Quantum magnetotransport properties of short quantum wires

The longitudinal and transverse quantum magnetotransport coefficients of a two-dimensional electron gas in a perpendicular magnetic field for short quantum wires are calculated in the low-magnetic-field region $(B\lesssim 0.3$ T) using the Kubo method. The quantum wire channel is simulated by controlling the steepness and strength of the potential barrier. The calculated results have steplike features in the transverse conductivities as the Fermi energy crosses a Landau level for weak modulation potentials and giant low-field peaks in the transverse resistivities when the potential is strong. In addition, the Hall resistivity is quenched in the low-magnetic-field region. An interesting feature is the negative Hall resistivity which arises from backscattering off the edges of confinement for short quantum wires.