Seminários

   The bloom of a variety of Hall effects (charge, spin, valley, ...) in the condensed-matter community is one of the driving forces propelling new discoveries in the field. To address these effects, experimentalists usually need samples with four- or six-terminal geometries to measure the transverse voltages and resistances.

The theoretical study of such systems with realistic sizes and disorder demands the use of numerical methods that are fast and able to treat multi-terminals.

In this talk, I discuss recent developments to both two- and multi-terminal electronic transport methods based on Green's functions. First, I discuss the use of nonlinear transport concepts to investigate the Hall voltage dependence on the model parameters from the difference between the two-terminal injectivities. I illustrate the proposed idea by studying the quantum spin Hall effect in graphene with disordered spin-orbit scattering centers induced by adatoms. In what follows I present a multi-probe recursive Green’s function (MPRGF) method that generalizes and improves the previous multi-terminal developments. The power of the method is illustrated by calculating longitudinal and Hall resistances for graphene in the quantum Hall regime using a Hall-bar geometry with six terminals. If time allows, in the last part of the presentation, I will discuss the inclusion of electron-electron interactions via mean field in the MPRGF method, which will lead to the state-of-the-art electronic transport method.