Piecewise-terminated spherical topological insulator as a virtual breadboard for Majorana circuitry

TL;DR

This paper presents a computational framework for designing and analyzing Majorana circuits on spherical topological insulators with various surface terminations, enabling virtual prototyping of quantum devices.

Contribution

It introduces a novel numerical approach to model and simulate Majorana modes on spherical topological insulators with different termination patterns, serving as a virtual testbed for quantum circuitry.

Findings

Demonstrated the formation of Majorana modes at interfaces and trijunctions.

Enabled calculation of energy spectra and eigenfunctions for complex termination patterns.

Prototyped a Majorana analog of a Mach-Zehnder interferometer.

Abstract

We consider the surface states of a spherical topological insulator piecewise-terminated by superconductivity or ferromagnetism over various regions of the spherical surface. Such terminations gap the surface states by breaking U(1) particle-number symmetry or time-reversal symmetry, respectively. Interfaces and trijunctions between differently terminated surface regions can host propagating and bound Majorana modes, and the finite size of the spherical system makes it easily amenable to numerical analysis via exact diagonalization of the Bogoliubov-de Gennes Hamiltonian within a truncated Hilbert space. Creative termination patterning therefore allows one to prototype a variety of Majorana circuits, calculating energy spectra and plotting eigenfunctions over the spherical surface. We develop the computational framework for this approach, establishing a virtual breadboard for Majorana circuitry, and apply it to circuits of interest, including the Majorana analog of a Mach-Zehnder interferometer.