[Paper Review] Ballistic charge transport in twisted bilayer graphene

Hadi Z. Olyaei, Bruno Amorim+2 more|arXiv (Cornell University)|Jul 28, 2020

Graphene research and applications4 citations

TL;DR

This study investigates ballistic charge transport in twisted bilayer graphene (tBLG) using two geometries: a graphene flake on a ribbon and two overlapping ribbons. It reveals three distinct regimes based on twist angle: strong commensurability effects at large angles, conductance features correlating with Van Hove singularities at intermediate angles, and smooth conductance linked to narrow bands at small angles, where spectral gaps in the density of states correspond to vanishing conductance, consistent with experiments.

ABSTRACT

We study conductance across a twisted bilayer graphene coupled to single-layer graphene leads in two setups: a flake of graphene on top of an infinite graphene ribbon and two overlapping semi-infinite graphene ribbons. We find conductance strongly depends on the angle between the two graphene layers and identify three qualitatively different regimes. For large angles ($θ\gtrsim 10^{\circ}$) there are strong commensurability effects for incommensurate angles the low energy conductance approaches that of two disconnected layers, while sharp conductance features correlate with commensurate angles with small unit cells. For intermediate angles ($3^{\circ}\lesssim θ\lesssim 10^{\circ}$), we find a one-to-one correspondence between certain conductance features and the twist-dependent Van Hove singularities arising at low energies, suggesting conductance measurements can be used to determine the twist angle. For small twist angles ($1^{\circ}\lesssimθ\lesssim 3^{\circ}$), commensurate effects seem to be washed out and the conductance becomes a smooth function of the angle. In this regime, conductance can be used to probe the narrow bands, with vanishing conductance regions corresponding to spectral gaps in the density of states, in agreement with recent experimental findings.

Motivation & Objective

• To understand how twist angle governs ballistic charge transport in tBLG across different geometries.
• To identify distinct transport regimes based on twist angle, particularly in the small-angle regime where flat bands emerge.
• To establish a connection between conductance features and electronic structure, including Van Hove singularities and spectral gaps.
• To validate theoretical predictions against recent experimental findings on transport gaps and insulating states.
• To demonstrate that conductance measurements can serve as a probe for twist angle and electronic correlations in tBLG.

Proposed method

• Numerical tight-binding calculations are used to model tBLG with varying twist angles, incorporating atomic-scale lattice structure and moiré superlattices.
• Conductance is computed using the Landauer-Büttiker formalism for two setups: a flake on a ribbon (1→1) and two overlapping ribbons (1→2).
• The density of states (DOS) and band structure are calculated via diagonalization of the Bloch Hamiltonian to analyze electronic structure.
• Commensurate angles are systematically studied using integer parameters (m,r) in the moiré unit cell definition to identify periodicity effects.
• Influence of edge states and open boundaries is assessed by comparing DOS from scattering region vs. bulk Bloch Hamiltonian.
• Theoretical results are benchmarked against experimental transport data, particularly from Cao et al. (2016, 2018a,b) and Yankowitz et al. (2019).

Experimental results

Research questions

• RQ1 How does the conductance in twisted bilayer graphene depend on the twist angle across different geometries?
• RQ2 To what extent do commensurability effects influence conductance at large twist angles?
• RQ3 Can conductance features at intermediate angles be correlated with Van Hove singularities in the density of states?
• RQ4 How do narrow bands at small twist angles (θ ≲ 3°) affect the conductance, and do they correlate with spectral gaps?
• RQ5 Can conductance measurements be used to infer the twist angle or detect electronic correlations in tBLG?

Key findings

• For large twist angles (θ ≳ 10°), conductance exhibits strong commensurability effects: sharp dips (peaks) in conductance for 1→1 (1→2) geometry occur at commensurate angles with small unit cells, while incommensurate angles show decoupled layer behavior.
• At intermediate angles (3° ≲ θ ≲ 10°), conductance features closely match low-energy Van Hove singularities in the density of states, suggesting conductance as a tool for twist angle determination.
• For small angles (1° ≲ θ ≲ 3°), commensurability effects are washed out, and conductance becomes a smooth function of angle, correlating with the emergence of narrow bands.
• In the small-angle regime, regions of vanishing conductance correspond to spectral gaps in the density of states, consistent with experimental observations of transport gaps at n = ±n_S and n = ±n_S/2.
• Theoretical conductance profiles for θ ≈ 2° match experimental data from Cao et al. (2016) and Yankowitz et al. (2019), supporting the validity of single-particle descriptions away from the first magic angle.
• Edge states in finite scattering regions contribute to non-zero DOS but do not affect conductance, confirming that transport gaps arise from bulk band structure rather than edge effects.