# Topological Crystalline Superconductivity in Dirac Semimetal Phase of Iron-based Superconductors

## TL;DR

This paper explores the topological properties of iron-based superconductors, revealing their potential to host various Majorana fermions and topological crystalline phases through theoretical modeling.

## Contribution

It introduces a theoretical framework demonstrating that iron-based superconductors can exhibit topological crystalline superconductivity with diverse Majorana surface states.

## Key findings

- Identification of odd-parity superconductivity from $d$- and $p$-orbital pairing
- Prediction of multiple Majorana fermion surface states
- Topological invariants characterized by crystal symmetry

## Abstract

In iron-based superconductors, band inversion of $d$- and $p$-orbitals yields Dirac semimetallic states. We theoretically investigate their topological properties in normal and superconducting phases, based on the tight-binding model involving full symmetry of the materials. We demonstrate that a Cooper pair between electrons with $d$- and $p$-orbitals relevant to the band structure yields odd-parity superconductivity. Moreover, we present the typical surface states by solving the Bogoliubov-de Gennes equation and characterize them by topological invariants defined with crystal symmetry. It is found that there appear various types of Majorana fermions such as surface flat band, Majorana quartet and M\"{o}bius twisted surface state. Our theoretical results show that iron-based superconductors are promising platforms to realize rich topological crystalline phases.