Exactly solvable pairing model for superconductors with a p+ip-wave symmetry

TL;DR

This paper provides an exact solution for a 2D p+ip-wave superconductor model, revealing a rich phase diagram with topological phases, phase transitions, and a duality relation, advancing understanding of topological superconductivity.

Contribution

It introduces an exact Bethe ansatz solution for the p+ip-wave pairing Hamiltonian and characterizes its topological phases and duality relations.

Findings

Identifies three distinct phases: weak coupling BCS, weak pairing, and strong pairing.

Discovers topologically protected phase boundaries with discontinuous ground-state energy.

Establishes a duality between weak and strong pairing phases via topological order parameters.

Abstract

We present the exact Bethe ansatz solution for the two-dimensional BCS pairing Hamiltonian with p_x + i p_y symmetry. Using both mean-field theory and the exact solution we obtain the ground-state phase diagram parameterized by the filling fraction and the coupling constant. It consists of three phases denoted weak coupling BCS, weak pairing, and strong pairing. The first two phases are separated by a topologically protected line where the exact ground state is given by the Moore-Read pfaffian state. In the thermodynamic limit the ground-state energy is discontinuous on this line. The other two phases are separated by the critical line, also topologically protected, previously found by Read and Green. We establish a duality relation between the weak and strong pairing phases, whereby ground states of the weak phase are "dressed" versions of the ground states of the strong phase by zero energy (Moore-Read) pairs and characterized by a topological order parameter.