Persistent current in 2D topological superconductors

TL;DR

This paper investigates how Majorana edge modes in 2D topological superconductors influence persistent currents, revealing two regimes with distinct flux periodicities related to tunneling strength and fermion parity conservation.

Contribution

It identifies and characterizes the regimes of strong and weak tunneling of Majorana fermions, linking them to different flux periodicities of the persistent current in 2D topological superconductors.

Findings

Strong tunneling leads to 2π-periodic persistent current with non-conserved fermion parity.

Weak tunneling results in 4π-periodic persistent current with conserved fermion parity.

Numerical analysis maps parameter regions for 2π and 4π harmonic emergence.

Abstract

A junction between two boundaries of a topological superconductor (TSC), mediated by localized edge modes of Majorana fermions, is investigated. The tunneling of fermions across the junction depends on the magnetic flux. It breaks the time-reversal symmetry at the boundary of the sample. The persistent current is determined by the emergence of Majorana edge modes. The structure of the edge modes depends on the magnitude of the tunneling amplitude across the junction. It is shown that there are two different regimes, which correspond to strong and weak tunneling of Majorana fermions, distinctive in the persistent current behavior. In a strong tunneling regime, the fermion parity of edge modes is not conserved and the persistent current is a $2\pi$-periodic function of the magnetic flux. When the tunneling is weak the chiral Majorana states, which are propagating along the edges have the same fermion parity. They form a $4\pi$-phase periodic persistent current along the boundaries. The regions in the space of parameters, which correspond to the emergence of $2\pi$- and of $4\pi$-harmonics, are numerically determined. The peculiarities in the persistent current behavior are studied.