Quantized conductance through an asymmetric narrow constriction in a three-dimensional electron gas

The quantized ballistic transmission of a three-dimensional electron gas through a narrow constriction modeled by an asymmetric hyperboloid is studied. The conductance as a function of voltage jumps by integer multiples of e²∕(πℏ) each time a new transition channel opens in the plane of narrowest restriction, which has the shape of an ellipse. There are two different modes (“whispering gallery modes” and “bouncing ball modes”) which lead to different conductance steps. The smoothing of the conductance steps is discussed in terms of phase space tunneling through a dynamical barrier. A comprehensive interpretation of the quantum mechanical results is obtained from relating them to the corresponding classical motions.