New aspects of variable-range hopping in finite one-dimensional wires

We analyze analytically the length dependence of the resistance for the case of variable-range hopping in finite one-dimensional systems. The resistance shows large fluctuations with variations in the chemical potential of the system and the average value ln(T0/T)1/2[ln(2L)]1/2, where is the inverse localization length and kT0=/N(0), N(0) being the density of states. This result is in good agreement with numerical simulations. Fluctuations of the log resistance, 2=(ln-ln)2, are conjectured to decrease with increasing length according to the relation (T0/T)1/2[ln(2 L)]-1/2. Numerical results show large fluctuations in for different ensembles of the same length which are characterized by the same set of parameters [T, N(0), etc.]. Averaging over many such ensembles yields a good agreement with the above prediction for. Numerical simulations also confirm that the product ln does not change with the length of the wire. Our results can be useful for future experiments on ultranarrow-channel metal-oxide-semiconductor field-effect transistors. © 1986 The American Physical Society.