Electron-electron interaction and electron-hole asymmetry in bilayer graphene (Supporting Materials)

TL;DR

This study measures the effective mass in bilayer graphene, revealing electron-hole asymmetry, band hyperbolicity, and strong electron-electron interaction effects through precise experimental and theoretical analysis.

Contribution

It provides the first detailed experimental quantification of electron-hole asymmetry and electron-electron interaction effects on effective mass in bilayer graphene.

Findings

Effective masses increase with density, showing band hyperbolicity.

Hole mass is 20-30% larger than electron mass.

Strong renormalization effects due to electron-electron interactions are observed.

Abstract

We report precision measurements of the effective mass m* in high-quality bilayer graphene using the temperature dependence of the Shubnikov-de Haas oscillations. In the density range of 0.7 x 10^12/cm^2 < n < 4.1 x 10^12 /cm^2, both the hole mass m*_h and the electron mass m*_e increase with increasing density, demonstrating the hyperbolic nature of the bands. The hole mass m*_h is approximately 20-30% larger than the electron mass m*_e. Tight-binding calculations provide a good description of the electron-hole asymmetry and yield an accurate measure of the inter-layer hopping parameter v_4 = 0.063. Both m*_h and m*_e are substantially suppressed compared to single-particle values, providing clear and unprecedented evidence for the strong renormalization effect of electron-electron interaction in the band structure of bilayer graphene.