On the Superconductivity of 2D System with Arbitrary Carrier Density in External Magnetic Field

TL;DR

This paper develops self-consistent equations to analyze superconductivity in 2D systems with arbitrary carrier density under magnetic fields, revealing differences in critical field behavior and the existence of inhomogeneous order parameters at high temperatures.

Contribution

It introduces a unified theoretical framework for 2D superconductors across different carrier densities and magnetic fields, highlighting the emergence of inhomogeneous order parameters.

Findings

Derivative of critical magnetic field with respect to temperature differs between low and high carrier densities.

In high magnetic fields, inhomogeneous order parameters can exist at elevated temperatures.

System behavior varies significantly depending on carrier density and magnetic field conditions.

Abstract

Selfconsistent equations which describe the order parameter and chemical potential behaviour in $2D$ metalic system as functions of external magnetic field, $H$, temperature, $T$, and carrier density, $n$, are obtained. It is shown that for the case of the local pairs (low carrier density and negative chemical potential $\mu$) the derivative $dH_{c_2}(T)/dT$ at $T=T_c$ is essentially less then that for the system with Cooper pairs (high carrier density and positive chemical potential $\mu\gg T_c$). It is found that in magnetic field satisfying the quantum limit criterium the system is characterized by non-trivial inhomogeneuos order parameter which can exist at rather high temperatures.