Modular recursive Green’s function method for ballistic quantum transport

Abstract

A modification of the standard recursive Green's function method for quantum transport through microstructures is presented which is based on the decomposition into separable substructures. The Green's functions for these modules are joined by discretized Dyson equations. Nonseparable structures can thereby be calculated with the help of a few recursions with high accuracy. We apply this method to the calculation of ballistic quantum transport through a circular and stadium-shaped quantum dot for high mode numbers to test semiclassical predictions in detail. Among other results we find the breakdown of the semiclassical approximation for long path lengths which is due to the spreading of wave packets in the cavity.

Optimal block-tridiagonalization of matrices for coherent charge transport

“…While for particular cases general transport algorithms, such as the RGF algorithm, cannot compete with more specialized algorithms, such as the modular recursive Green's function technique [35,36] that is optimized for special geometries, they are very versatile and easily adapted to two-terminal geometries-provided that the leads are arranged collinearly. Amongst other things, this restriction will be lifted by the approach presented in this work.…”

Isolated resonances in conductance fluctuations and hierarchical states

“…Numerically, the challenge is the observation of fractal fluctuations of the conductance, which go beyond one order of magnitude [25]. This requires calculations with a drastically increased number of modes, the use of improved techniques like the modular recursive Green's function method [26], and the search for suitable billiard systems where the turnstile fluxes across partial barriers are particularly large. Isolated resonances will easily appear as soon as the parameter is varied on a sufficiently small scale.…”

Numerical toolkit for electronic quantum transport at finite frequency

“…Equations (3) and (4) are the typical raw output of, say, recursive techniques [38][39][40][41]79,80 from which one can calculate various physical observables such as conductance or current noise. For instance, the celebrated Landauer formula for the current flowing from lead m reads in this context 29,78 ,…”