Majorana zero modes on a 1D chain for quantum computation

TL;DR

This paper numerically investigates Majorana zero modes in a one-dimensional chain, confirming their exponential decay, robustness to noise, and controllable parity reversal via bias voltage, with implications for quantum computation.

Contribution

It provides detailed numerical analysis of Majorana zero modes in 1D chains, including phase diagrams, decay properties, noise robustness, and ground state parity control, extending prior theoretical predictions.

Findings

Majorana zero modes occur at chain ends and decay exponentially.

Long chains exhibit the predicted parameter domain for zero modes.

Zero modes are robust against noise disturbances.

Abstract

Numerical calculations for Majorana zero modes on a one-dimensional chain are performed using the technique of block diagonalization for general parameter settings. It is found that Majorana zero modes occur near the ends of the chain and decay exponentially away from the ends. The phase diagrams show that Majorana zero modes of a long-enough chain indeed have a parameter domain of $2t>|\mu|$ as predicted from the bulk property of the chain, but a short chain has a much smaller parameter domain than the prediction. Through a numerical simulation Majorana zero modes are found to be robust under the disturbance of noise. Finally the reversion of the parity of the ground states is studied by applying a bias voltage on the quantum dot at an end of the chain. It is found that for a weak coupling between a chain and a quantum dot the parity of the ground states can be reversed through adiabatically tuning the bias voltage.