Spin-momentum locking from topological quantum chemistry: applications to multifold fermions

TL;DR

This paper investigates how the nontrivial topology of chiral multifold fermions influences spin textures in crystals, using topological quantum chemistry to analyze spin-momentum locking and its variation across different materials.

Contribution

It introduces a method to determine spin-momentum locking in multifold fermions from band representations and applies it to real materials, revealing diverse spin winding behaviors.

Findings

Spin textures can have winding numbers from 0 to ±7.

On-site spin-orbit coupling and crystal field splitting affect spin textures.

Application to PtGa demonstrates practical relevance.

Abstract

In spin-orbit coupled crystals, symmetries can protect multifold degeneracies with large Chern numbers and Brillouin zone spanning topological surface states. In this work, we explore the extent to which the nontrivial topology of chiral multifold fermions impacts the spin texture of bulk states. To do so, we formulate a definition of spin-momentum locking in terms of reduced density matrices. Using tools from the theory of topological quantum chemistry, we show how the reduced density matrix can be determined from the knowledge of the basis orbitals and band representation forming the multifold fermion. We show how on-site spin orbit coupling, crystal field splitting, and Wyckoff position multiplicity compete to determine the spin texture of states near chiral fermions. We compute the spin texture of multifold fermions in several representative examples from space groups $P432$ (207) and $P2_13$ (198). We show that the winding number of the spin around the Fermi surface can take many different integer values, from zero all the way to $\pm 7$. Finally, we conclude by showing how to apply our theory to real materials using the example of PtGa in space group $P2_13$.