Multiband strong-coupling superconductors with spontaneously broken time-reversal symmetry

TL;DR

This paper demonstrates the existence of time-reversal symmetry breaking states in three-band strong-coupling superconductors using Eliashberg theory, providing a microscopic foundation for understanding TRSB in materials like iron pnictides.

Contribution

It extends the analysis of TRSB states from weak-coupling to strong-coupling regimes using a microscopic Eliashberg framework, relevant for real materials.

Findings

TRSB states exist in strong-coupling three-band systems.

Calculated free energy confirms the stability of TRSB states.

Method can guide the search for TRSB superconductors.

Abstract

We study superconducting three-band systems within strong-coupling Eliashberg theory. In particular, we search for phase-frustrated superconducting systems with spontaneous time-reversal symmetry breaking (TRSB) states. The emergence of TRSB states in multiband systems has so far been studied using microscopic weak-coupling BCS theory or more phenomenological effective field theories such as multi-component Ginzburg-Landau theories. For systems with three disjoint Fermi surfaces whose electrons experience interactions mediated by phonons, we present a microscopic analysis showing that TRSB states also exist within a strong-coupling microscopic theory. The systems we consider have sizable electron-phonon couplings, putting them into the strong-coupling regime. They are thus a fitting description for strong-coupling materials such as some of the iron pnictides. Moreover, as the TRSB states are challenging to find numerically, we calculate the free energy of multiband systems within strong-coupling theory and make explicit use of it to pin down the TRSB states' elusive nature. Since Eliashberg theory is well incorporated with first-principles calculations, our strong-coupling approach might help facilitate a more efficient search for candidate materials that can exhibit TRSB.