Longitudinal drag and Hall drag in a bilayer system with pinholes

The transresistance and Hall transresistance of dirty two-dimensional bilayer systems in the presence of tunneling bridges (pinholes) are studied theoretically. We find, at weak magnetic field, a nonzero Hall transresistance. In a geometry where the pinholes are concentrated in the middle of the sample, a quantum process gives the dominant contribution to both the ordinary transresistance and the Hall transresistance. Arising from the interplay between Coulomb repulsion, disorder, and tunneling, the quantum contribution increases in a singular way as the temperature decreases.