Time-reversal symmetry breaking superconductivity in the coexistence phase with magnetism in Fe-pnictides

TL;DR

This paper predicts a novel time-reversal symmetry breaking superconducting state in Fe-pnictides within the coexistence phase with magnetism, involving mixed pairing components and a complex phase structure.

Contribution

It introduces a new superconducting state with broken time-reversal symmetry arising from coexistence with SDW order in Fe-pnictides, not previously described.

Findings

Coexistence of $s^{+-}$ and $t$-type orders with a nontrivial phase.

Time-reversal symmetry can break before superconductivity fully develops.

The state emerges in a minimal model with one hole and two electron pockets.

Abstract

We argue that superconductivity in the coexistence region with spin-density-wave (SDW) order in weakly doped Fe-pnictides differs qualitatively from the ordinary $s^{+-}$ state outside the coexistence region, as it develops an additional gap component which is a mixture of intra-pocket singlet ($s^{++}$) and inter-pocket spin-triplet pairings (the $t-$state). The coupling constant for the $t-$channel is proportional to the SDW order and involves interactions that do not contribute to superconductivity outside of the SDW region. We argue that the $s^{+-}$ and $t-$type superconducting orders coexist at low temperatures, and the relative phase between the two is in general different than $0$ or $\pi$, manifesting explicitly the breaking of the time-reversal symmetry promoted by long-range SDW order. We show that this exotic state emerges already in the simplest model of Fe-pnictides, with one hole pocketand two symmetry-related electron pockets. We argue that in some parameter range time-reversal gets broken even before long-range superconducting order develops.