New rules of resistance in small resistors

Abstract

The well known rules of electrical resistance of macroscopic length scales that (i) it should increase monotonically as a narrow flat sample approaches one dimensionality, and (ii) the resistances of two wires joined in series should add as RA+RB, do not hold at 'mesoscopic' length scales (μm's) as found in recent experiments. In place of (i) the resistance is found to be quantized as h (n2e2) and (ii) is replaced by a simpler rule that the total resistance R=RA if RA > RB or R = RB if RB > RA. These new results are explained in this paper. © 1990.