One-dimensional transport and the quantisation of the ballistic resistance

The authors present experimental results, and a supporting theory, showing that a one-dimensional system in which transport is ballistic possesses a quantised resistance, h/2ie2, where i is the number of occupied 1D sub-bands and the spin degeneracy is two. A short narrow channel is defined in the 2DEG of a GaAs-AlGaAs heterojunction and as the width of the system is changed, the sub-bands pass through the Fermi energy and the resistance jumps between quantised values. The value of the quantised resistance is derived and the accuracy of the quantisation is discussed. The effect can be strong at temperatures approximately 0.1 K, with up to 17 sub-bands being observed. The action of a transverse magnetic field is to depopulate the sub-bands and form hybrid levels; a parallel field lifts the spin degeneracy and brings about a further quantisation of resistance at values h/2(i+1/2)e2.