# Quantum transport in small disordered samples from the diffusive to the ballistic regime

## Abstract

The authors review conductance effects in small samples at low temperatures where quantum confinement and quantum interference are significant perturbations on the classical Drude conductance. In disordered materials, the elastic scattering of the carriers from impurities leads to random conductance fluctuations or resistance fluctuations. The fluctuations arise because of interference among the scattered waves, and they are random and sample specific because the impurity potential is. The fluctuations appear in response to changes in many extrinsic parameters such as the carrier density, the applied measuring current, external electric fields and external fields. The interface fluctuations have consequences for much larger samples, particularly in flicker noise, even though quantum coherence is obtained only over regions much smaller than the sample size, in completely phase coherent conductors a number of purely quantum effects are observed, including non-local response and Aharonov-Bohm effects. Other 'applications' of the quantum fluctuations include studies of reciprocity (which is related to time-reversal symmetry) and of the effects of the measurement probes on a quantum system. Interestingly, these are two areas where disagreements remain with theoretical calculations. The size and correlation scale of the fluctuations, however, are mainly in agreement with theoretical calculations of the same quantities, although one or two other small disagreements of detail remain. In very clean semiconductor heterostructures, the mean free path length between scattering events is large enough to allow for studies of ballistic transport that reveal a variety of conductance anomalies that result from device shape (as opposed to fortuitous placement of impurities as in the metals). These ballistic effects are reviewed briefly and connection is made to the effects of disorder in ballistic systems, and experiments on disordered metal samples are reviewed in detail.