Fusion Rules of Majorana-Kramer-Pairs in Time-Reversal-Invariant Topological Superconductors

TL;DR

This paper explores the fusion rules and non-Abelian statistics of Majorana Kramers pairs in time-reversal-invariant topological superconductors, revealing supersymmetry and proposing schemes for nontrivial fusion processes.

Contribution

It introduces a theoretical framework for understanding fusion rules of Majorana Kramers pairs, including supersymmetry and fusion schemes, in time-reversal-invariant topological superconductors.

Findings

Fusion of Majorana Kramers pairs follows independent Ising anyon fusion in two sectors.

Supersymmetry emerges in the full fusion process.

Feasible differentiation between fusion processes despite local adiabatic mixing.

Abstract

We theoretically investigate the fusion rules of Majorana Kramers pairs in time-reversal-invariant topological superconductors. We find that the fusion of Majorana Kramers pairs is a process that Ising anyons fuse independently in the two distinct time-reversal sectors. Considering the full fusion including the initialization and the fusion, we explore the observation of a supersymmetry that emerges in time-reversal-invariant topological superconductors, and design the schemes for the nontrivial fusion and the trivial fusion to show the non-Abelian statistics of Majorana Kramers pairs. We also show the possible influence of local adiabatic mixing on the fusion and the differentiation between distinct fusion processes remains feasible even in the presence of such mixing. Our proposals are applied in $d_{x^2-y^2}$-wave topological superconductors, and the theoretical framework can be extended to the fusion of multiple Majorana zero modes protected by unitary symmetry.