Transport through a finite Hubbard chain connected to reservoirs

TL;DR

This paper analytically studies the zero-temperature conductance of a finite Hubbard chain connected to leads, revealing oscillatory behavior and perfect transmission for odd N due to Kondo resonance.

Contribution

It provides an analytical calculation of the conductance in a finite Hubbard chain at T=0, highlighting the role of electron-hole symmetry and Kondo effects for different chain lengths.

Findings

Perfect transmission for odd N due to Kondo resonance.

Oscillatory conductance behavior as a function of N.

Conductance decreases with N and U for even N.

Abstract

The dc conductance through a finite Hubbard chain of size N coupled to two noninteracting leads is studied at T = 0 in an electron-hole symmetric case. Assuming that the perturbation expansion in U is valid for small N (=1,2,3,...) owing to the presence of the noninteracting leads, we obtain the self-energy at \omega = 0 analytically in the real space within the second order in U. Then, we calculate the inter-site Green's function which connects the two boundaries of the chain, G_{N1}, solving the Dyson equation. The conductance can be obtained through G_{N1}, and the result shows an oscillatory behavior as a function of N. For odd N, a perfect transmission occurs independent of U. This is due to the inversion and electron-hole symmetries, and is attributed to a Kondo resonance appearing at the Fermi level. On the other hand, for even N, the conductance is a decreasing function of N and U.