Electronic Structure of Bilayer Graphene: A Real-space Green's Function Study

TL;DR

This paper derives an analytical real-space Green's function for bilayer graphene, revealing spatial anisotropy and predicting local density of states features that align with experimental STM observations, including vacancy effects.

Contribution

It provides the first analytical real-space Green's function for bilayer graphene and explores vacancy-induced LDOS interference patterns.

Findings

Green's function exhibits three-fold rotational symmetry.

LDOS features match STM observations at low bias.

Vacancy-induced interference patterns depend on symmetry.

Abstract

In this paper, a real-space analytical expression for the free Green's function (propagator) of bilayer graphene is derived based on the effective-mass approximation. Green's function displays highly spatial anisotropy with three-fold rotational symmetry. The calculated local density of states (LDOS) of a perfect bilayer graphene produces the main features of the observed scanning tunneling microscopy (STM) images of graphite at low bias voltage. Some predicted features of the LDOS can be verified by STM measurements. In addition, we also calculate the LDOS of bilayer graphene with vacancies by using the multiple-scattering theory (scatterings are localized around the vacancy of bilayer graphene). We observe that the interference patterns are determined mainly by the intrinsic properties of the propagator and the symmetry of the vacancies.