Transport in serial spinful multiple-dot systems: The role of electron-electron interactions and coherences

Abstract

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 ħ.

Violation of Onsager's theorem in approximate master equation approaches

“…It has long been known that, without a rotating-wave approximation, this equation is not of Lindblad form [10] and does not conserve the positivity of the reduced density matrix [11]. In some cases this can lead to unphysical behavior, such as large negative currents [12]. A rotating-wave approximation corresponds to neglecting all off-diagonal elements [11], which suggests that the behavior of the WBR equation very much depends on the treatment of coherences.…”

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

“…[19,30], but most of this Appendix is based on Refs. [34,54]. Here we derive the necessary equations to define the second-order von Neumann approach.…”

“…In Ref. [34] the effect of different kinds of Coulomb matrix elements was considered in such a system. For the purposes of an example we here restrict ourselves to the dipole-dipole scattering of electrons between different quantum dots (U sc ).…”

“…Also we neglect the principal part Figure 7: A spinful serial triple-dot structure studied in Ref. [34]. It has 10 single-particle states and 1024 many-body states in total.…”

“…One reason is that depending on parameter regime these methods can fail and a good knowledge of the method is required to know whether to trust the result or not. For example, these methods can violate positivity [6] of the reduced density matrix and lead to large currents flowing against the bias [34]. Nevertheless, we think it is important to have a package where a user can duplicate existing calculations, check the applicability of different methods, or simply discover new kind of physics using different approximate master equations.…”