On the theory of two-dimensional materials with tilted Dirac cones

Abstract

The electronic quasiparticles in graphene behave as massless relativistic fermions which are governed by the Dirac equation and described by two inequivalent Dirac cones or valleys within the electronic band structure. Beyond graphene, there is an emerging class of materials in which the Dirac cones are tilted within the band structure; this tilt appears as an additional term to the Dirac equation that profoundly impacts the physical properties of these materials. In this thesis, we investigate two prospective tilted Dirac cone systems, explore the fundamental optical and optovalleytronic properties of tilted Dirac cone materials, and study the effects of external magnetic fields and application of electrostatic waveguides.

We begin by investigating the emergence of gapless and gapped tilted Dirac cones in two systems: an electrostatically gated bipolar array in graphene and a planar array of quasi-metallic carbon nanotubes. In particular, we demonstrate that the tilt and band gap of the Dirac cones in a bipolar graphene superlattice can be tuned after device fabrication by varying the applied gate voltages. The ability to modify the geometry of Dirac cones provides a route to tune the emergent electronic and optical properties of the system via band structure engineering.

One of graphene’s most well-known properties is its universal sheet absorption in which 2.3% of light passing through the monolayer is absorbed. In stark contrast to graphene, we show that tilted Dirac cone materials will preferentially absorb certain polarisations of light more than others thus finding application as thin-film polarisers. We also demonstrate that illuminating tilted Dirac cone materials results in the spatial separation of carriers according to their valley occupation number. This mechanism of optovalleytronics does not require an electronic band gap and thus combines optical valley control with the exceptional graphene-like transport properties of gapless Dirac materials. We then study the behaviour of tilted and gapped Dirac cone materials in the presence of magnetic fields, investigating the formation of Landau levels. In the case of the bipolar array, electronic control over the Dirac cone geometry leads to a gate-tunable Landau level spectra. Lastly, we investigate one-dimensional electrostatic waveguides applied to tilted Dirac cone materials, comparing the properties of one-dimensional square wells and experimentally-viable smooth waveguides.