dc voltage step-up transformer based on a bilayer $\nu =1\mathrm{}$ quantum Hall system

A bilayer electron system in a strong magnetic field at low temperatures, with total Landau-level filling factor $\nu =1,$ can enter a strongly coupled phase, known as the (111) phase or the quantum Hall pseudospin ferromagnet. In this phase there is a large quantized Hall drag resistivity between the layers. Here we consider structures where the regions of (111) phase are separated by regions in which one of the layers is depleted by means of a gate, and various of the regions are connected together by wired contacts. We note that with suitable designs, one can create a dc step-up transformer where the output voltage is larger than the input, and we show how to analyze the current flows and voltages in such devices.