Coherent electronic transport properties of quasi-one-dimensional systems

Abstract

The linear response theory of the frequency dependent conductance is applied to non-interacting spin-less electrons. The Hamiltonian is defined on a square lattice that is infinitely long in one direction and of finite extend in the other. Disorder, and a magnetic field perpendicular to the system are taken into account by respectively randomizing the diagonal matrix elements of the Hamiltonian, and introducing magnetic field dependent phase factors into the hopping matrix elements between nearest neighbors. The DC-properties of the model describe the results of the recent experiments in the ballistic regime quantitatively. New coherent transport phenomena are predicted, (i) The frequency dependence of the conductance shows oscillations which are due to interference between the electron and the hole wavefunctions. These provide insight into the spatial behavior of the electric field, (ii) In the presence of weak disorder sharp antiresonances appear at the onsets of the conductance plateaus, (iii) The root mean square deviation of the conductance increases quadratically with disorder, and saturates at a value of 0.3 e 2/ h at the value of the disorder where the plateaus vanish.