2 research outputs found
Density-operator approaches to transport through interacting quantum dots: Simplifications in fourth-order perturbation theory
Various theoretical methods address transport effects in quantum dots beyond
single-electron tunneling while accounting for the strong interactions in such
systems. In this paper we report a detailed comparison between three prominent
approaches to quantum transport: the fourth-order Bloch-Redfield quantum master
equation (BR), the real-time diagrammatic technique (RT), and the scattering
rate approach based on the T-matrix (TM). Central to the BR and RT is the
generalized master equation for the reduced density matrix. We demonstrate the
exact equivalence of these two techniques. By accounting for coherences
(nondiagonal elements of the density matrix) between nonsecular states, we show
how contributions to the transport kernels can be grouped in a physically
meaningful way. This not only significantly reduces the numerical cost of
evaluating the kernels but also yields expressions similar to those obtained in
the TM approach, allowing for a detailed comparison. However, in the TM
approach an ad hoc regularization procedure is required to cure spurious
divergences in the expressions for the transition rates in the stationary
(zero-frequency) limit. We show that these problems derive from incomplete
cancellation of reducible contributions and do not occur in the BR and RT
techniques, resulting in well-behaved expressions in the latter two cases.
Additionally, we show that a standard regularization procedure of the TM rates
employed in the literature does not correctly reproduce the BR and RT
expressions. All the results apply to general quantum dot models and we present
explicit rules for the simplified calculation of the zero-frequency kernels.
Although we focus on fourth-order perturbation theory only, the results and
implications generalize to higher orders. We illustrate our findings for the
single impurity Anderson model with finite Coulomb interaction in a magnetic
field.Comment: 29 pages, 12 figures; revised published versio
Charge transport through single molecules, quantum dots, and quantum wires
We review recent progresses in the theoretical description of correlation and
quantum fluctuation phenomena in charge transport through single molecules,
quantum dots, and quantum wires. A variety of physical phenomena is addressed,
relating to co-tunneling, pair-tunneling, adiabatic quantum pumping, charge and
spin fluctuations, and inhomogeneous Luttinger liquids. We review theoretical
many-body methods to treat correlation effects, quantum fluctuations,
nonequilibrium physics, and the time evolution into the stationary state of
complex nanoelectronic systems.Comment: 48 pages, 14 figures, Topical Review for Nanotechnolog