Linear combination of harmonic orbitals and configuration interaction method for the voltage control of exchange interaction in gated lateral quantum dot networks

Abstract

We present a computational LCHO-CI approach allowing for the simulation of exchange interactions in gated lateral quantum dot networks. The approach is based on single-particle states calculated using a linear combination of harmonic orbitals ͑LCHOs͒ of each of the dots and a configuration interaction ͑CI͒ approach to the interacting electron problem. The LCHO-CI method is applied to a network of three quantum dots with one-electron spin per dot, and a Heisenberg spin Hamiltonian is derived. The manipulation of spin states of a three-spin molecule by applying bias to one of the dots is demonstrated and related to the bias dependence of effective exchange interaction parameters. A. Single electron states in a quantum dot networkWe describe here the LCHO method for the calculation of single electron states in a network of two-dimensional quan-PHYSICAL REVIEW B 76, 075336 ͑2007͒

Quantum theory of the charge-stability diagram of semiconductor double-quantum-dot systems

“…50 and 51, the microscopic calculation 39,72,[82][83][84][85][86][87] is required to constrain the parameters of the Hubbard model in the physically relevant regime. In other words, although the Hubbard model by itself can have arbitrary parameters, a given physical double-dot system is restricted by the realistic confinement potential, which would severely restrict the physical Hubbard parameters for the system.…”

“…The classical aspect of the charge-stability diagram is well understood using the capacitance circuit model. [46][47][48][49] On the other hand, microscopic calculations are usually carried out for other aspects of the quantum-dot system, 39,72,[82][83][84][85][86][87] but only rarely for the charge-stability diagram. 56 This means that our understanding of the quantum aspect of the charge-stability diagram has largely been limited to the quantum-mechanical two-level model, 37,[52][53][54][55] with only a few exceptions.…”

Greenberger-Horne-Zeilinger states in a quantum dot molecule

“…A lateral triple quantum dot molecule (TQDM) [5][6][7]17,[24][25][26] with one electron per dot is the simplest realization of the three spin system discussed in the previous section. Assuming a single orbital per dot and arbitrary occupation, as shown in Refs.…”

“…Such GHZ ground states of spin molecules could be used as long-lived sources of entanglement. 3,4 One can envisage using lateral triple quantum dot molecules [5][6][7] with one electron on each dot to realize a three spin system. However, the spin-spin interaction in quantum dot molecules is necessarily antiferromagnetic and such a simple quantum dot molecule is not possible.…”

“…In this paper, we propose a theoretical model of six coupled quantum dots 6,7,15,16 with interacting electrons to generate the GHZ state as a ground state. The model consists of three equally spaced quantum dots with one electron spin each.…”