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

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.

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• Long-Range Free Fermions: Lieb-Robinson Bound, Clustering Properties, and Topological Phases
• Staircase to Higher-Order Topological Phase Transitions
• Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications
• Topological quantum phase transitions and criticality in a longer-range Kitaev chain
• Bound state dynamics in the long-range spin-$\frac{1}{2}$ XXZ model
• Effects of geometric frustration in Kitaev chains
• Topological quantum optical states in quasiperiodic cold atomic chains
• Effective Long-Range Pairing and Hopping in Topological Nanowires Weakly Coupled to $s$-Wave Superconductors
• Edge states, Majorana fermions and topological order in superconducting wires with generalized boundary conditions
• Resilience of topological superconductivity under particle current
• Interacting spinless fermions on the square lattice: Charge order, phase separation, and superconductivity
• Can multipartite entanglement be characterized by two-point connected correlation functions ?
• Solvable 2D superconductors with l-wave pairing
• Band twisting and resilience to disorder in long-range topological superconductors