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

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 $P{2}_{1}3$ (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 $P{2}_{1}3$.

28 pages, 6 figures

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• Diversity of Radial Spin Textures in Chiral Materials
• Fundamental laws of chiral band crossings: local constraints, global constraints, and topological phase diagrams
• Projected spin texture as a bulk indicator of fragile topology
• Weak localization at arbitrary disorder strength in systems with generic spin-dependent fields
• Understanding spin textures in PT-broken systems through universal symmetry-constrained rules
• Discovery of nodal-line superconductivity in chiral crystals
• Investigating Quantum Spin-Textures Using Universal MJ Hamiltonians
• Radial Rashba spin-orbit fields in commensurate twisted transition-metal dichalcogenide bilayers