Topological quantum phase transitions in the spin–singlet superconductor with Rashba and Dresselhaus (110) spin–orbit couplings

2013/06/11 by Jia-Bin You, Jiabin You, A. H. Chan +2
Physics and Astronomy · #Advanced Condensed Matter Physics #Condensed matter physics #Fermion #Hamiltonian (control theory) #Invariant (physics) #MAJORANA #Pfaffian #Physics #Quantum many-body systems #Quantum mechanics #Superconductivity #Topological Materials and Phenomena #Topology (electrical circuits) #Winding number #cond-mat.str-el #cond-mat.supr-con

paper · pdf · doi:10.1016/j.aop.2014.06.009

arxiv created 2013/06/11 · openalex publication_date 2014/06/25 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We examine the topological properties of a spin-singlet superconductor with Rashba and Dresselhaus (110) spin-orbit couplings. We demonstrate that there are several topological invariants in the Bogoliubov-de Gennes (BdG) Hamiltonian by symmetry analysis. We use the Pfaffian invariant P for the particle-hole symmetry to demonstrate all the possible phase diagrams of the BdG Hamiltonian. We find that the edge spectrum is either Dirac cone or flat band which supports the emergence of the Majorana fermion in this system. For the Majorana flat bands, a higher symmetric BdG Hamiltonian is needed to make them topologically stable. The Pfaffian invariant P(k_y) and the winding number W(k_y) are used in determining the location of the Majorana flat bands.

Citations

• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Helical liquids and Majorana bound states in quantum wires
• Edge state in graphene ribbons: Nanometer size effect and edge shape dependence
• Non-Abelian Anyons and Topological Quantum Computation
• Unpaired Majorana fermions in quantum wires