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Topological superconductivity in a one-dimensional s+p-wave Kitaev chain: Particle current and localization of Majorana modes

Ali Ashtari and Ali Khademi*

  • *Contact author: khademi@sharif.edu
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Phys. Rev. B 114, 084506 – Published 17 August, 2026

DOI: https://doi.org/10.1103/pls3-5829

Abstract

We investigate the topological properties and phase diagrams of a one-dimensional Kitaev chain with spin-orbit coupling, subject to an external magnetic field, and hosting coexisting singlet s-wave and triplet p-wave pairings. To drive the system out of equilibrium, we introduce a phase in the hopping parameter that accounts for a uniform particle current. Using symmetry analysis, we identify the conditions under which the system belongs to the topological class BDI with a Z invariant. Breaking chiral symmetry by introducing the particle current reduces the classification to topological class D with a Z2 invariant. We calculate the winding number for class BDI and the Pfaffian invariant for class D to obtain the corresponding phase diagrams. In addition, we compute the energy spectrum for class D to determine the phase boundaries analytically, and employ the real-space formulation to numerically obtain the Majorana number maps and verify the analytical results. Our findings highlight how mixed pairing channels and current-induced symmetry breaking enrich the landscape of one-dimensional topological superconductivity and provide new insights into the stability of Majorana modes under nonequilibrium conditions.

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Phys. Rev. B 114, 084506– Published 17 August, 2026
  • Received 25 February 2026
  • Revised 24 May 2026
  • Accepted 23 June 2026
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