Edge effects in graphene nanostructures: II. Semiclassical theory of spectral fluctuations and quantum transport

TL;DR

This paper develops a semiclassical theory to analyze how different edge types influence spectral fluctuations and quantum transport in graphene nanostructures, highlighting the role of edge-induced pseudospin interference and intervalley coupling.

Contribution

It introduces a semiclassical Green's function approach for graphene, deriving analytical expressions for spectral and transport properties considering edge effects, especially pseudospin interference and intervalley scattering.

Findings

Edge characteristics significantly affect spectral correlations and conductance.

Intervalley coupling via armchair edges governs quantum interference effects.

Edge-induced pseudospin interference impacts spectral and transport properties.

Abstract

We investigate the effect of different edge types on the statistical properties of both the energy spectrum of closed graphene billiards and the conductance of open graphene cavities in the semiclassical limit. To this end, we use the semiclassical Green's function for ballistic graphene flakes that we have derived in Reference 1. First we study the spectral two point correlation function, or more precisely its Fourier transform the spectral form factor, starting from the graphene version of Gutzwiller's trace formula for the oscillating part of the density of states. We calculate the two leading order contributions to the spectral form factor, paying particular attention to the influence of the edge characteristics of the system. Then we consider transport properties of open graphene cavities. We derive generic analytical expressions for the classical conductance, the weak localization correction, the size of the universal conductance fluctuations and the shot noise power of a ballistic graphene cavity. Again we focus on the effects of the edge structure. For both, the conductance and the spectral form factor, we find that edge induced pseudospin interference affects the results significantly. In particular intervalley coupling mediated through scattering from armchair edges is the key mechanism that governs the coherent quantum interference effects in ballistic graphene cavities.