Off-diagonal long-range order in the ground state of the Kitaev chain

Abstract

We study a one-dimensional Kitaev model with uniform phase gradient pairing term. We show that the gradient constant dramatically affects the phase diagram, which consists of topologically trivial and nontrivial phases, associated with Majorana edge modes. Based on the exact solution, a Bardeen-Cooper-Schrieffer (BCS)-pair order parameter is introduced to characterize the phase diagram by its value and nonanalytic behavior at phase boundaries. We find that this order parameter obtains its maxima at the triple critical points, at which the pairing phase gradient suppresses the single-particle scattering process due to the coherent destructive interference. In particular, we show that the ground state at such a point possesses exact off-diagonal long-range order (ODLRO), in the thermodynamic limit. Our result provides an example of a gapless $p$-wave superconducting ground state possessing ODLRO.

References in corpus (5)

• Non-Abelian Anyons and Topological Quantum Computation
• Gate-controlled BCS-BEC crossover in a two-dimensional superconductor
• Tuning topological superconductivity in helical Shiba chains by supercurrent
• Majorana Bound States in Double Nanowires with Reduced Zeeman Thresholds due to Supercurrents
• Supercurrent-induced topological phase transitions

Cited by in corpus (3)

• Lifshitz transitions and Weyl semimetals from a topological superconductor with supercurrent flow
• Polarity of the fermionic condensation in the $p$-wave Kitaev model on a square lattice
• Electron density and compressibility in the Kitaev model with a spatially modulated Phase in the superconducting pairing