Asymmetric $d$-wave superconducting topological insulator in proximity with a magnetic order

TL;DR

This paper studies how asymmetric $d$-wave superconductivity affects transport and Majorana states in topological insulator hybrid structures with magnetic order, revealing sensitive dependence of conductance on magnetization and pairing orientation.

Contribution

It introduces a model for topological insulator N/F/FS junctions with $d$-wave pairing, analyzing the impact on tunneling conductance and magnetoresistance, highlighting the role of pairing asymmetry and magnetization.

Findings

Zero-bias conductance depends on magnetization magnitude and pairing angle.

Negative magnetoresistance occurs only at zero orbital rotated angle.

Distinct Majorana bound states are formed at the interface.

Abstract

In the framework of the Dirac-Bogoliubov-de Gennes formalism, we investigate the transport properties in the surface of a 3-dimensional topological insulator-based hybrid structure, where the ferromagnetic and superconducting orders are simultaneously induced to the surface states via the proximity effect. The superconductor gap is taken to be spin-singlet $d$-wave symmetry. The asymmetric role of this gap respect to the electron-hole exchange, in one hand, affects the topological insulator superconducting binding excitations and, on the other hand, gives rise to forming distinct Majorana bound states at the ferromagnet/superconductor interface. We propose a topological insulator N/F/FS junction and proceed to clarify the role of $d$-wave asymmetry pairing in the resulting subgap and overgap tunneling conductance. The perpendicular component of magnetizations in F and FS regions can be at the parallel and antiparallel configurations leading to capture the experimentally important magnetoresistance (MR) of junction. It is found that the zero-bias conductance is strongly sensitive to the magnitude of magnetization in FS region $m_{zfs}$ and orbital rotated angle $\alpha$ of superconductor gap. The negative MR only occurs in zero orbital rotated angle. This result can pave the way to distinguish the unconventional superconducting state in the relating topological insulator hybrid structures.