Superconductivity of Quasi-One and Quasi-Two Dimensional Tight-Binding Electrons in Magnetic Field

TL;DR

This paper investigates the upper critical magnetic field and superconducting transition behavior of tight-binding electrons in quasi-one and quasi-two dimensional lattices, revealing deviations from previous models and oscillatory effects in transition temperature.

Contribution

It presents new analysis of the critical field and transition temperature in tight-binding electron systems under magnetic fields, accounting for previously neglected hopping effects.

Findings

Transition lines in quasi-one dimensional systems deviate from earlier models.

Transition temperature oscillates and approaches the zero-field value in strong magnetic fields.

Superconductivity persists and exhibits unique behavior in quasi-two dimensional systems.

Abstract

The upper critical field $H_{c2}(T)$ of the tight-binding electrons in the three-dimensional lattice is investigated. The electrons make Cooper pairs between the eigenstates with the same energy in the strong magnetic field. The transition lines in the quasi-one dimensional case are shown to deviate from the previously obtained results where the hopping matrix elements along the magnetic field are neglected. In the absence of the Pauli pair breaking the transition temperature $T_c(H)$ of the quasi-two dimensional electrons is obtained to oscillationally increase as the magnetic field becomes large and reaches to $T_c(0)$ in the strong field as in the quasi-one dimensional case.