Superconductivity on a M\"obius strip: numerical studies on order parameter and quasiparticles

TL;DR

This paper numerically investigates superconducting states on a M"obius strip, analyzing order parameters and quasiparticles using Ginzburg-Landau and Bogoliubov-de Gennes theories, revealing phase diagrams, metastable states, and zero-energy bound states.

Contribution

It provides a comprehensive numerical study of superconductivity on a M"obius strip, including phase diagrams and microscopic quasiparticle states, which was not previously explored in detail.

Findings

Confirmed phase diagram of superconducting states on M"obius strip with magnetic flux.

Identified metastable and nonequilibrium states during magnetic field variation.

Demonstrated existence of zero-energy bound states in the nodal superconducting state.

Abstract

Superconducting states of an anisortopic s-wave superconductor on a M\"obius strip are studied numerically based on the Ginzburg-Landau theory and the Bogoliubov-de Gennes theory. In both, the equations are solved numerically on discitized lattice and the nonlinearity and the self-consistency are fully taken into account. First, we study the superconducting states on the M\"obius strip in the presence of the Aharonov-Bohm flux threading the ring by employing the Ginzburg-Landau theory, and confirm the phase diagram previously proposed by Hayashi and Ebisawa [J. Phys. Soc. Jpn. {\bf 70}, 3495 (2002)]. The metastable states as well as the equilibrium energy state are studied and the nonequiriblium processes when the magnetic field is varied at a fixed temperature are discussed. Next, we study the microscopic superconducting states on the M\"obius strip based on the Bogoliubov-de Gennes theory, especially focusing on the state with a real-space node in the superconducting gap, which is expected to appear when the flux threading the ring is half the superconducting flux quantum. The local density of states in this {\it nodal state} is calculated in detail and the existence of the zero-energy bound states is shown.