Contributor info: Mr Michał Pacholski

M. J. Pacholski, G. Lemut, J. Tworzydło, C. W. J. Beenakker

SciPost Phys. 11, 105 (2021) · published 14 December 2021 | Toggle abstract · pdf

The spatial discretization of the single-cone Dirac Hamiltonian on the surface of a topological insulator or superconductor needs a special "staggered" grid, to avoid the appearance of a spurious second cone in the Brillouin zone. We adapt the Stacey discretization from lattice gauge theory to produce a generalized eigenvalue problem, of the form ${\mathcal H}\psi=E {\mathcal P}\psi$, with Hermitian tight-binding operators ${\mathcal H}$, ${\mathcal P}$, a locally conserved particle current, and preserved chiral and symplectic symmetries. This permits the study of the spectral statistics of Dirac fermions in each of the four symmetry classes A, AII, AIII, and D.

İnanç Adagideli, Fabian Hassler, Aurélien Grabsch, Michał Pacholski, Carlo W. J. Beenakker

SciPost Phys. 8, 013 (2020) · published 29 January 2020 | Toggle abstract · pdf

A $\boldsymbol{2\pi}$ phase shift across a Josephson junction in a topological superconductor injects vortices into the chiral edge modes at opposite ends of the junction. When two vortices are fused they transfer charge into a metal contact. We calculate the time dependent current profile for the fusion process, which consists of $\boldsymbol{\pm e/2}$ charge pulses that flip sign if the world lines of the vortices are braided prior to the fusion. This is an electrical signature of the non-Abelian exchange of Majorana zero-modes.