Short-time dynamics in $s+is$-wave superconductor with incipient bands

TL;DR

This paper investigates the short-time dynamics and collective modes of an $s+is$-wave superconductor with incipient bands, revealing new coupled soft modes and comparing them with other pairing states.

Contribution

It introduces a theoretical analysis of collective modes in an $s+is$ superconductor with incipient bands, highlighting the emergence of a new coupled soft mode.

Findings

Higgs mode observed at frequencies similar to two-band models.

Absence of Leggett mode in the $s^{ ext{±}}$ state.

Discovery of a new coupled soft mode in $s+is$ and $s^{++}$ states.

Abstract

Motivated by the recent observation of the time-reversal symmetry broken state in K-doped BaFe$_2$As$_2$ superconducting alloys, we theoretically study the collective modes and the short time dynamics of the superconducting state with $s+is$-wave order parameter using an effective four-band model with two hole and two electron pockets. The superconducting $s+is$ state emerges for incipient electron bands as a result of hole doping and appears as an intermediate state between $s^{\pm}$ (high number of holes) and $s^{++}$ (low number of holes). The amplitude and phase modes are coupled giving rise to a variety of collective modes. In the $s^{\pm}$ state, we find the Higgs mode at frequencies similar to a two-band model with an absent Leggett mode, while in the $s+is$ and $s^{++}$ state, we uncover a new coupled collective soft mode. Finally we compare our results with the $s+id$ solution and find similar behaviour of the collective modes.