Gate-modulated thermopower of disordered nanowires: II. Variable-range hopping regime

We study the thermopower of a disordered nanowire in the field effect transistor configuration. After a first paper devoted to the elastic coherent regime (Bosisio R., Fleury G. and Pichard J.-L. 2014 \textit{New J. Phys.} \textbf{16} 035004), we consider here the inelastic activated regime taking place at higher temperatures. In the case where charge transport is thermally assisted by phonons (Mott Variable Range Hopping regime), we use the Miller-Abrahams random resistor network model as recently adapted by Jiang et al. for thermoelectric transport. This approach previously used to study the bulk of the nanowire impurity band is extended for studying its edges. In this limit, we show that the typical thermopower is largely enhanced, attaining values larger that $10\, k_B/e \sim 1\, \mathrm{mV\,K}^{-1}$ and exhibiting a non-trivial behaviour as a function of the temperature. A percolation theory by Zvyagin extended to disordered nanowires allows us to account for the main observed edge behaviours of the thermopower.