Modified Dirac Hamiltonian for Efficient Quantum Mechanical Simulations of Micron Sized Devices

TL;DR

This paper introduces a modified Dirac Hamiltonian with an added quadratic term that effectively solves the Fermion Doubling problem, enabling faster and accurate quantum simulations of micron-sized Dirac fermion devices like graphene.

Contribution

The paper presents a new modified Dirac Hamiltonian that reduces computational complexity and improves efficiency for simulating systems with massless Dirac fermions.

Findings

Hamiltonian matrix is significantly smaller and more efficient for numerical simulations.

Accurate simulation of transport phenomena in graphene using the modified Hamiltonian.

Applicable to other systems with massless Dirac fermions such as Topological Insulators.

Abstract

Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian circumvents this problem. We show that the modified Hamiltonian with the additional term results in a very small Hamiltonian matrix when discretized on a real space square lattice. The resulting Hamiltonian matrix is considerably more efficient for numerical simulations without sacrificing on accuracy and is several orders of magnitude faster than the atomistic tight binding model. Using this Hamiltonian and the Non-Equilibrium Green's Function (NEGF) formalism, we show several transport phenomena in graphene, such as magnetic focusing, chiral tunneling in the ballistic limit and conductivity in the diffusive limit in micron sized graphene devices. The modified Hamiltonian can be used for any system with massless Dirac fermions such as Topological Insulators, opening up a simulation domain that is not readily accessible otherwise.