Solid State Quantum Interferometers (with and without the Warts)

Abstract

A brief review of quantum interference in small conductors is followed by a discussion of quantum interference in ballistic conductors. The ballistic conductors are characterized by conservation of the momentum vector and this leads to a simple model for the details of the conductance of the system. In contrast, for diffusive conductors one can only predict the statistical behavior of the interference contributions to the conductance. The response of the ballistic interferometers is governed by semiclassical physics of the electron momentum states (i.e. the modes) in the quantum conductor. Under circumstances of reduced backscattering of the modes, the interference pattern appears to imitate that from a simple optical interferometer. New results from ballistic interferometers are reviewed briefly.PACS numbers: 73.20.DxThe advent some years ago of quantum interference experiments led to a small revolution in the understanding of transport of electrons in the solid state [1]. First [2] in samples of size L much greater than the quantum coherence length Lô f the carriers and later [3] in samples of size L L, quantum interference was shown to be a significant perturbation on the average (classical) conductance. The quantum corrections to the average conductance arise through the interference of coherently propagating carriers, which contribution was ignored in the calculations of the average (Dude) conductance. Carrier excitations from the Fermi sea propagate for some distance and are scattered elastically by static impurities (lattice defects) along the way. The probability for a carrier to propagate from a certain point to another is given by the usual sum over all Feynman paths W = | Σn Qn |2 where Qn is a complex amplitude to propagate along the n-th trajectory between the two points. The total conductance of a conductor with two ports is G = (e2 /h) Σm Wm, where Wm is the transmission probability for the m-th mode in the conductor. The excitations are annihilated by inelastic scattering from dynamic excitations such as other carriers, phonons, spins, etc. [1]. At low