# Pairing symmetry and topological surface state in iron-chalcogenide superconductors

## TL;DR

This paper explores how different pairing symmetries in iron-chalcogenide superconductors influence topological surface states, especially regarding time-reversal symmetry breaking and the resulting gapped Dirac cones.

## Contribution

It identifies possible pairing symmetries that break time-reversal symmetry and links these to topological surface state properties in iron-chalcogenide superconductors.

## Key findings

- Time-reversal symmetry breaking pairing can gap the surface Dirac cone.
- Specific pairing symmetries are constrained by crystalline symmetry.
- Coupling between magnetization and gap functions is modeled for iron-chalcogenides.

## Abstract

The symmetries of superconducting gap functions remain an important question of iron-based superconductivity. Motivated by the recent angle-resolved photoemission spectroscopic measurements on iron-chalcogenide superconductors, we investigate the influence of pairing symmetries on the topological surface state. If the surface Dirac cone becomes gapped in the superconducting phase, it implies magnetization induced from time-reversal symmetry breaking pairing via spin-orbit coupling. Based on the crystalline symmetry constraints on the Ginzburg-Landau free energy, the gap function symmetries are among the possibilities of $A_{1g(u)}\pm iA_{2g(u)}$, $B_{1g(u)}\pm iB_{2g(u)}$, or, $E_{g(u)}\pm i E_{g(u)}$. This time-reversal symmetry breaking effect can exist in the normal state very close to $T_c$ with the relative phase between two gap functions locked at $\pm \frac{\pi}{2}$. The coupling between magnetization and superconducting gap functions is calculated based on a three-orbital model for the band structure of iron-chalcogenides. This study provides the connection between the gap function symmetries and topological properties of the surface state.