Transport signatures of bulk topological phases in double Rashba nanowires probed by spin-polarized STM

Manisha Thakurathi,Jelena Klinovaja,Daniel Loss,Denis Chevallier

doi:10.1103/physrevresearch.2.023197

Abstract

We study a double-nanowire setup proximity coupled to an $s$-wave superconductor and search for the bulk signatures of the topological phase transition that can be observed experimentally, for example, with an STM tip. Three bulk quantities, namely, the charge, the spin polarization, and the pairing amplitude of intrawire superconductivity are studied in this work. The spin polarization and the pairing amplitude flip sign as the system undergoes a phase transition from the trivial to the topological phase. In order to identify promising ways to observe bulk signatures of the phase transition in transport experiments, we compute the spin current flowing between a local spin-polarized probe, such as an STM tip, and the double-nanowire system in the Keldysh formalism. We find that the spin current contains information about the sign flip of the bulk spin polarization and can be used to determine the topological phase transition point.

Highlights

Majorana bound states (MBSs) have attracted a lot of attention in recent years due to their potential application in topological quantum computing [1,2,3,4,5]
Magnetic field and superconductivity have detrimental effects on each other, which has motivated proposals for time-reversal invariant topological superconductors to avoid the need of magnetic fields, particular examples being double-NW setups with Karmers pairs of MBSs [22,23,24,25,26,27,28,29,30,31,32,33,34,35,36], see Fig. 1
We studied a double-NW setup proximity coupled to an s-wave superconductor in the presence of Rashba spin-orbit interaction (SOI) and subjected to a magnetic field along the NW

Summary

INTRODUCTION

Majorana bound states (MBSs) have attracted a lot of attention in recent years due to their potential application in topological quantum computing [1,2,3,4,5]. It is important to note that E1 = 0 (E2 = 0) corresponds to the topological phase transition point indicating change from zero to one MBS (from one MBS to two MBSs) We consider equilibrium properties of the double-NW setup, in particular the charge and spin densities as well as the intrawire pairing amplitude density in a given eigenstate, and study their behavior as function of momentum (position) and topological phase. The spin component along the magnetic field Sηzλ and the intrawire pairing amplitude Fηλ flip their sign as we go along the line n1-n2 or n3-n4, indicating the topological phase transition from trivial to topological phase. Due to the translation invariance of the setup, one can argue that the sign flip occurs for both the local Sηzl ( j) and the global spin component Sηzl

CALCULATION OF THE SPIN CURRENT PROBED BY A SPIN-POLARIZED STM

CONCLUSIONS