a -0.2 0.0 0.2 -0.2 0.0 0.2 -0.2 0.0 0.2 -0.2 0.0 0.2 -0.2 0.0 0.2 120 K 100 K 80 K 50 K 30 K E-E F (eV) E - E F ( e V ) X k x k y Y k x k y X k x k y Y k x k y X k x k y Y k x k y d xy d xz T s Figure 3: Temperature evolution of the electronic structure. ( a ) Temperature dependent ARPESdata along the k x -direction near the Y point. Momentum distribution curves (MDCs) at 5 meVabove E F are also shown at the top of the figure. Underlying d xy and d xz contributions are shownin blue and red curves, respectively. Peak positions of the d xz band are indicated by red arrows.( b ) Temperature dependent energy distribution curves (EDCs) at X and Y points, showing upward(downward) shift of the d yz ( d xz ) band upon cooling. ( c ) The peak position of the d xz (red square)and d yz (green square) band as a function of temperature. ( d ) Schematic illustration of the bandreconstruction at the zone corner across the nematic phase transition.18 XAS ( a . u . ) Energy (eV) 10 K E || b E || a XLD x 10 Fe L -edges 700 ab h v Temperature (K) X L D a r ea ( a . u . ) o r t ho r ho m b i c i t y x T S [Ref. 17] S a m p l e S t r a i n P i e z o S a m p l e c Energy (eV) X L D ( a . u . ) 10 K 30 K 40 K 90 K 60 K BaFe As n xz > n yz FeSe [Ref. 14] n xz < n yz b de X L D ( a . u . ) Energy (eV) Figure 4: Observation of orbital occupancy by XLD. ( a ) Schematic illustration of the experi-mental geometry. Beam is incident normal to the sample surface. a - and b -axis are determinedby the strain direction of the piezo. ( b ) Fe L edge absorption spectra from detwinned FeSe takenat 10 K with E (cid:107) a (blue, inverted triangle) and E (cid:107) b (red, triangle) polarizations. The XLD (blackcurve) is the difference (E (cid:107) a - E (cid:107) b). XLD spectrum is multiplied by 10 for a better view. ( c ) XLDspectra at various temperatures. Overlaid black solid lines are fitting results with two Gaussianfunctions. ( d ) Temperature dependence of XLD area (left, blue circle) and orthorhombicity (right,red square). XLD area is calculated by integrating the absolute value of the fit curves in Figure4 ( c ). The error bars are obtained from the standard fitting error. The orthorhombicity of FeSe isfrom diffraction measurement result . ( e ) XLD spectrum of FeSe (blue) at 10 K and BaFe As (red,14