Modeling ballistic magnetoconductance and magnetic focusing in SiGe cavities

Ballistic transport in mesoscopic structures is characterized by resonance phenomena that are differently influenced by decoherence due to interactions with the environment. Considering chaotic cavities in SiGe heterostructures, it is possible to observe both tunable resonances in the conductance like magnetic focusing or Shubnikov-de Haas (SdH) oscillations, and a superimposed rich structure of oscillations due to multiple reflections inside the cavity. Luckily, it often occurs that experimentally only magnetic focusing and SdH oscillations are observed, that are more robust to the effects of decoherence. Here, we present numerical simulations of magnetoconductance properties of a cavity obtained by shifting the central section of wire in a SiGe heterostructure, and compare them with experimental results. The subband profile is obtained solving the Schrödinger equation with density functional theory, local density approximation [1] in the wire and in the cavity, and semiclassically elsewhere. In particular, we are able to take into account the the effect of the strain on the minima of the conduction band and on the effective masses. The conductance of the SET is obtained with the scattering matrix (S-matrix) technique in the framework of the Landauer-Büttiker theory of transport [2]. The conductance is related to the transmission probability matrix T = tt† by the formula G = g e 2 h ∑ n Tn, where t is the transmission amplitude matrix, g is a degeneracy factor (g = 4 in our case due to the valley degeneracy) and the sum is over all eigenvalues Tn of the transmission matrix T . The partial density of states ρ(xi, yj , E) = |Ψ(xi, yj , E)|2 at each point (xi, yj) of the grid domain is computed to highlight electron trajectories and density patterns. We introduce in our description the effects of decoherence as a dephasing of the wave function [3]. The coherent propagation through the j-th slice is described by a diagonal transmission matrix with elements ej,mjδmn, where dj = xj+1 − xj . We modify the transmission matrix by adding to each diagonal term a random phase φR so that the generic element of the transmission matrix becomes tmn = ej,mjRδmn. The random phase φR is extracted by a random number generator and obeys a zero average Gaussian distribution with variance σ2 j = dj/lφ. The scattering matrix