Abstract

Multilayer transistors based on graphene and other van der Waals crystals exhibit interesting physical properties, high on-off current switching ratios, mechanical flexibility and resonant tunnelling with gate voltage-tuneable negative differential conductance at room temperature [1-3]. In these devices, we have recently demonstrated the strong sensitivity of in-plane momentum conserving tunnel transitions to any small misalignment or twist angle between the crystalline lattices of the two graphene electrodes [4]. Following a brief review of this recent work, we will present new results which investigate the effect of a magnetic field applied perpendicular to the graphene layers on the current-voltage characteristics of devices in which the graphene lattices are carefully aligned to within 1 degree. The magnetic field quantises the electronic states in the conical, gapless conduction and valence bands into a ladder of unequally-spaced Landau levels.

Tunnelling of electrons between the Landau levels of the two graphene electrodes gives rise to a complex pattern of sharp resonant peaks in the differential conductance (dI/dV). To analyse these data, we use a Bardeen transfer Hamiltonian approach which incorporates the two-component spinor-spatial character of the Dirac-Weyl fermions. We demonstrate how the intensity of the energy- and momentum- conserving tunnel transitions reveal the effects of chirality [5], which is a unique feature of electron dynamics in graphene and related materials.

[1] L. Britnell et al., Science 335, 947 (2012). [2] T. Georgiou et al., Nature Nanotechnology 2, 100 (2013). [3] L. Britnell et al., Nature Communications 4, 1794 (2013). [4] A. Mishchenko et al., Nature Nanotechnology 9, 808 (2014). [5] M. Greenaway et al., Nature Physics 11, 1057 (2015).