Basic variables to be reproduced in the first-principles theory for superconductors: Fluctuation of the particle number

TL;DR

This paper proposes using the diagonal elements of the second-order reduced density matrix, related to particle number fluctuation, as a fundamental variable in a density functional theory for superconductors, offering a new first-principles approach.

Contribution

It introduces a novel density functional scheme for superconductors based on the pair-density, emphasizing particle number fluctuation as a key indicator.

Findings

Diagonal RDM2 elements relate to particle number fluctuation.

Particle number fluctuation can indicate superconductivity.

Proposes a new first-principles theoretical framework.

Abstract

We show that the diagonal elements of the second-order reduced density matrix (RDM2) can be chosen as basic variables for describing the superconducting state, instead of the off-diagonal elements of the RDM2 that are usually adopted as basic variables in the density functional scheme. The diagonal elements of the RDM2 are called pair-density (PD), which is explicitly related to the fluctuation of the particle number of the system. In this paper, we argue that the fluctuation of the particle number can become an indication of the superconducting state, and that the density functional scheme in which the PD is chosen as a basic variable would be a promising first-principles theory for superconductors.