Current-Density Functional Theory for the superconductor

TL;DR

This paper develops a current-density functional theory for superconductors in magnetic fields, defining key variables and deriving an exchange-correlation energy functional to accurately describe equilibrium properties.

Contribution

It introduces a new theoretical framework incorporating current density and order parameter as fundamental variables for superconductors in magnetic fields.

Findings

Derived a rigorous expression for the xc-energy functional.

Proposed an approximate xc functional consistent with the energy gap.

Formulated an effective single-particle equation for equilibrium densities.

Abstract

We present the current-density functional theory for the superconductor immersed in the magnetic field. The order parameter of the superconducting state, transverse component of the paramagnetic current-density, and electron density are chosen as basic variables that uniquely determine the equilibrium properties of the system. In order to construct this theory, the development of the approximate form of the exchange-correlation (xc) energy functional is indispensable as well as the derivation of the effective single-particle equation which makes it possible to reproduce the equilibrium densities mentioned above. The rigorous expression of the xc-energy functional is derived using the technique of the coupling-constant integration. Furthermore, the approximate form of the xc energy functional is proposed such that the energy gap resulting from the effective single-particle equation is consistent with the attractive interaction energy of the system.