Anomalies in one-dimensional electron transport: quantum point contacts and wires

Over the last several decades, interest in quasi-one dimensional charge transport has progressed from the seminal discoveries of Landauer quantization of conductance as a function of carrier density, to significant finer-scale phenomena. Those include: (i) fractional conductance, or '0.7 anomaly'; (ii) zero-bias anomaly; (iii) Rashba-effect anomalies; and (iv) apparent violation of the Landauer upper bound on conductance. In this work we present a very short summary of the first three items. The last anomaly, which remained theoretically unexamined until recently, is discussed in detail with emphasis on novel low-dimensional physics.