Identification of topological superconductivity in magnetic impurity systems using bulk spin polarization

Mahdi Mashkoori,Saurabh Pradhan,Jonas Fransson,Kristofer Björnson,Annica M Black-Schaffer

doi:10.1103/physrevb.102.104501

Abstract

Magnetic impurities on the surface of spin-orbit coupled but otherwise conventional superconductors provide a promising way to engineer topological superconductors with Majorana bound states as for boundary modes. In this work, we show that the spin-polarization in the interior of both one-dimensional impurity chains and two-dimensional islands can be used to determine the topological phase, as it changes sign exactly at the topological phase transition. This offers an independent probe of the topological phase, beyond the zero-energy Majorana bound states appearing at the boundaries of the topological region.

Highlights

Topological states of matter have been at the center of attention in condensed matter physics for the past decade [1,2,3,4,5]
We show that for both ferromagnetic chains and islands deposited on conventional superconductors with large spin-orbit coupling (SOC), this spin-polarization remains and encodes the topological phase transition (TPT) as an interchange of the spin-polarization between negative and positive low-energy states
Motivated by the fact that a spin-helical impurity chain (SHC) is topologically equivalent to a ferromagnetic impurity chain (FMC) plus an additional SOC [53], we find a way to map the spin-polarized local density of states (SP-LDOS) and still identify the TPT: We evaluate the SP-LDOS along the SHC where at each lattice point i the spin-polarization is projected on S(i): ρn(i, E ) = cos(khxi)ρx (i, E ) + sin(khxi)ρy(i, E )

Summary

INTRODUCTION

Topological states of matter have been at the center of attention in condensed matter physics for the past decade [1,2,3,4,5]. We show that for both ferromagnetic chains and islands deposited on conventional superconductors with large spin-orbit coupling (SOC), this spin-polarization remains and encodes the topological phase transition (TPT) as an interchange of the spin-polarization between negative and positive low-energy states. We calculate the SP-LDOS within a Bogoliubov–de Gennes (BdG) formulation of Eq (1) by using a Chebyshev expansion of the Green’s function [35,36,37,38,39]

RESULTS

Ferromagnetic impurity chain

Spin-helical impurity chain

Dilute FMCs

Ferromagnetic impurity island

CONCLUDING REMARKS