Spectroscopic Evidence for an Additional Symmetry Breaking in the Nematic State of FeSe Superconductor

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Spectroscopic Evidence for an Additional Symmetry Breaking in the Nematic State of FeSe Superconductor

Cong Li et al.

Phys. Rev. X 10, 031033 – Published 12 August 2020

Abstract

The iron-based superconductor FeSe has attracted much recent attention because of its simple crystal structure, distinct electronic structure, and rich physics exhibited by itself and its derivatives. Determination of its intrinsic electronic structure is crucial to understanding its physical properties and superconductivity mechanism. Both theoretical and experimental studies so far have provided a picture that FeSe consists of one holelike Fermi surface around the Brillouin zone center in its nematic state. Here we report direct observation of two holelike Fermi surface sheets around the Brillouin zone center, and the splitting of the associated bands, in the nematic state of FeSe by taking high-resolution laser-based angle-resolved photoemission measurements. These results indicate that, in addition to nematic order and spin-orbit coupling, there is an additional order in FeSe that breaks either inversion or time-reversal symmetries. The new Fermi surface topology asks for reexamination of the existing theoretical and experimental understanding of FeSe and stimulates further efforts to identify the origin of the hidden order in its nematic state.

Received 13 February 2020
Revised 11 May 2020
Accepted 16 June 2020

DOI:https://doi.org/10.1103/PhysRevX.10.031033

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Electronic structure Fermi surface

Iron-based superconductors

Angle-resolved photoemission spectroscopy Laser techniques Photoelectron techniques Photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

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Popular Summary

The iron-based superconductor FeSe has a simple crystal structure and a rich electronic behavior that carries over to superconductors derived from it. To take full advantage of FeSe and better understand its physical properties and superconductivity mechanism, researchers need a clear picture of its electronic structure. To that end, we conduct experiments that take a deeper look at FeSe’s electronic structure and find greater complexity than was previously known.

To get a complete picture of a material’s electronic structure, researchers need information about its Fermi surface and band structure. The Fermi surface is a “surface” in momentum space that separates occupied electron states from unoccupied ones; the band structure describes the range of energy levels that electrons may occupy.

We use angle-resolved photoemission spectroscopy—a technique that uses light to liberate electrons, whose energy and momentum provide details about the electronic structure—to probe the Fermi surface and band structure of FeSe. Contrary to previous work, we find a two-hole-like Fermi surface sheet and a splitting of one band into two. We attribute these findings to some additional unknown “order”—or state of matter—in FeSe. It is already known that FeSe features nematicity, a state where the crystal structure differs little along perpendicular axes, while the electronic and physical properties differ a lot. Some have suggested that this nematicity is related to the superconductivity, but we find that it alone cannot explain the observed electronic structure.

We hope this work can stimulate further effort to identify the hidden order and provide new information in understanding the nematicity and superconductivity in FeSe.

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Vol. 10, Iss. 3 — July - September 2020

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Figure 1
Observation of two holelike Fermi surface sheets in single-domain FeSe. (a)–(c) Constant energy contours of the single-domain FeSe at 2.4 K under the $P A$ polarization (a), at 2.4 K under the $P B$ polarization (b), and at 11 K under a mixed polarization (c). The direction of the electric field vector $E$ corresponding to the three polarization geometries is marked by double arrows in the leftmost panels in (a)–(c). Blue and red ellipses in the leftmost panels are the guide lines of the observed Fermi surface. (d) Top view of FeSe crystal structure. The blue, red, and yellow circles represent Fe atom, Se atom above the Fe plane (Se top), and Se atom below the plane (Se bottom), respectively. The red dashed line represents the 1-Fe unit cell while the green solid line represents 2-Fe unit cell. We define the $x$ axis parallel to the $a_{Fe}$ axis and the $y$ axis parallel to the $b_{Fe}$ axis. In the normal state, FeSe has $C_{4}$ symmetry with $a_{Fe} = b_{Fe}$ , but it breaks into $C_{2}$ symmetry in the nematic state with $a_{Fe} > b_{Fe}$ . (e) The extracted Fermi surface of FeSe which consists of two holelike Fermi surface sheets around the BZ center. The dominant orbital character of the two Fermi surfaces is also marked.
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Figure 2
Fermi surface mapping of twinned FeSe. (a)–(c) The Fermi surface mappings of the single-domain FeSe measured under the $P A$ (a), the $P B$ (b), and a mixed (c) polarization geometries. (d)–(f) The Fermi surface mappings of the twinned FeSe measured under the LH (d), the LV (e), and a mixed (f) polarization geometries. The measurement temperatures are marked at the bottom left corner in (a)–(f). (g)–(i) Simulated Fermi surface from the single-domain data in (a)–(c). Under the $P A$ polarization geometry, (g) is obtained by summing up the signal of the vertical domain in (a) and that of the horizontal domain in (b) but rotated by 90°. Under the $P B$ polarization geometry, (h) is obtained by rotating the data in (g) by 90°. Under the mixed polarization geometry, (i) is obtained by the summation of signals from the vertical domain in (c) and from the horizontal domain also in (c) but rotated 90°. (j)–(l) Schematic of the observed Fermi surface in twinned FeSe from the horizontal domain (green lines) and the vertical domain (red lines) corresponding to data in (d)–(f). (m) Schematic drawing of the experimental geometry with LV and LH polarizations. $X$ , $Y$ , and $Z$ axes are defined as laboratory coordinates (LC). (n) Schematic drawing of two domains in nematic state in lab coordinates. The two domains are rotated 90° with each other. For domain $V$ , the $x$ ( $y$ ) axis is parallel to $X$ ( $Y$ ) axis in LC while for domain H, it is reversed. (o) Summary of the allowed orbitals under LV and LH polarization geometries defined for lab coordinates and each domain along the high-symmetry cuts. (p)–(q) The photoemission spectra (EDCs) on the Fermi surface of two domains. The location of the 4-momenta is marked in (e). For each EDC, the peak area is obtained after subtracting the background. The obtained area ratio between the P1 and $P 1^{'}$ points is 7.3 in (p) and between the P2 and $P 2^{'}$ points is 5.3 in (q). The ratio is used to estimate the orbital components of $d_{x z}$ and $d_{y z}$ for the measured momentum points.
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Figure 3
Band structure of single-domain FeSe along high-symmetry cuts and their orbital nature. (a)–(c) Band structure measured along the vertical momentum cut under $P A$ (a), $P B$ (b), and a mixed (c) polarization geometries. The location of the momentum cut is shown in the inset of (a). The left-hand panels of (a)–(c) represent the original data while the right-hand panels are corresponding second derivative images with respect to energy in order to enhance the contrast. Some observed bands are marked by the guide lines and arrows. (d)–(f) Same as (a)–(c) but for the horizontal momentum cut as marked in the inset of (d). (g),(h) Extracted band structure for the vertical momentum cut (g) and horizontal momentum cut (h) obtained from (a)–(c) and (d)–(f), respectively. The observed bands are labeled as three branches of $α$ , $β$ , and $γ$ . (i) Schematic of the band structure along the vertical (left-hand panel) and horizontal (right-hand panel) momentum cuts from $α$ (red lines), $β$ (green lines), and $γ$ (blue lines) orbitals. (j) Same as (i) but only considering the hybridization between different bands. (k) Same as (i) but only considering the splitting of each band. (l) Same as (i) but considering both band hybridization and splitting of each band. The red, green, and blue colors represent the $d_{x z}$ , $d_{y z}$ , and $d_{x y}$ orbitals, respectively.
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Figure 4
Calculated Fermi surface and band structure of FeSe and their comparison with the measured results. (a)–(c) The Fermi surface mappings of the single-domain FeSe measured under the $P A$ (a), the $P B$ (b), and a mixed (c) polarization geometries. The momentum cuts here are defined by the Fermi surface angle $θ$ . (d)–(f) Band structure for the momentum cuts at different Fermi surface angles $θ$ corresponding to (a)–(c). (g),(h) Calculated Fermi surface around $Γ$ point in considering the ferromagnetic order and the Rashba spin-orbit coupling in the nematic state of FeSe, respectively. Their corresponding band structures are shown in (i),(j). The $d_{x z}$ , $d_{y z}$ , and $d_{x y}$ orbital components are represented by red, green, and blue colors, respectively.
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