Nematic Energy Scale and the Missing Electron Pocket in FeSe

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Nematic Energy Scale and the Missing Electron Pocket in FeSe

M. Yi, H. Pfau, Y. Zhang, Y. He, H. Wu, T. Chen, Z. R. Ye, M. Hashimoto, R. Yu, Q. Si, D.-H. Lee, Pengcheng Dai, Z.-X. Shen, D. H. Lu, and R. J. Birgeneau

Phys. Rev. X 9, 041049 – Published 6 December 2019

Abstract

Superconductivity emerges in proximity to a nematic phase in most iron-based superconductors. It is therefore important to understand the impact of nematicity on the electronic structure. Orbital assignment and tracking across the nematic phase transition prove to be challenging due to the multiband nature of iron-based superconductors and twinning effects. Here, we report a detailed study of the electronic structure of fully detwinned FeSe across the nematic phase transition using angle-resolved photoemission spectroscopy. We clearly observe a nematicity-driven band reconstruction involving $d_{x z}$ , $d_{y z}$ , and $d_{x y}$ orbitals. The nematic energy scale between $d_{x z}$ and $d_{y z}$ bands reaches a maximum of 50 meV at the Brillouin zone corner. We are also able to track the $d_{x z}$ electron pocket across the nematic transition and explain its absence in the nematic state. Our comprehensive data of the electronic structure provide an accurate basis for theoretical models of the superconducting pairing in FeSe.

Received 12 March 2019
Revised 21 September 2019

DOI:https://doi.org/10.1103/PhysRevX.9.041049

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)

Nematic order Superconductivity

Iron-based superconductors

Angle-resolved photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

M. Yi ^1,2,*, H. Pfau^3,4,5, Y. Zhang^6,7, Y. He^4,2, H. Wu¹, T. Chen¹, Z. R. Ye⁶, M. Hashimoto⁸, R. Yu⁹, Q. Si¹, D.-H. Lee^2,10, Pengcheng Dai¹, Z.-X. Shen^4,5, D. H. Lu^8,†, and R. J. Birgeneau^2,10,11,‡

¹Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
²Department of Physics, University of California Berkeley, Berkeley, California 94720, USA
³Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, Berkeley, California 94720, USA
⁴Stanford Institute of Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
⁵Departments of Physics and Applied Physics, and Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA
⁶International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
⁷Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
⁸Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
⁹Department of Physics, Renmin University of China, Beijing 100872, China
¹⁰Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
¹¹Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA

^*mingyi@rice.edu
^†dhlu@slac.stanford.edu
^‡robertjb@berkeley.edu

Popular Summary

Nematicity, originating from the Greek word for thread, is the breaking of fourfold rotational symmetry. In the family of iron-based superconductors, the orthogonal directions of a crystal become inequivalent in the nematic phase, which is also manifested in electronic states that become quite different along the two directions. Many materials become nematic in a regime close to superconductivity, suggesting that understanding how electronic states transform in the nematic phase may lead to important clues about the fundamental mechanism of superconductivity. Here, we provide a detailed high-resolution measurement of the changes in the electronic states as nematicity develops in FeSe, the structurally simplest member of the iron-based superconductors.

To carry out this study, one technical difficulty must be overcome. As nematicity develops, different regions in the crystal break the fourfold rotational symmetry along different directions, forming structural domains that are rotated 90° with respect to each other. When experimental probes average over these domains, the difference along the orthogonal directions washes out, preventing the investigation of nematic properties of a single domain. To overcome this difficulty, we use a strain technique that aligns all the structural domains, hence enabling measurement pertaining to the intrinsic electronic structure in the nematic phase of FeSe. The resulting measurement via electron spectroscopy allows for clear identification of the energy scales of the nematic order and the detailed reconstructed low-energy electronic states in the nematic phase.

Our work provides a precise experimental basis for constructing microscopic theoretical models to understand the superconducting pairing in the iron-based superconductors, particularly regarding the role of the preceding electronic nematicity.

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Vol. 9, Iss. 4 — October - December 2019

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Figure 1
Effectiveness of detwinning by uniaxial strain. (a) The mechanical uniaxial strain setup consists of a clamp that presses a single crystal of ${BaFe}_{2} {As}_{2}$ , which transfers the strain to the FeSe single crystal glued on top. Both the ${BaFe}_{2} {As}_{2}$ and FeSe are oriented such that the $Fe ─ Fe$ bond is aligned to the direction of strain. When cooled below $T_{S}$ , the shorter (longer) $Fe ─ Fe$ bond is along (perpendicular to) the strain direction, defining the $Γ - M_{Y}$ ( $Γ - M_{X}$ ) momentum direction. (b) ARPES spectra taken along the $Γ - M$ direction on a twinned FeSe. (c),(d) ARPES spectra taken on detwinned FeSe along the $Γ - M_{X}$ and $Γ - M_{Y}$ directions, respectively. (e),(f) EDCs taken at the momentum pointed to by arrows in (b)–(d). All measurements are taken with 70 eV photons under odd polarization with respect to the cut direction.
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Figure 2
Measured dispersions on detwinned FeSe at 56 eV (close to $k_{z} = π$ ). (a) ARPES spectra measured along $Γ - M_{X}$ with odd polarization. (b),(c) Second energy derivatives of measured spectra along $Γ - M_{X}$ under odd and even polarization with respect to the cut direction, respectively. A schematic of bands of orbital symmetries with the allowed intensity under each polarization is overlaid. (d) The complete band schematic from both polarizations is summarized for $Γ - M_{X}$ . (e)–(h) A similar measurement as (a)–(d) but for the $Γ - M_{Y}$ direction.
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Figure 3
Temperature evolution across the nematic transition on detwinned FeSe along $Γ - M_{X}$ and $Γ - M_{Y}$ . (a) Second energy derivative of spectra around the $M_{X}$ point along the $a$ direction, taken under odd polarization at 56 eV. (b) Corresponding measurement for the $M_{Y}$ point along the $b$ direction. (c) Temperature evolution of the EDC’s second energy derivative taken at $M_{X}$ . (d) Corresponding temperature evolution for the $M_{Y}$ point. (e) Fitted band positions for the $d_{y z}$ and $d_{x z}$ bands from (c). (f) Corresponding fits for (d). (g) The $d_{x z}$ and $d_{y z}$ band splitting as a function of the temperature extracted for (e). (h),(i) The raw EDCs at $M_{X}$ and $M_{Y}$ at selected temperatures.
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Figure 4
Temperature evolution of the electron bands orthogonal to $Γ - M_{Y}$ . (a)–(c) Raw spectra taken at selected temperatures across $M_{Y}$ on a detwinned FeSe. The cut direction is shown in the inset in (g), perpendicular to the $Γ - M_{Y}$ high symmetry. Polarization is even with respect to the cut. All cuts are divided by the Fermi-Dirac function convolved with the instrumental resolution. Fitted MDC peaks of the inner electron band are shown for the left half (red circles), along with the fitted even function for the inner electron band (green). (d) Temperature evolution of the MDC taken at $E_{F}$ of the cut in (a). The yellow dotted line marks the outer MDC peak position at 120 K for reference. Fitted MDC peaks for the outer $d_{x y}$ electron band are shown. (e) Temperature evolution of the MDC taken at $+ 10 meV$ of the cut in (a), with fitted MDC peaks for the inner $d_{x z}$ band shown. (f) The EDCs taken at the $M_{Y}$ point in (a) taken from 30 to 120 K. (g) Fitted peak separation in energy in (f) as a function of the temperature. (h) Fitted MDC peak positions for the outer $d_{x y}$ and the inner $d_{x z}$ electron bands reproduced from (d),(e). (i) The projected energy of the inner $d_{x z}$ electron band bottom with the temperature estimated from the shift in MDC peaks and the $k$ -to- $E$ conversion based on the assumption of a rigid band shift from the 120 K data in (a).
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Figure 5
Schematic of the nematic band reconstruction. (a),(b) Summary of the band structure in the tetragonal (a) and orthorhombic (b) phases in the unfolded 1-Fe BZ. Band hybridizations and the effect of spin-orbit coupling (SOC) are omitted for simplicity. (c) Note that, at $M_{Y}$ in the nematic phase, the downshifted $d_{x z}$ band crosses the $d_{x y}$ band, opening up a hybridization gap. (d),(e) Summary of the band structure in the tetragonal and orthorhombic phases in the folded 2-Fe BZ. Band hybridizations and SOC are incorporated here for a direct comparison to the data. The colors correspond to $d_{x z}$ (red), $d_{y z}$ (green), and $d_{x y}$ (blue, with cyan marking portions with weak photoemission matrix elements).
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Figure 6
Finding the missing second electron pocket by surface doping. (a) Raw spectra taken across $M_{Y}$ on a freshly cleaved detwinned FeSe, at 56 eV. (b) Second energy derivative of (a) with a schematic of band dispersions. (c) The same measurement as (a) but after doping the surface with potassium. The MDC at $E_{F}$ is plotted in red, with arrows indicating the new electron band induced by potassium doping. (d) Second energy derivative of (c), where the bands from the undoped bulk from (b) are reproduced as dotted lines and the new doped surface bands are marked by solid lines.
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