Braiding Majorana corner modes in a second-order topological superconductor

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.Comment: A different physical system is considered in this version (topological superconductor), however, the topological and symmetry features are closely related to those of the two-layer topological insulator of version 2 (arXiv:1904.07822v2). A more accurate distinction is made between the fractional statistics of the Majorana corner states and their potential non-Abelian propertie

Braiding Majorana corner modes in a two-layer second-order topological insulator

The recent advances in the field of topological materials have established a novel understanding of material physics. Besides theoretical achievements, a number of proposals for decoherence-protected topological quantum computation were provided. It is, however, a yet unanswered question, what material could be the most feasible candidate in engineering the building blocks of a quantum computer (qubits). Here we propose a possible answer by describing a device based on a two-dimensional second-order topological insulator with particle-hole symmetry (PHS). This material has one-dimensional boundaries, but exhibits two zero-dimensional Majorana quasiparticles localized at the corners of a square-shaped sample. The two states reside at zero energy as long as PHS is conserved, whereas their corner-localization can be adjusted by in-plane magnetic fields. We consider an adiabatic cycle performed on the degenerate ground-state manifold and show that it realizes the braiding of the two zero-energy corner modes. We find that each zero-mode accumulates a non-trivial statistical phase π within a cycle, which confirms that, indeed, PHS ensures non-Abelian Majorana excitation braiding in the proposed device. The fractional statistics of the corner states opens the possibility to perform logical operations and, ultimately, might enable building robust qubits for large scale implementations. We also suggest possible paths for experimental realizations of this proposal