Entanglement entropy and entanglement spectrum of triplet topological superconductors

Abstract

We analyse the entanglement entropy properties of a two-dimensional p-wave superconductor with Rashba spin-orbit coupling, which displays a rich phase-space that supports non-trivial topological phases, as the chemical potential and the Zeeman term are varied. We show that the entanglement entropy and its derivatives clearly signal the topological transitions and provides a sensible signature of each topological phase. We separately analyse the contributions to the entanglement entropy that are proportional to or independent of the perimeter of the system, as a function of the Hamiltonian coupling constants and the geometry of the subsystem. We conclude that both contributions are generically non-universal depending on the specific Hamiltonian parameters and on the particular geometry. Nevertheless, contributions to the entanglement entropy due to different kinds of boundaries or edges simply add up. We also observe a relationship between a topological contribution to the entanglement entropy in a half- cylinder geometry and the number of edge states, and that the entanglement spectrum has robust modes associated with each edge state.

9 pages, 8 figures

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• Magnetic chains on a triplet superconductor
• Analytic Expression for the Entanglement Entropy of a 2D Topological Superconductor
• Entanglement entropy and entanglement spectrum of Bi${}_{1-x}$Sb${}_x$ (111) bilayers
• Disorder-induced topological superconductivity in a spherical quantum-Hall--superconductor hybrid
• The BCS wave function, matrix product states, and the Ising conformal field theory
• Entanglement entropy of a three-spin interacting spin chain with a time-reversal breaking impurity at one boundary
• Entanglement as a topological marker in harmonically confined attractive Fermi-Hubbard chains
• Topological states of generalized dissipative Majorana wires