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

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Developing novel materials and metamaterials with "designer" spectra for electrons, photons, magnons and phonons is the growing trend in contemporary condensed matter physics. The tide of research is turning towards theoretical predictions followed by experimental observations of exotic quasiparticles in solid state systems such as Weyl and Majorana fermions. Since the 1980's, two-dimensional (2D) systems provided a particularly rich playground for the discovery of new quasiparticles, including fractionally charged anyons in quantum Hall systems and massless Dirac fermions in graphene and topological insulators as the most spectacular examples. Simultaneously, the most recent advances in nanotechnology include the development of van der Waals heterostructures (artificial few-layer materials held by van der Waals forces) and finding a way of producing carbon nanotubes of selected chirality. The proposed theoretical PhD research will focus on the electronic properties of a novel designer 2D van der Waals material formed by a planar regular array of single-walled carbon nanotubes. Single-walled carbon nanotubes are long cylindrical molecules with electronic properties defined entirely by the way they are rolled from a graphene sheet. Namely, they can be semiconducting with a bandgap up to several electron-volts, metallic without any bandgap or quasi-metallic with a tiny bandgap of a few meV induced by curvature effects. Combining the tubes in a regular planar array should result in a strongly anisotropic dispersion of the emerging 2D quasiparticles. The most interesting results are expected for arrays of metallic and quasi-metallic nanotubes for which the motion normal to the nanotube axis will result in the most dramatic changes in the electronic properties. In particular, a bandgap may be opened in an array of metallic tubes or collapse for quasi-metallic nanotubes. The motion normal to the tube axis will also result in lifting the valley degeneracy in highly-symmetric zigzag nanotubes leading to tilted Dirac cones supporting a new type of 2D Weyl fermions with hyperbolic dispersion. An analytic description of the peculiar low-energy electronic dispersion (dependence of energy on the 2D momentum) in this system will be at the core of the proposed research. We will study a plethora of unique physical effects stemming from this dispersion including unusual magneto-transport phenomena and interband dipole transitions, which are expected to be in the highly sought-after terahertz frequency range.