Non-equilibrium transport in chiral quantum wires coupled through a point-contact

The exact dynamical non-equilibrium Green functions (NEGF) are obtained analytically for a system of two quantum wires with non-interacting fermions of opposite chirality coupled through a point contact tunnel junction driven out of equilibrium by the application of a generic time-dependent bias [1]. The NEGF is written down in a closed form in terms of simple functions of position and time. This allows us to obtain the tunneling I-V characteristics in the presence of an arbitrary time-dependent bias. In addition to this, our method is able to account for transient behaviour in the Green functions as well as approach to steady state. In the present work we also consider the case of a finite momentum bandwidth in the point-contact and show that the nonequilibrium transport properties exhibit non-Markovian behaviour. Upon sudden switch on of a subsequently constant bias, the tunneling current shows a transient buildup before attaining its steady state value. This is in contrast to the infinite bandwidth case where no transients are present in the I-V characteristics. The expression for the tunneling current involves an integral over the past history of the system and hence it is of a non-Markovian nature. Previous numerical simulations of lattice systems using time-dependent DMRG (tDMRG) [2] that predict this transient property suggests that this transient buildup arises merely due to the presence of a short-distance cutoff in the problem description.

From the exact expressions for the non-equilibrium two-point functions we also obtain the four-point functions using Wick’s theorem. These correlations can be used in conjunction with powerful novel bosonization techniques [3,4,5] to study non-equilibrium transport between chiral fermionic edges with mutually interacting particles like in the case of fractional quantum Hall edge states. As a precursor to this we formulate an unconventional bosonization ansatz and use it to obtain the NEGF for the noninteracting problem [6]. Extending this bosonization scheme to include interparticle interactions will be dealt with in a future work of ours.