Edge insulating topological phases in a two-dimensional long-range superconductor

TL;DR

This paper investigates a two-dimensional long-range superconductor, revealing novel topological phases with unique edge modes and entropy properties, expanding understanding of topological matter beyond short-range interactions.

Contribution

It introduces new long-range topological phases in a 2D superconductor, characterized by semi-integer Chern numbers and edge modes with nonzero mass, not connected to short-range phases.

Findings

Long-range pairing induces new topological phases.

Violation of the area law for Von Neumann entropy.

Presence of massive edge modes with no single-fermion edge conductivity.

Abstract

We study the zero-temperature phase diagram of a two dimensional square lattice loaded by spinless fermions, with nearest neighbor hopping and algebraically decaying pairing. We find that for sufficiently long-range pairing, new phases, not continuously connected with any short-range phase, occur, signaled by the violation of the area law for the Von Neumann entropy, by semi-integer Chern numbers, and by edge modes with nonzero mass. The latter feature results in the absence of single-fermion edge conductivity, present instead in the short- range limit. The definition of a topology in the bulk and the presence of a bulk-boundary correspondence is still suggested for the long-range phases. Recent experimental proposals and advances open the stimulating possibility to probe the described long-range effects in next-future realistic set-ups.