The two dimensional Hubbard model:a theoretical tool for molecular electronics

TL;DR

This paper introduces the two-dimensional Hubbard model as a theoretical framework for molecular electronics, demonstrating its application in calculating electrical conductivity in planar systems like graphene and rectangular lattices.

Contribution

It presents the 2D Hubbard model as a practical tool for molecular electronics and shows how to compute conductivity without full Hamiltonian formalism, including applications to graphene.

Findings

Electrical conductivity of a rectangular lattice can be calculated without the 2D Hamiltonian.

Graphene's conductivity can be derived from a reformulated 1D Hubbard model.

The 2D Hubbard model is suitable for describing certain molecular electronic systems.

Abstract

When speaking about molecular electronics, the obvious question which occurs is how does one study it theoretically. The simplest theoretical model suitable for application in molecular electronics is the two dimensional Hubbard model. The aim of the present paper is to introduce this model, and give some examples of the systems which it can describe. After a short mathematically oriented discussion, it will be shown how to calculate the electrical conductivity of a particular planar system: a rectangular lattice with mutually independent conductivities along the two axes,but without using the 2D Hamiltonian. This system could find applications in high Tc studies. It will finally be shown that the electrical conductivity of graphene can be determined not by using the full formalism of the $2D$ Hubbard model, but by a slight reformulation of the Hamiltonian of the 1D Hubbard model