Strained graphene Hall bar

Numerical quasiconformal transformations for electron dynamics on strained graphene surfaces

The dynamics of low-energy electrons in general static strained graphene surface is modelled mathematically by the Dirac equation in curved space-time. In Cartesian coordinates, a parametrization of the surface can be straightforwardly obtained, but the resulting Dirac equation is intricate for general surface deformations. Two different strategies are introduced to simplify this problem: the diagonal metric approximation and the change of variables to isothermal coordinates. These coordinates are obtained from quasiconformal transformations characterized by the Beltrami equation, whose solution gives the mapping between both coordinate systems. To implement this second strategy, a least-squares finite-element numerical scheme is introduced to solve the Beltrami equation. The Dirac equation is then solved via an accurate pseudospectral numerical method in the pseudo-Hermitian representation that is endowed with explicit unitary evolution and conservation of the norm. The two approaches are compared and applied to the scattering of electrons on Gaussian shaped graphene surface deformations. It is demonstrated that electron wave packets can be focused by these local strained regions.

Quantum Hall Response to Time-Dependent Strain Gradients in Graphene

Mechanical deformations of graphene induce a term in the Dirac Hamiltonian that is reminiscent of an electromagnetic vector potential. Strain gradients along particular lattice directions induce local pseudomagnetic fields and substantial energy gaps as indeed observed experimentally. Expanding this analogy, we propose to complement the pseudomagnetic field by a pseudoelectric field, generated by a time-dependent oscillating stress applied to a graphene ribbon. The joint Hall-like response to these crossed fields results in a strain-induced charge current along the ribbon. We analyze in detail a particular experimental implementation in the (pseudo)quantum Hall regime with weak intervalley scattering. This allows us to predict an (approximately) quantized Hall current that is unaffected by screening due to diffusion currents.