QmeQ 1.0: An open-source Python package for calculations of transport through quantum dot devices

Abstract

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), firstorder 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. Keywords: Open quantum systems, Quantum dots, Anderson-type model, Coulomb blockade, Python Program summaryProgram Title: QmeQ Licensing provisions: BSD 2-Clause Programming language: Python External libraries: NumPy, SciPy, Cython Nature of problem: Calculation of stationary state currents through quantum dots tunnel coupled to leads. Solution method: Exact diagonalisation of the quantum dot Hamiltonian for a given set of single particle states and Coulomb matrix elements. Numerical solution of the stationary-state master equation for a given approximate approach. Restrictions: Depending on the approximate approach the temperature needs to be sufficiently large compared to the coupling strength for the approach to be valid.

Phenomenological position and energy resolving Lindblad approach to quantum kinetics

“…Compared to the Redfield approach, it provides results even closer to the exact solution and, most importantly, avoids negative probabilities. Lastly, we note that the simulations of the double-dot structure using PERLind, Redfield, and Pauli approaches were produced with the QMEQ package [46] using the kerntype options Lindblad, Redfield, and Pauli, respectively. This publicly available package allows to perform corresponding calculations for more complex systems in a straightforward way.…”

Heat Driven Transport in Serial Double Quantum Dot Devices

“…These parameters are motivated in the SI , where additional simulation details are given. All transport simulations are done with the open source simulation tool QMEQ [Quantum Master Equation for Quantum dot transport calculations] 54 with the recent inclusion of phonon scattering. 49 To model the side-heating, we assume the phonon temperature as the heating bias dV H should have a stronger impact on the phonons in the DQD than on the electrons in the leads, compare eq 2 which is simultaneously used here.…”

Quantum interference in transport through almost symmetric double quantum dots

“…Nonetheless, we have used the methods described in Refs. 36,39 to verify that processes which are next-to-leading order in the tunneling coupling do not affect our conclusions. It would be interesting to, in a future study, investigate the regime Γ T where cotunneling and other higher order tunnel processes become important.…”