Gauge invariance and absence of exact conductance quantization in quantum ballistic transport.

Abstract

Using a generalized version of the gauge argument introduced by Laughlin in the discussion of the quantum Hall effect, the quantized conductance in a one-dimensional gas of charged fermions is related to the quotient of fermion charge and magnetic flux quantum, both in the presence and absence of a magnetic field. It is furthermore shown from the same arguments that, in the absence of a strong magnetic field, quantization is destroyed due to scattering. Finally, the crossover to the quantum Hall regime is discussed, employing the gauge argument.