Mesoscopic Coulomb Drag

TL;DR

This thesis develops a theoretical framework for Coulomb drag in mesoscopic systems, revealing significant sample-to-sample fluctuations and potential sign changes in the induced current due to disorder.

Contribution

It introduces a unified linear-response theory for Coulomb drag in mesoscopic systems, applicable to both ballistic and disordered regimes, with analysis via scattering matrices, Green functions, and random matrix theory.

Findings

Sample-to-sample fluctuations of drag conductance can be as large as or larger than the mean.

Disorder can cause the sign of the induced current to change.

The formalism applies to quantum wires and quantum dots, demonstrating diverse mesoscopic effects.

Abstract

This thesis describes the merging of the two fields of Coulomb drag and mesoscopic physics. The thesis presents a theory for Coulomb drag between two mesoscopic systems based on linear-response theory. The formalism expresses the drag in terms of either scattering matrices and wave functions or Green functions, and its range of validity covers both ballistic and disordered phase-coherent systems. The consequences are worked out either by analytic means, such as the random matrix theory, or by numerical simulations. The formalism is applied to i) drag between mesoscopic quantum wires and ii) drag between mesoscopic quantum dots. In these systems it is found that for even weak disorder the mesoscopic sample-to-sample fluctuations of the drag conductance can be of the order of - or even exceed - the mean value. Depending on the particular disorder configuration this is giving rise to a possible sign change of the induced current.