Abstract
We propose the concept of a device based on a square-shaped sample of a two-dimensional second-order topological helical superconductor which hosts two zero-dimensional Majorana quasiparticles at the corners. The two zero-energy modes rely on particle-hole symmetry (PHS) and their spacial position can be shifted by rotating an in-plane magnetic field and tuning proximity-induced spin-singlet pairing. We consider an adiabatic cycle performed on the degenerate ground-state manifold and show that it realizes the braiding of the two modes whereby they accumulate a non-trivial statistical phase $\pi$ within one cycle. Alongside with the PHS-ensured operator algebra, the fractional statistics confirms the Majorana nature of the zero-energy excitations. A schematic design for a possible experimental implementation of such a device is presented, which could be a step towards realizing non-Abelian braiding.
Highlights
Standard d-dimensional topological insulators and superconductors have a gapped bulk spectrum and exhibit conducting surface states in (d − 1) dimensions [1,2,3,4,5,6,7,8]
The two zero-energy modes rely on particle-hole symmetry (PHS) and their spatial position can be shifted by rotating an in-plane magnetic field and tuning proximity-induced spin-singlet pairing
Possible topological phases protected by discrete crystalline symmetries were studied [12,13,14,15,16,17,18,19,20,21,22,23,24] and, lastly, another class of exotic noninteracting topological phases was discovered, namely the second-order topological insulators (SOTIs) and superconductors (SOTSs) [25,26,27,28,29,30,31]
Summary
Pahomi ,1,* Manfred Sigrist, and Alexey A. We propose the concept of a device based on a square-shaped sample of a two-dimensional second-order topological helical superconductor which hosts two zero-dimensional Majorana quasiparticles at the corners. The two zero-energy modes rely on particle-hole symmetry (PHS) and their spatial position can be shifted by rotating an in-plane magnetic field and tuning proximity-induced spin-singlet pairing. We consider an adiabatic cycle performed on the degenerate ground-state manifold and show that it realizes the braiding of the two modes whereby they accumulate a nontrivial statistical phase π within one cycle. Alongside the PHS-ensured operator algebra, the fractional statistics confirms the Majorana nature of the zero-energy excitations. A schematic design for a possible experimental implementation of such a device is presented, which could be a step towards realizing non-Abelian braiding
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