Effects of momentum-dependent quasiparticle renormalization on the gap structure of iron-based superconductors

Shinibali Bhattacharyya, P. J. Hirschfeld, Thomas A. Maier, and Douglas J. Scalapino

Phys. Rev. B 101, 174509 – Published 11 May 2020

Abstract

We discuss the influence of momentum-dependent correlations on the superconducting gap structure in iron-based superconductors. Within the weak coupling approach including self-energy effects at the one-loop spin-fluctuation level, we construct a dimensionless pairing strength functional which includes the effects of quasiparticle renormalization. The stationary solution of this equation determines the gap function at $T_{c}$ . The resulting equations represent the simplest generalization of spin fluctuation pairing theory to include the effects of an anisotropic quasiparticle weight. We obtain good agreement with experimentally observed anisotropic gap structures in LiFeAs, indicating that the inclusion of quasiparticle renormalization effects in the existing weak-coupling theories can account for the observed anomalies in the gap structure of Fe-based superconductors.

Received 22 December 2019
Accepted 20 April 2020

DOI:https://doi.org/10.1103/PhysRevB.101.174509

Physics Subject Headings (PhySH)

Eliashberg theory Superconductivity Superconductors

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Shinibali Bhattacharyya¹, P. J. Hirschfeld ¹, Thomas A. Maier ², and Douglas J. Scalapino³

¹Department of Physics, University of Florida, Gainesville, Florida 32611, USA
²Computational Sciences and Engineering Division and Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
³Department of Physics, University of California, Santa Barbara, California 93106, USA

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Vol. 101, Iss. 17 — 1 May 2020

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Images

Figure 1
(a) Fermi surface at $k_{z} = π$ plane for LiFeAs represented by its corresponding dominant orbital character as indicated in the color legend. (b) Orbital weight along the $β_{1}$ electron pocket plotted as a function of angle $ϕ$ shown in (a). (c) Diagonal orbital components of the static particle-particle effective interaction ${[V_{p p p p} (q, 0)]}_{A}$ along high-symmetry path $Z − R − X^{'} − Z − Y^{'}$ with $U$ and $J$ as indicated. Plots as a function of the angle $ϕ$ around the Fermi pockets are done with the angle measured counterclockwise from the $k_{x}$ axis.
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Figure 2
$Z (ϕ)$ along Fermi pockets $α_{2}, β_{1}$ , and $γ$ evaluated from the static particle-hole effective interaction defined in Eq. (10).
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Figure 3
Results for LiFeAs: (a) Angular plot of the $s$ -wave gap function evaluated from traditional spin-fluctuation theory, around the $Z$ -centered outer hole pocket $α_{2}, X^{'}$ -centered electron pocket $β_{1}$ , and $R$ -centered hole pocket $γ$ . (b) The modified gap function obtained from the linearized Eliashberg equations (9) and (10) with quasiparticle renormalization $Z (k)$ included. (c) Experimental results: Measured magnitudes of the gap from an ARPES experiment [20], symmetrized and displayed as diamonds and those from Bogoliubov QPI experiment [26] displayed as crosses. All calculations are done for $U$ and $J$ as indicated.
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Figure 4
Heat map plots of (a) the singlet pairing vertex ${[V (k_{μ}, k_{ν}^{'}, 0)]}_{A}$ matrix resulting in the gap function plotted in Fig. 3 from the tight-binding model. (b) Matrix elements of the quantity ${[V (k_{μ}, k_{ν}^{'}, 0)]}_{A} d k_{ν}^{'} / | v_{F} (k_{ν}^{'}) |$ . (c) Matrix elements of the quantity ${[V (k_{μ}, k_{ν}^{'}, 0)]}_{A} d k_{ν}^{'} / | v_{F} (k_{ν}^{'}) | / Z (k_{ν}^{'})$ . The value at any given point is proportional to the brightness of the color. The rows and the columns of the tiles of (a)–(c) correspond to the Fermi points $k_{μ}$ and $k_{ν}^{'}$ arranged in ascending order of their corresponding polar angle $ϕ = 0^{\circ}$ to $360^{\circ}$ around each Fermi sheet. Band indices $μ$ and $ν$ represent the Fermi sheets $α_{1}, α_{2}$ at the $Z, γ$ at the $R, β_{1}$ at the $X^{'}$ , and $β_{2}$ at the $Y^{'}$ point. Unequal areas of the tiles are due to unequal number of Fermi points around each of the sheets.
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Figure 5
Angular plots of the gap function evaluated around the Fermi pockets as indicated by the color legend. The calculations show a change in the gap symmetry of the leading eigenfunction from (left) $d$ wave (obtained from traditional spin-fluctuation theory with $Z (k) = 1)$ to (right) $s$ wave [obtained from linearized Eliashberg equations with $Z (k)$ included]. Both calculations are done for $U$ and $J$ as indicated.
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Figure 6
The frequency dependence of the effective interaction $V (k - k^{'}, ω_{m} - ω_{n})$ .
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