High-throughput Investigations of Topological and Nodal Superconductors

TL;DR

This paper develops a comprehensive database and computational tools to predict topological and nodal superconductivity in materials based on symmetry indicators, aiding the search for Majorana fermions for quantum computing.

Contribution

It introduces a new approach to predict topological superconductivity using symmetry indicators for materials in the Inorganic Crystal Structure Database.

Findings

Approximately 90% of analyzed materials are topological or nodal superconductors.

Identified positions and shapes of nodes in representation-enforced nodal superconductors.

Provided a user-friendly subroutine for analyzing topological superconductivity in any material.

Abstract

The theory of symmetry indicators has enabled database searches for topological materials in normal conducting phases, which has led to several encyclopedic topological material databases. To date, such a database for topological superconductors is yet to be achieved because of the lack of information about pairing symmetries of realistic materials. In this work, sidestepping this issue, we tackle an alternative problem: the predictions of topological and nodal superconductivity in materials for each single-valued representation of point groups. Based on recently developed symmetry indicators for superconductors, we provide comprehensive mappings from pairing symmetries to topological or nodal superconducting nature for nonmagnetic materials listed in Inorganic Crystal Structure Database. We quantitatively show that around 90\% of computed materials are topological or nodal superconductors when a pairing that belongs to a one-dimensional nontrivial irrep of point groups is assumed. When materials are representation-enforced nodal superconductors, positions and shapes of the nodes are also identified. These data are aggregated at \textit{Database of Topological and Nodal Supercoductors}. We also provide a subroutine \textit{Topological Supercon}, which allows users to examine the topological nature in the superconducting phase of any material themselves by uploading the result of first-principles calculations as an input. Our database and subroutine, when combined with experiments, will help us understand the pairing mechanism and facilitate realizations of the long-sought Majorana fermions promising for topological quantum computations.