Exact solutions for a type of electron pairing model with spin-orbit interactions and Zeeman coupling

Abstract

A type of electron pairing model with spin-orbit interactions or Zeeman coupling is solved exactly in the framework of Richardson ansatz. Based on the exact solutions for the case with spin-orbit interactions, it is shown rigorously that the pairing order parameter has always the $p+ip$-wave symmetry regardless of the strength of pairing interaction, justifying an important conclusion obtained by the mean field theory. Analytical results are derived for two simple systems with respectively spin-orbit interactions and Zeeman coupling.

4 pages, minor corrections made. This latest version was submitted to Phys. Rev. Lett

References in corpus (6)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Quantum Spin Hall Effect and Enhanced Magnetic Response by Spin-Orbit Coupling
• Probing non-Abelian statistics of Majorana fermions in ultracold atomic superfluid
• Delocalization of relativistic Dirac particles in disordered one-dimensional systems and its implementation with cold atoms