Three-dimensional electronic structure of LiFeAs

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Three-dimensional electronic structure of LiFeAs

R. P. Day, M. X. Na, M. Zingl, B. Zwartsenberg, M. Michiardi, G. Levy, M. Schneider, D. Wong, P. Dosanjh, T. M. Pedersen, S. Gorovikov, S. Chi, R. Liang, W. N. Hardy, D. A. Bonn, S. Zhdanovich, I. S. Elfimov, and A. Damascelli

Phys. Rev. B 105, 155142 – Published 21 April 2022

Abstract

Among the iron-based superconductors, LiFeAs is unrivaled in the simplicity of its crystal structure and phase diagram. However, our understanding of this canonical compound suffers from conflict between mutually incompatible descriptions of the material's electronic structure, as derived from contradictory interpretations of the photoemission record. Here we explore the challenge of interpretation in such experiments. By combining comprehensive photon energy- and polarization-dependent angle-resolved photoemission spectroscopy (ARPES) measurements with numerical simulations, we establish the providence of several contradictions in the present understanding of this and related materials. We identify a confluence of surface-related issues which have precluded unambiguous identification of both the number and the dimensionality of the Fermi-surface sheets. Ultimately, we arrive at a scenario which supports indications of topologically nontrivial states while also being incompatible with superconductivity as a spin-fluctuation-driven Fermi-surface instability.

Received 27 September 2021
Revised 14 March 2022
Accepted 21 March 2022

DOI:https://doi.org/10.1103/PhysRevB.105.155142

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

R. P. Day^1,2,*, M. X. Na^1,2, M. Zingl³, B. Zwartsenberg^1,2, M. Michiardi^1,2, G. Levy^1,2, M. Schneider ^1,2, D. Wong^1,2, P. Dosanjh^1,2, T. M. Pedersen ⁴, S. Gorovikov⁴, S. Chi^1,2, R. Liang^1,2, W. N. Hardy^1,2, D. A. Bonn^1,2, S. Zhdanovich ^1,2, I. S. Elfimov^1,2, and A. Damascelli ^1,2,†

¹Department of Physics & Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada
²Quantum Matter Institute, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
³Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
⁴Canadian Light Source Inc., 44 Innovation Boulevard, Saskatoon, SK S7N 2V3, Canada

^*rpday7@gmail.com
^†damascelli@physics.ubc.ca

Looking beyond the surface with angle-resolved photoemission spectroscopy

R. P. Day, I. S. Elfimov, and A. Damascelli

Phys. Rev. B 108, 045106 (2023)

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Vol. 105, Iss. 15 — 15 April 2022

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Figure 1
Crystal and electronic structure of LiFeAs. In (a), the experimentally determined crystal structure described in Ref. [5] with Fe in orange, As in red, and Li in blue. The coordinate axes used throughout the text are inscribed on the basal plane of the unit cell. In (b), the DFT-predicted Fermi surface of LiFeAs, projected in the $k_{x} − k_{z}$ plane in the upper panel, and the $k_{y} − k_{x}$ plane in the lower panel. Principal orbital textures are represented by the colorscales, with $d_{x y}$ in black, $d_{y z}$ in red, and $d_{x z}$ in blue.
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Figure 2
ARPES Fermi surface of LiFeAs: Experimental Fermi surface of LiFeAs in the (a) $k_{z} = 0$ ( $h ν = 26 eV$ near $Γ$ and $h ν = 31 eV$ near $M$ ), (b) $k_{z} = π / c$ ( $h ν = 38 eV$ near $Z$ and $h ν = 21 eV$ near $A$ ) planes, and the (c) $k_{y} = 0$ plane. Panels (a) and (b) were acquired with linear vertical polarization (parallel to $k_{y}$ ). In (c), hole pockets $α$ , $β$ are the sum over vertical and horizontal polarizations for $h ν \in [20, 70]$ eV; electron pockets $γ$ and $δ$ were acquired with linear vertical polarization over $h ν \in [18, 76] eV$ . In panel (d), a schematic Fermi surface based on MDC fits over the 3D Brillouin zone is plotted. Electron pockets are indicated in blue, and holes are indicated in orange. The appearance of a small $α$ sheet near $Γ$ in panel (a) is the result of SOC and residual intensity from features at lower energy, as expanded on in Fig. 3.
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Figure 3
SOC effects on apparent Fermi surface of LiFeAs. In (a) and (b), constant energy contours at $E = 0 eV$ in the $k_{x} − k_{z}$ plane, acquired with linear vertical (a) and horizontal (b) polarizations over $h ν \in [20, 70] eV$ . In (c) and (d), a single spectrum at $k_{z} = 0$ ( $h ν = 26 eV$ ) under the same experimental configurations as in (a) and (b), respectively. Although LV data suggest a warped cylindrical $α$ Fermi-surface sheet, a closed 3D Fermi surface is evident from composite data including both channels. In (e), MDCs at $E = 0$ for the sum over linear vertical, horizontal polarizations along the $k_{z}$ axis. MDC peak fits are indicated by gray cursors. In (f), a composite image of both polarizations, along with MDC fits, indicating the $α$ band maximum at $E = - 5 meV$ at $k_{z} = 0$ .
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Figure 4
The $k_{z}$ dispersion of the $α^{'}$ band. In (a), dispersion of hole bands along $Γ M$ ( $h ν = 26 eV$ ) and $Γ Z$ directions ( $h ν \in [26, 54] eV$ ). As anticipated from the DFT band structure in (d), a strongly dispersive feature near $Z$ pulls the top of $α^{'} \sim 200 meV$ below $E_{F}$ as indicated by EDC peak positions overlain with a parabolic fit. This seems at odds with the appearance of the smaller of two Fermi surfaces in (e); a dashed contour is superimposed as a guide. The broad holelike feature in the spectra in (b) taken at $k_{z} = Z$ ( $h ν = 38 eV$ ) corroborates this impression of a small hole-pocket. In (c), simulated photoemission at the $Z$ point for slab (left) and bulk (right) models. The bulk simulations disregard the presence of a surface in the photoemission experiment. Comparison with the experiment in (b) emphasizes the prominence of surface-related features. In particular, a linearly dispersive TSS is observed in the slab calculation near $E_{F}$ in panel (c). The simulated Fermi surface in (f) confirms this TSS as the progenitor of the small Fermi-surface contour in (e). Data in (e) have been symmetrized about both diagonal axes.
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Figure 5
Electron Fermi surface: Low energy spectra at M ( $h ν = 31 eV$ (a) and A ( $h ν = 44 eV$ ) (b) reveal the dispersive $d_{x z / y z}$ band oscillating from inside to outside the 2D $d_{x y}$ state; cursors indicate MDC peak centres and parabolic fits. Oscillation of $k_{F} (k_{z})$ is illustrated most clearly in the curvature (as defined in Ref. [47]) of the Fermi surface, plot in (c) along the $k_{z}$ axis ( $h ν \in [18, 76] eV$ ). The surface sensitivity of UV-ARPES can affect the correspondence between bulk and measured $k_{F} (k_{z})$ oscillations. This is demonstrated with simulated MDCs in (d), computed at $k_{z} = A$ as a function of photoelectron escape depth.
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