Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1543611 | Physica E: Low-dimensional Systems and Nanostructures | 2016 | 9 Pages |
The scattering theory of electron transport allows for a compact and powerful description in terms of gˇ2=1 Green functions, the so-called circuit theory of quantum transport. A scatterer in the theory is characterized by an action, most generally a Keldysh one, that can be further used as a building bock of theories describing statistics of electron transport, superconducting correlations, time-dependent and interaction effects. The action is usually used in the form suitable for a two-terminal scatterer.Here we provide a comprehensive derivation of a more general form of the action that is especially suitable and convenient for general multi-terminal scatterers. The action is expressed as a determinant of a block of the scattering matrix obtained by projection on the positive eigenvalues of the Green functions characterizing the reservoirs. We start with traditional Green function formalism introducing gˇ2=1 matrices and give a first example of multi-terminal counting statistics. Further we consider one-dimensional channels and discuss chiral anomaly arising in this context. Generalizing on many channels and superconducting situation, we arrive at the block-determinant relation. We give the necessary elaborative examples reproducing basic results of counting statistics and super-currents in multi-terminal junctions.