Topological Massive Dirac Edge Modes and Long-Range Superconducting Hamiltonians

TL;DR

This paper explores how long-range modifications to the Kitaev chain induce new topological phases, including massive Dirac edge modes, with potential implications for quantum computing.

Contribution

It introduces a novel topological phase with massive Dirac fermions arising from long-range superconducting pairings in the Kitaev chain.

Findings

Long-range couplings enhance topological sectors.

Massive Dirac fermions emerge at the edges.

Fractional topological numbers are observed.

Abstract

We discover novel topological effects in the one-dimensional Kitaev chain modified by long-range Hamiltonian deformations in the hopping and pairing terms. This class of models display symmetry-protected topological order measured by the Berry/Zak phase of the lower band eigenvector and the winding number of the Hamiltonians. For exponentially-decaying hopping amplitudes, the topological sector can be significantly augmented as the penetration length increases, something experimentally achievable. For power-law decaying superconducting pairings, the massless Majorana modes at the edges get paired together into a massive non-local Dirac fermion localised at both edges of the chain: a new topological quasiparticle that we call topological massive Dirac fermion. This topological phase has fractional topological numbers as a consequence of the long-range couplings. Possible applications to current experimental setups and topological quantum computation are also discussed.