Band-like Exact Zero-energy Andreev Bound States and Superconducting Diode Effect in Mixed ${s+p}$-wave Josephson Junctions

TL;DR

This paper investigates mixed s+p-wave topological Josephson junctions, revealing band-like zero-energy Andreev bound states, their controllability by external fields, and a significant superconducting diode effect near topological phase transitions.

Contribution

It introduces the concept of band-like zero-energy Andreev bound states in mixed s+p-wave junctions and explores their manipulation and associated diode effects.

Findings

Existence of symmetric zero-energy Andreev bound state crossings.

Linear and quadratic Zeeman field dependence based on p-wave d-vector alignment.

High-efficiency superconducting diode effect near topological phase transition.

Abstract

Topological Josephson junctions enable nonreciprocal transport involving Majorana fermions (MFs). Here we examine a topological Josephson junction with mixed $s$+$p$-wave pairing, where topological phase transition can be driven by adjusting the ratio between the pairing components. There exist two exact symmetrically positioned zero-energy level crossings for the Andreev-bound states, which can be shifted by external fields, and can be destroyed or recreated in pairs by a time-reversal breaking Zeeman field or inhomogeneities, exhibiting band-like structure. The dependence of the shift on the Zeeman field is linear when the two $p$-wave $\boldsymbol{d}$-vectors on both sides are identical while quadratic when they are distinct. Near the topological phase transition, the topological $p$-wave dominant junctions host MF-induced pronounced superconducting diode effect with high efficiency factor $Q$ up to 30 %, in contrast to the trivial $s$-wave dominant junctions possessing relatively small $Q$.