Cooper-pair transport through a Hubbard chain sandwiched between two superconductors: Density matrix renormalization group calculations

TL;DR

This paper introduces a numerical method using DMRG to analyze Cooper pair transport in a Hubbard chain between superconductors, highlighting the importance of contacts for perfect Andreev reflection and validating results with Bethe Ansatz.

Contribution

It develops a novel DMRG-based approach to measure pair transport and superfluid weight in open Hubbard chains, aligning with Bethe Ansatz predictions.

Findings

Effective superfluid weight matches Bethe Ansatz results.

Contacts significantly influence Andreev reflection.

Method enables detailed study of Cooper pair transport.

Abstract

We present a numerical approach to study the coherent transport of Cooper pairs through a Hubbard chain, and study the role of the contacts in achieving perfect Andreev reflection. We calculate the pair transport using the Density Matrix Renormalization Group by measuring the response of the system to quantum pair fields with complex phases on the two ends of an open system. This approach gives an effective superfluid weight which is in close agreement with the Bethe Ansatz results for the superfluid weight for closed Hubbard rings.