Time-reversal symmetry-breaking nematic superconductivity in FeSe

Jian Kang, Andrey V. Chubukov, and Rafael M. Fernandes

Phys. Rev. B 98, 064508 – Published 20 August 2018

Abstract

FeSe is a unique member of the family of iron-based superconductors, not only because of the high values of $T_{c}$ in FeSe monolayer, but also because in bulk FeSe superconductivity emerges inside a nematic phase without competing with long-range magnetic order. Near $T_{c}$ , superconducting order necessarily has $s + d$ symmetry, because nematic order couples linearly the $s$ -wave and $d$ -wave harmonics of the superconducting order parameter. Here we argue that the near-degeneracy between $s$ -wave and $d$ -wave pairing instabilities in FeSe, combined with the sign-change of the nematic order parameter between hole and electron pockets, allows the superconducting order to break time-reversal symmetry at a temperature $T^{*} < T_{c}$ . The transition from an $s + d$ state to an $s + e^{i α} d$ state should give rise to a peak in the specific heat and to the emergence of a soft collective mode that can be potentially detected by Raman spectroscopy.

Received 17 May 2018

DOI:https://doi.org/10.1103/PhysRevB.98.064508

Physics Subject Headings (PhySH)

Nematic order Phase transitions Superconductivity

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jian Kang^1,*, Andrey V. Chubukov², and Rafael M. Fernandes²

¹National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32304, USA
²School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA

^*jian.kang@fsu.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 98, Iss. 6 — 1 August 2018

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Schematic figure summarizing our main results. As function of a tuning parameter $g$ (which in our paper is the ratio between intraorbital and interorbital interband pairing interactions), the superconducting state changes from $d$ -wave to $s^{+ -}$ -wave in the tetragonal phase, giving rise to an $s + i d$ state near the degeneracy point (dashed red curves). In the nematic phase, the superconducting state becomes $s + d$ near $T_{c}$ , which is enhanced near the $s$ -wave/ $d$ -wave degeneracy point. At low temperatures, an $s + e^{i α} d$ state can be stabilized (solid blue curves). Such an exotic state, which breaks both time-reversal and tetragonal symmetries, is much more favored for a sign-changing nematic state, as compared to a sign-preserving nematic state.
Reuse & Permissions
Figure 2
The Fermi surface and its orbital content in the tetragonal (left) and nematic (right) phases of FeSe in the 1-Fe Brillouin zone. In the tetragonal phase, there are two hole pockets centered at $Γ$ / $Z = (0, 0)$ and two electron pockets $X$ and $Y$ centered at $(π, 0)$ and $(0, π)$ . Deep in the nematic phase there is one hole ( $h$ ) pocket centered at $Γ$ / $Z = (0, 0)$ (another sinks below the Fermi level) and two electron pockets $X$ and $Y$ centered at $(π, 0)$ and $(0, π)$ , respectively. STM and ARPES data [15, 20] show that the $h$ pocket is an ellipse elongated along $Y$ , and that the $X$ electron pocket has a peanut-type form with the minor axis along the $Y$ direction.
Reuse & Permissions
Figure 3
(a) The two leading eigenvalues $λ = {(ln (Λ / T))}^{- 1}$ of the linearized BCS gap equation at $T = T_{c}$ as function of the ratio $V / W$ . Here, $V$ is the intraorbital, interpocket interaction, and $W$ is the interorbital, intrapocket interaction. When $V ≪ W$ , the leading pairing instability is $d$ -wave. When $V ≫ W$ , the leading instability is $s^{+ -}$ pairing. (b) The phase difference $α$ between the $s^{+ -}$ -wave and $d$ -wave gaps at $T = 0$ . When $V ≫ W$ or $V ≪ W$ , the pairing is either purely $s$ -wave or purely $d$ -wave, and $α$ is not well-defined. But when $V \sim W$ , the system spontaneously breaks time-reversal symmetry by forming an $s + i d$ state with $α = \pm π / 2$ .
Reuse & Permissions
Figure 4
Pairing instabilities in the nematic phase. The red solid and dashed curves refer to the sign-changing nematic state $[sign (Φ_{h}) = - sign (Φ_{e})]$ , whereas the blue solid and dashed curves refer to the sign-preserving nematic state $[sign (Φ_{h}) = sign (Φ_{e})]$ . The splitting of the two leading pairing instabilities, corresponding to “bonding” and “antibonding” mixing of the $s^{+ -}$ and $d$ -wave gaps, is smaller in the case of sign-changing nematicity, illustrating the reduced impact of nematic order on SC in this case.
Reuse & Permissions
Figure 5
The phase difference $α$ between the $s^{+ -}$ and $d$ -wave gaps at $T = 0$ in the nematic phase. When $α$ is neither $0, π$ , or $π / 2$ the SC state breaks both tetragonal and time-reversal symmetries. The solid red and dashed blue curves refer to the case of opposite-sign nematicity and same-sign nematicity, respectively. In the former, we find a much larger regime in which the SC state breaks time-reversal symmetry.
Reuse & Permissions
Figure 6
Energy $ω_{r}$ of the collective mode associated with the relative phase between the gaps at the $X$ and $Y$ pockets at $T = 0$ as function of the ratio $V / W$ . Note that $ω_{r}$ becomes soft when the transition to the time-reversal symmetry-breaking state takes place.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics