Probing Majorana-like states in quantum dots and quantum rings

TL;DR

This paper theoretically explores chiral p-wave superconductivity in quantum dots and rings, demonstrating conditions for Majorana-like edge modes and analyzing their properties and finite-size effects.

Contribution

It introduces a theoretical framework for realizing and studying Majorana modes in quantum dots and rings with chiral p-wave superconductivity, including effects of magnetic flux and size.

Findings

Chiral edge modes appear at boundaries in the topological regime.

Majorana-like zero-energy modes can be induced by specific magnetic flux conditions.

Finite-size effects influence the degeneracy and energy splitting of edge modes.

Abstract

Engineering chiral $p$-wave superconductivity in semiconductor structures offers fascinating ways to obtain and study Majorana modes in a condensed matter context. Here, we theoretically investigate chiral $p$-wave superconductivity in quantum dots and quantum rings. Using both analytical as well as numerical methods, we calculate the quasiparticle excitation spectra in these structures and the corresponding excitation amplitudes and charge densities. In the topological regime, we can observe the chiral edge modes localized at the boundaries and possessing finite energy in quantum dots and quantum rings. By applying a magnetic field which is expelled from the quantum ring, but which creates a flux that is an odd integer multiple of $\Phi_0/2=\pi\hbar/e$, Majorana modes, that is, (approximately) degenerate edge modes with zero energy and zero charge density, become possible in the topological regime. Furthermore, we investigate finite-size effects that split these degenerate edge modes as well as the effect of a magnetic field penetrating into the superconducting region that can under certain circumstances still support edge modes with approximately zero energy and charge.