Quasi-local quantum mechanics for disordered 2D electron gases at high magnetic fields
Thierry Champel, Université Joseph Fourier
We have developed a semicoherent-state Green’s function formalism which rigorously describes quantum mechanical motion of an electron in a perpendicular magnetic field and a 2D disordered potential landscape beyond the semi-classical guiding center picture. Our general technique is connected to the deformation (Weyl) quantization theory in phase space developed in mathematical physics. For generic 2D quadratic potentials, we exactly solve the limit of large cyclotron frequency (yet at finite magnetic length) where Landau level mixing becomes negligible, both for the ordinary two-dimensional electron gas and for graphene (relativistic dispersion). Furthermore, the coherent-state representation is shown to display a hierarchy of local energy scales ordered by powers of the magnetic length and successive spatial derivatives of the local potential, which allows one to devise controlled approximation schemes at finite temperature for arbitrary and possibly disordered potential landscapes. As an application, we derive general analytical expressions for the local density of states, which allow us to account for many puzzling features recently observed in high magnetic field scanning tunneling spectroscopies on semiconducting heterostructures and graphene. Our recent theoretical developments in relation with percolative transport at high magnetic fields will also be evoked.
T. Champel and S. Florens, PRB 80, 125322 (2009);
T. Champel and S. Florens, PRB 82, 045421 (2010);
M. Flöser, S. Florens, and T. Champel, PRL 107, 176806 (2011).