Interlayer Transport through a Graphene / Rotated-Boron-Nitride / Graphene Heterostructure

TL;DR

This paper investigates how the misorientation angle in a graphene/h-BN/graphene heterostructure affects interlayer electron transport, revealing different mechanisms in small and large angles through theoretical models.

Contribution

It introduces a comparative analysis of transport mechanisms in heterostructures at varying angles using two models, highlighting the role of Umklapp processes at small angles and bandgap effects at large angles.

Findings

Resistance increases with angle, peaking at 30°.

Umklapp processes create non-monotonic resistance features at small angles.

High bias induces additional current peaks due to Umklapp processes.

Abstract

Interlayer electron transport through a graphene / hexagonal boron-nitride (h-BN) / graphene heterostructure is strongly affected by the misorientation angle $\theta$ of the h-BN with respect to the graphene layers with different physical mechanisms governing the transport in different regimes of angle, Fermi level, and bias. The different mechanisms and their resulting signatures in resistance and current are analyzed using two different models, a tight-binding, non-equilibrium Green function model and an effective continuum model, and the qualitative features resulting from the two different models compare well. In the large-angle regime ($\theta > 4^\circ$), the change in the effective h-BN bandgap seen by an electron at the $K$ point of the graphene causes the resistance to monotonically increase with angle by several orders of magnitude reaching a maximum at $\theta = 30^\circ$. It does not affect the peak-to-valley current ratios in devices that exhibit negative differential resistance. In the small-angle regime ($\theta < 4^\circ$), Umklapp processes open up new conductance channels that manifest themselves as non-monotonic features in a plot of resistance versus Fermi level that can serve as experimental signatures of this effect. For small angles and high bias, the Umklapp processes give rise to two new current peaks on either side of the direct tunneling peak.