Weak Localization of Dirac Fermions in Graphene

TL;DR

This paper investigates how weak localization affects the electrical conductivity of Dirac fermions in graphene, considering factors like impurities, temperature, and sample size, and compares findings with experimental data.

Contribution

It provides a detailed analysis of weak localization effects in graphene, incorporating electron-electron interactions and sample size, which advances understanding of quantum interference in Dirac materials.

Findings

Weak localization occurs in large, doped graphene samples.

Sample size influences the strength of localization, diminishing at micron scales.

The calculated minimum conductivity aligns with experimental observations.

Abstract

In the presence of the charged impurities, we study the weak localization (WL) effect by evaluating the quantum interference correction (QIC) to the conductivity of Dirac fermions in graphene. With the inelastic scattering rate due to electron-electron interactions obtained from our previous work, we investigate the dependence of QIC on the carrier concentration, the temperature, the magnetic field and the size of the sample. It is found that WL is present in large size samples at finite carrier doping. Its strength becomes weakened/quenched when the sample size is less than a few microns at low temperatures as studied in the experiments. In the region close to zero doping, the system may become delocalized. The minimum conductivity at low temperature for experimental sample sizes is found to be close to the data.