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

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.

References in corpus (17)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Reflection symmetric second-order topological insulators and superconductors
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• Measurement-Only Topological Quantum Computation
• Topological States in a One-Dimensional Fermi Gas with Attractive Interactions
• Fusion of Majorana Bound States with Mini-Gate Control in Two-Dimensional Systems
• Majorana Kramers pairs in Rashba double nanowires with interactions and disorder
• Braiding by Majorana Tracking and Long-Range CNOT Gates with Color Codes
• Local Adiabatic Mixing of Kramers Pairs of Majorana Bound States
• Double Majorana vortex zero modes in superconducting topological crystalline insulators with surface rotation anomaly
• Manipulation of Majorana Kramers Qubit and its Tolerance in Time-Reversal-Invariant Topological Superconductor
• Survival of the fractional Josephson effect in time-reversal-invariant topological superconductors
• Unitary Symmetry-Protected Non-Abelian Statistics of Majorana Modes