Calculation of Band Structure Using Local Sampling and Green's Functions

TL;DR

This paper introduces a novel band structure calculation method combining Green's functions and local sampling, offering a potentially efficient alternative to traditional ab-initio approaches for materials like Silicon, Germanium, and Graphene.

Contribution

The paper presents a new approach that uses local sampling and Green's functions to compute band structures, incorporating multipole expansion and Fourier transform techniques.

Findings

Accurate band structures for Silicon, Germanium, and Graphene.

Reduced computational time with low-order local analysis.

Good agreement with ab-initio non-local pseudopotential results.

Abstract

A new method for calculation of band structure has been proposed based on the Green's function theory and local sampling. Potential energy in the Hamiltonian of Schrodinger's equation is approximated with a series of sampled Dirac delta functions weighted by appropriate factors. These factors are found from multipole expansion of atomic potentials in the crystal lattice, with considering effects such as screening. Fourier transform was then applied to describe the wave function in reciprocal space. Sampling can be uniform or non-uniform throughout space; however rate and interval optimization is essential. Theory was implemented for Silicon, Germanium and Graphene sheet individually, while results were compared with the ab-initio non-local pseudopotential (AINLPS) method. Also for Silicon, the pseudopotential used in orbital-free density functional theory (OF-DFT) was employed as a suitable sampling source. Phase variations of the dispersion formula are analyzed, introducing adapting parameters to improve compatibility with ab-initio results. Local analysis with low order truncation in real space, reduces implementation time while giving acceptable results.