Analytic expression for the entanglement entropy of a two-dimensional topological superconductor

Abstract

We study a model of two dimensional, topological superconductivity on a square lattice. The model contains hopping, spin orbit coupling and a time reversal symmetry breaking Zeeman term. This term, together with the chemical potential act as knobs that induce transitions between trivial and topological superconductivity. As previously found numerically, the transitions are seen in the entanglement entropy as cusps as a function of model parameters. In this work we study the entanglement entropy analytically by keeping only its most important components. Our study is based on the intuition that the number of Fermi surfaces in the system controls the topological invariant. With our approximate expression for the entanglement entropy we are able to extract the divergent entanglement entropy derivative close to the phase transition.

Flat bands and entanglement in the Kitaev ladder

“…Each degenerate state contributes an amount ln 2 to entanglement entropy and so the magnitude of the jump in S h is ln 2 times the degeneracy at the band-crossing point in question. It can be seen that the derivative [51] of entanglement entropy nicely captures this feature. The staircase structure starts at t = 2t − µ and saturates at t = 2t + µ.…”

Proximity-Induced Magnetism in a Topological Insulator/Half-Metallic Ferromagnetic Thin Film Heterostructure

“…Figure 4c shows that the resistivity of pure Bi2Se3 thin films varied with temperature The Bi 2 Se 3 samples with deposition time t = 3 min exhibited complete insulation behavior in the whole measured temperature range, which was likely due to much stronger scattering from disorder and porosity [39]. These three samples (t ≥ 5 min) showed a metallic R vs T due to the existence of Se vacancies, as shown in Figure 4b [29].…”