9 research outputs found
A phenomenological position and energy resolving Lindblad approach to quantum kinetics
A general theoretical approach to study the quantum kinetics in a system
coupled to a bath is proposed. Starting with the microscopic interaction, a
Lindblad master equation is established, which goes beyond the common secular
approximation. This allows for the treatment of systems, where coherences are
generated by the bath couplings while avoiding the negative occupations
occurring in the Bloch-Wangsness-Redfield kinetic equations. The versatility
and accuracy of the approach is verified by its application to three entirely
different physical systems: (i) electric transport through a double-dot system
coupled to electronic reservoirs, (ii) exciton kinetics in coupled chromophores
in the presence of a heat bath, and (iii) the simulation of quantum cascade
lasers, where the coherent electron transport is established by scattering with
phonons and impurities.Comment: accepted version (minor changes with respect to version 1), to appear
in Physical Review
Cotunneling renormalization in carbon nanotube quantum dots
We determine the level-shifts induced by cotunneling in a Coulomb blockaded
carbon nanotube quantum dot using leading order quasi-degenerate perturbation
theory within a single nanotube quartet. It is demonstrated that otherwise
degenerate and equally tunnel-coupled and states are mixed by
cotunneling and therefore split up in energy except at the
particle/hole-symmetric midpoints of the Coulomb diamonds. In the presence of
an external magnetic field, we show that cotunneling induces a gate-dependent
-factor renormalization, and we outline different scenarios which might be
observed experimentally, depending on the values of both intrinsic
splitting and spin-orbit coupling.Comment: 12 pages, 7 figure
Transport in serial spinful multiple-dot systems: The role of electron-electron interactions and coherences
Quantum dots are nanoscopic systems, where carriers are confined in all three
spatial directions. Such nanoscopic systems are suitable for fundamental
studies of quantum mechanics and are candidates for applications such as
quantum information processing. It was also proposed that linear arrangements
of quantum dots could be used as quantum cascade laser. In this work we study
the impact of electron-electron interactions on transport in a spinful serial
triple quantum dot system weakly coupled to two leads. We find that due to
electron-electron scattering processes the transport is enabled beyond the
common single-particle transmission channels. This shows that the scenario in
the serial quantum dots intrinsically deviates from layered structures such as
quantum cascade lasers, where the presence of well-defined single-particle
resonances between neighboring levels are crucial for device operation.
Additionally, we check the validity of the Pauli master equation by comparing
it with the first-order von Neumann approach. Here we demonstrate that
coherences are of relevance if the energy spacing of the eigenstates is smaller
than the lead transition rate multiplied by .Comment: 12 pages, 7 figure
Designing -stacked molecular structures to control heat transport through molecular junctions
We propose and analyze a new way of using stacking to design molecular
junctions that either enhance or suppress a phononic heat current, but at the
same time remain conductors for an electric current. Such functionality is
highly desirable in thermoelectric energy converters, as well as in other
electronic components where heat dissipation should be minimized or maximized.
We suggest a molecular design consisting of two masses coupled to each other
with one mass coupled to each lead. By having a small coupling (spring
constant) between the masses, it is possible to either reduce, or perhaps more
surprisingly enhance the phonon conductance. We investigate a simple model
system to identify optimal parameter regimes and then use first principle
calculations to extract model parameters for a number of specific molecular
realizations, confirming that our proposal can indeed be realized using
standard molecular building blocks.Comment: 5 pages + supplemental material, 3 figure
Yu-Shiba-Rusinov states in phase-biased S-QD-S junctions
We study the effects of a phase difference on Yu-Shiba-Rusinov (YSR) states
in a spinful Coulomb-blockaded quantum dot contacted by a superconducting loop.
In the limit where charging energy is larger than the superconducting gap, we
determine the subgap excitation spectrum, the corresponding supercurrent, and
the differential conductance as measured by a normal-metal tunnel probe. In
absence of a phase difference only one linear combination of the superconductor
lead electrons couples to the spin, which gives a single YSR state. With finite
phase difference, however, it is effectively a two-channel scattering problem
and therefore an additional state emerges from the gap edge. The energy of the
phase-dependent YSR states depend on the gate voltage and one state can cross
zero energy twice inside the valley with odd occupancy. These crossings are
shifted by the phase difference towards the charge degeneracy points,
corresponding to larger exchange couplings. Moreover, the zero-energy crossings
give rise to resonant peaks in the differential conductance with magnitude
. Finally, we demonstrate that the quantum fluctuations of the dot spin
do not alter qualitatively any of the results.Comment: 13 pages, 7 figure
QmeQ 1.0: An open-source Python package for calculations of transport through quantum dot devices
QmeQ is an open-source Python package for numerical modeling of transport
through quantum dot devices with strong electron-electron interactions using
various approximate master equation approaches. The package provides a
framework for calculating stationary particle or energy currents driven by
differences in chemical potentials or temperatures between the leads which are
tunnel coupled to the quantum dots. The electronic structures of the quantum
dots are described by their single-particle states and the Coulomb matrix
elements between the states. When transport is treated perturbatively to lowest
order in the tunneling couplings, the possible approaches are Pauli
(classical), first-order Redfield, and first-order von Neumann master
equations, and a particular form of the Lindblad equation. When all processes
involving two-particle excitations in the leads are of interest, the
second-order von Neumann approach can be applied. All these approaches are
implemented in QmeQ. We here give an overview of the basic structure of the
package, give examples of transport calculations, and outline the range of
applicability of the different approximate approaches.Comment: 34 pages, 10 figure