Drag and Hall drag in a bi-layer system with pinholes

The transresistance and the Hall transresistance of dirty two-dimensional bi-layer systems in the presence of tunneling bridges (pinholes) are studied theoretically. We find, at weak magnetic field, a non-zero 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.