Superconducting proximity effect in three-dimensional topological insulators in the presence of a magnetic field

TL;DR

This paper investigates how magnetic fields influence the superconducting proximity effect in topological insulators, revealing a transition to a topologically nontrivial state characterized by odd-frequency triplet pairing and distinctive conductance signatures.

Contribution

It provides a theoretical analysis of the interplay between magnetic fields and superconducting correlations in topological insulator-superconductor junctions, highlighting signatures of topological transitions.

Findings

Transition from gapped conductance to zero-energy peak indicates topological regime

Odd-frequency triplet pairing dominates in the nontrivial phase

Magnetic field orientation and strength critically affect the proximity effect

Abstract

The proximity induced pair potential in a topological insulator-superconductor hybrid features an interesting superposition of a conventional spin-singlet component from the superconductor and a spin-triplet one induced by the surface state of the topological insulator. This singlet-triplet superposition can be altered by the presence of a magnetic field. We study the interplay between topological order and superconducting correlations performing a symmetry analysis of the induced pair potential, using Green functions techniques to theoretically describe ballistic junctions between superconductors and topological insulators under magnetic fields. We relate a change in the conductance from a gapped profile into one with a zero-energy peak with the transition into a topologically nontrivial regime where the odd-frequency triplet pairing becomes the dominant component in the pair potential. The nontrivial regime, which provides a signature of odd-frequency triplet superconductivity, is reached for an out-of-plane effective magnetization with strength comparable to the chemical potential of the superconductor or for an in-plane one, parallel to the normal-superconductor interface, with strength of the order of the superconducting gap. Strikingly, in the latter case, a misalignment with the interface yields an asymmetry with the energy in the conductance unless the total contribution of the topological surface state is considered.