Electron-hole asymmetry and band gaps of commensurate double moire patterns in twisted bilayer graphene on hexagonal boron nitride

TL;DR

This paper investigates how commensurate double moire patterns in twisted bilayer graphene on hexagonal boron nitride influence electronic properties, revealing electron-hole asymmetry, band gap evolution, and topological features relevant for optical and electronic applications.

Contribution

It classifies double moire patterns in tBG/BN, analyzes their electronic band structures, and explores the effects of substrate and sliding vectors on band narrowing and topological properties.

Findings

Finite valley Chern numbers $\u00b1 1$ in certain parameter regimes.

Weak impact of BN substrate on local density of states in flat bands.

Potential to achieve narrow, isolated band bundles at small twist angles.

Abstract

Spontaneous orbital magnetism observed in twisted bilayer graphene (tBG) on nearly aligned hexagonal boron nitride (BN) substrate builds on top of the electronic structure resulting from combined G/G and G/BN double moire interfaces. Here we show that tBG/BN commensurate double moire patterns can be classified into two types, each favoring the narrowing of either the conduction or valence bands on average, and obtain the evolution of the bands as a function of the interlayer sliding vectors and electric fields. Finite valley Chern numbers $\pm 1$ are found in a wide range of parameter space when the moire bands are isolated through gaps, while the local density of states associated to the flat bands are weakly affected by the BN substrate invariably concentrating around the AA-stacked regions of tBG. We illustrate the impact of the BN substrate for a particularly pronounced electron-hole asymmetric band structure by calculating the optical conductivities of twisted bilayer graphene near the magic angle as a function of carrier density. The band structures corresponding to other $N$-multiple commensurate moire period ratios indicate it is possible to achieve narrow width $W \lesssim 30$ meV isolated folded band bundles for tBG angles $\theta \lesssim 1^{\circ}$.