Fully analytical equation of motion approach for the double quantum dot in the Coulomb blockade regime

TL;DR

This paper presents a fully analytical equation of motion approach to study spectral properties and orbital occupations in an interacting double quantum dot within the Coulomb blockade regime, providing explicit Green's function expressions.

Contribution

The work introduces an analytical solution for the double quantum dot's Green's function, improving understanding of Coulomb interactions and spectral features in equilibrium.

Findings

Analytical Green's function matches numerical methods in spectral peak positions.

Explicit expressions relate spectral properties to Coulomb interactions.

Results are consistent with grand canonical ensemble in uncontacted limit.

Abstract

A fully analytical approach based on the equation of motion technique to investigate the spectral properties and orbital occupations in an interacting double quantum dot in equilibrium is presented. By solving a linear system for the density correlators analytically, an explicit expression for the one body Green's function in terms of local occupations, intra- and inter-dot Coulomb interactions, and the model parameters is derived. In the uncontacted limit, the results coincide with those obtained from the grand canonical ensemble. The analytical results compare favourably with numerical results obtained with the non-crossing approximation and the hierarchical equation of motion methods accurately reproducing peak positions and spectral weight distributions in the Coulomb blockade regime.