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

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.

arXiv comment10 pages, 5 figures

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