Normal and `Anomalous' in Nonlinear Quantum Conductance for Mesoscopic Systems

Abstract

Practical mesoscopic devices must function at operating points involving large internal driving fields. Experimental evidence has long accumulated that certain apparently anomalous nonlinear features of quantum transport lie beyond the descriptive capacity of accepted models. We review the physical setting for these anomalous effects and suggest how microscopically argued quantum kinetic descriptions can overcome the predictive limitations of standard theories of quantized resistance. I. INTRODUCTIONPhenomena in quantum transport unique to two-dimensionally constrained electronic systems, formerly considered exotic, have since become bread-and-butter items for condensed-matter physics. Already for some time, in the form of quantum-well-confined structures, they have been deeply embedded in the design even of prosaic consumer electronics.Slightly later than the basic two-dimensional breakthroughs of the 1970s came those at the next level, for structures essentially at one dimension (1D). Their fundamental exploration is very much a current research focus for the physics of electronic transport. While one might argue that their truly large-scale applications have some way to go to outdo the widespread success of their two-dimensional predecessors, it is taken for granted that this is a basic matter of concerted technical development. It is the physical underpinning of the 1D device realm that forms the topic in the following, somewhat condensed, review.We concentrate on aspects of observed 1D transport behaviour that appear to go against accepted theoretical models. Both experimentalists and theorists tend to refer to these laboratory results as "anomalous"; but any consistent departure from experimental expectations will always be perceived as abnormal -until a tenable explanation emerges. The question is: "anomalous" relative to what? The answer is: relative to the received theoretical understanding. Nature entertains no anomalies. It is we as investigators who are subject to a momentary cognitive dissonance. Anomalous results, by their very presence, tell us that more is demanded of a quantitative theory than anything in common currency.Anomalies in nonlinear 1D transport emerged around the turn of this century. The actual surprise, there, is not their discovery but that they seemed to remain in the "too-hard basket", practically unattended to in the literature.Here we review two cases that have now been addressed, and cite a third intriguing instance still defying analysis.Our first example is excess 1D conductance in a working region where the conductance quantum e 2 /πh is supposed never to be exceeded [1,2]; the second is anomalous hot-electron noise in a 1D wire, or quantum point contact (QPC) [3]. The third striking example, which we can discuss only in passing, is the nonlinear Aharanov-Bohm effect [4]. These measurements, largely bypassed by theorists, supply appreciable evidence for reconsidering the limits of accepted mesoscopic transport models [5]. II. BACKGROUNDWe begin by recapitulating the distinc...