Distinctive orbital anisotropy observed in the nematic state of a FeSe thin film

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Distinctive orbital anisotropy observed in the nematic state of a FeSe thin film

Y. Zhang, M. Yi, Z.-K. Liu, W. Li, J. J. Lee, R. G. Moore, M. Hashimoto, M. Nakajima, H. Eisaki, S.-K. Mo, Z. Hussain, T. P. Devereaux, Z.-X. Shen, and D. H. Lu

Phys. Rev. B 94, 115153 – Published 26 September 2016

Abstract

The nematic state, where a system is translationally invariant but breaks rotational symmetry, has drawn great attention recently due to the experimental observations of such a state in both cuprates and iron-based superconductors. The origin of nematicity and its possible tie to the pairing mechanism of high- $T_{c}$ , however, still remain controversial. Here, we study the electronic structure of a multilayer FeSe film using angle-resolved photoemission spectroscopy. The band reconstruction in the nematic state is clearly delineated. We find that the energy splitting between $d_{x z}$ and $d_{y z}$ bands shows a nonmonotonic distribution in momentum space. From the Brillouin zone center to the Brillouin zone corner, the magnitude of splitting first decreases, then increases, and finally reaches the maximum value of $\sim 70$ meV. Moreover, besides the $d_{x z}$ and $d_{y z}$ bands, band splitting was also observed on the $d_{x y}$ bands with a comparable energy scale around 45 meV. Our results suggest that the electronic anisotropy in the nematic state cannot be explained by a simple on-site ferro-orbital order. Instead, strong anisotropy exists in the hopping of all $d_{x z}, d_{y z}$ , and $d_{x y}$ orbitals, the origin of which holds the key to a microscopic understanding of the nematicity in iron-based superconductors.

Received 24 December 2015
Revised 5 September 2016

DOI:https://doi.org/10.1103/PhysRevB.94.115153

Physics Subject Headings (PhySH)

Nematic order

Chalcogenides Thin films

Angle-resolved photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Y. Zhang^1,2, M. Yi^1,3, Z.-K. Liu^1,3, W. Li¹, J. J. Lee^1,3, R. G. Moore¹, M. Hashimoto⁴, M. Nakajima^5,6, H. Eisaki^5,6, S.-K. Mo², Z. Hussain², T. P. Devereaux^1,3, Z.-X. Shen^1,3,*, and D. H. Lu^4,†

¹Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
²Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
³Geballe Laboratory for Advanced Materials, Department of Physics and Department of Applied Physics, Stanford University, Stanford, California 94305, USA
⁴Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
⁵National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japan
⁶JST, Transformative Research-Project on Iron Pnictides, Tokyo, 102-0075, Japan

^*zxshen@stanford.edu
^†dhlu@slac.stanford.edu

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Vol. 94, Iss. 11 — 15 September 2016

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Images

Figure 1
Absence of magnetic order in the FeSe thin film. (a) The Fermi surface mapping taken at 70 and 20 K in NaFeAs. The Brillouin zone (BZ) boundary in the magnetic state is shown by the green solid line. The structural transition temperature and magnetic transition temperature are abbreviated as $T_{s}$ and $T_{N}$ , respectively. (b) The second derivative photoemission intensity distribution taken along the $Γ − M$ direction. The main (solid line) and folded (dashed line) bands are illustrated in the top panels. (c) and (d) The corresponding data taken on a 35-ML FeSe film at 160 and 20 K, respectively. The data were taken with 38 eV photons with $k_{z}$ near the $Γ$ point. The nematic transition temperature is abbreviated as $T_{nem}$ .
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Figure 2
Nontrivial momentum dependence of the band reconstruction. (a) The second derivative photoemission intensity distribution taken on a 35-ML FeSe film along the $Γ − M$ direction at 140 K. (b) The same as (a), but taken at 70 K. The red dashed lines show the high-temperature band dispersion extracted from (a). The data were taken with 25 eV photons. The hole bands show moderate $k_{z}$ dispersion and cross $E_{F}$ when the 25 eV photon energy selects $k_{z}$ between $Γ$ and Z. (c) The temperature dependence of the energy distribution curves (EDCs) taken at five different momenta after the division of Fermi-Dirac function. The peak positions are determined via a combination of the spectral weight maximum and second-derivative-curve minimum. The top red and blue bars illustrate the energy scale of the band shift. We note that there is constant finite-energy splitting between the inner and outer hole bands at $Γ$ above $T_{nem}$ , which could be due to spin-orbit coupling. (d) The temperature dependence of the band positions extracted from the data in (c).
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Figure 3
Momentum dependence of the band splitting along the $Γ − M$ direction in the nematic state. (a) Momentum dependence of the band splitting between $d_{x z}$ and $d_{y z}$ bands along the $Γ − M$ direction. The shaded area is illustrated to guide the eye. (b) Illustration of the $d_{x z}$ and $d_{y z}$ band splitting in the nematic state considering the on-site occupation difference between $d_{x z}$ and $d_{y z}$ bands. (c) Illustration of the $d_{x z}$ and $d_{y z}$ band splitting in the nematic state considering the band shift reversion from $Γ$ to $M$ .
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Figure 4
Band structure reconstruction near the $M$ point in the nematic state. (a) Temperature dependence of the Fermi surface mapping near the $M$ point. (b) Temperature dependence of the second derivative of photoemission intensity distribution taken along the $Γ − M$ direction. The cut direction is shown by the cyan solid line in (a). The solid lines mark the energy positions of either the band tops of holelike bands or bottoms of electronlike bands. The dashed lines are a guide to the eyes for the band dispersion and Fermi surface. (c) Schematic of the band shift and hybridization of the $d_{x z}$ and $d_{x y}$ bands near the $M_{Y}$ point. (d) Schematic of the band shift of the $d_{y z}$ and $d_{x y}$ bands near the $M_{X}$ point. The data were taken with 38 eV photons.
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Figure 5
Schematics of band reconstruction near the $M$ point through the nematic transition. Illustration of (a) the reconstruction of the Fermi surface and (b) and (c) band structure around the $M$ point in a one-Fe BZ. For simplicity, we neglect the hole bands and associated hole pockets near the $Γ$ point. The bands are stretched in three-dimensional plots for a better view of the band reconstruction. (d) Illustration of the low-temperature electronic structure in two-Fe BZ by folding the corresponding bands between $M_{X}$ and $M_{Y}$ (left panel) and in the twinned sample by overlapping the bands in two perpendicular domains (right panel). (e) Temperature dependence of the energy splitting extracted from the band tops and bottoms at the $M$ point.
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