Aharonov-Bohm effect in a helical ring with long-range hopping: Effects of Rashba spin-orbit interaction and disorder

TL;DR

This paper investigates the Aharonov-Bohm effect in a helical ring with long-range hopping, analyzing how Rashba spin-orbit interaction and disorder influence energy spectra and transport properties, revealing the fragility of zero-energy states.

Contribution

It introduces a detailed analysis of zero-energy crossings and transport in a helical ring with long-range hopping, considering Rashba spin-orbit interaction and disorder effects.

Findings

Zero-energy crossings occur at specific magnetic flux values.

Rashba spin-orbit interaction suppresses zero-energy transmission peaks.

Disorder destroys zero-energy crossings and transmission peaks.

Abstract

We study Aharonov-Bohm effect in a two-terminal helical ring with long-range hopping in presence of Rashba spin-orbit interaction. We explore how the spin polarization behavior changes depending on the applied magnetic flux and the incoming electron energy. The most interesting feature that we articulate in this system is that zero-energy crossings appear in the energy spectra at $\Phi=0$ and also at integer multiples of half-flux quantum values ($n \Phi_0/2$, $n$ being an integer) of the applied magnetic flux. We investigate the transport properties of the ring using Green's function formalism and find that the zero energy transmission peaks corresponding to those zero energy crossings vanish in presence of Rashba spin-orbit interaction. We also incorporate static random disorder in our system and show that the zero energy crossings and transmission peaks are not immune to disorder even in absence of Rashba spin-orbit interaction. The latter prevents the possibility of behaving these helical states in the ring like topological insulator edge states.