11 - Quantum Impedance of Electrons

Abstract

In circuits, particularly linear systems, impedance is a universal concept that characterizes input/output (I/O). For waves, an additional parameter, the propagation constant, together with the impedance, characterizes the operation of a system. In the electromagnetic case, the wave nature leads to a wave impedance of free space that is purely real. The wave impedance of wave guides is different, depending on the propagation constants. The characteristic impedance of a waveguide contains further geometrical factors. These three are all different, yet share the same origin, the wave nature of photons. Similar to electromagnetic waves, the wave impedance or wave conductance for various cases are different in detail, although all of them share the same origin, the wave nature of the electron. This chapter clearly identifies the so-called universal conductance as the input conductance from a contact to a structure, whether a section of a Qwire, a QW, or a QD. Generally contacts are not reflectionless, but the effects of reflection, as in the case of resonant tunneling, are accounted for by the transmission term in addition to the “prefactor” G0. If the transmission is very small, reflection is very large, so that the input impedance will be very large and the conductance will be very small. All this fit into the description of input impedance.