Statics and dynamics of single-electron solitons in two-dimensional arrays of ultrasmall tunnel junctions

Abstract We have analyzed the distribution and transfer of electric charge in a uniform two-dimensional array of ultrasmall tunnel junctions. The effects can be most adequately described in terms of topological solitons with charge ±e. Field distribution in the soliton, its intrinsic energy, and the energy of interaction between the solitons and array edges have been calculated and compared with those for the one-dimensional case studied earlier. Numerical simulations have shown that the solitons tend to form a two-dimensional Wigner crystal which can be driven along the array without melting, on certain conditions. Such a correlated transfer of charge induces narrow-band “SET” oscillations of frequency f s = I e , where I is the average current carried by the solitons. Conditions of experimental observation of this effect have been analyzed and compared with those for the one-dimensional arrays.