Exchange coupling between two electrons in double quantum dot structures D.V. Melnikov 1 , L.-X. Zhang 2 , J.-P. Leburton * Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, 401 North Mathews Avenue, Urbana, IL 61801, United States Received 31 January 2006; accepted 21 November 2006 Abstract General properties of the stability diagram and the exchange energy for a few-electron laterally coupled quantum dots in magnetic fields are investigated. The calculations are performed by numerically exact diagonalization of the Schro ¨ dinger equation. The behavior of the exchange energy extracted from the stability diagram obtained with the model potential is qualitatively consistent with a more comprehensive approach based on multiscale modeling of the whole quantum dot device interacting with its environment. In particular, the variation of the curvature and the double–triple point separation in the stability diagrams confirms the weakening of the inter-dot coupling with increasing magnetic fields. We also find that the exchange energy in experimental system shows profound variations as the confinement gate biases (effective barrier between the dots) are changed while the singlet–triplet transition is insensitive to the latter and remains fixed at about 1.5 T. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Coupled quantum dots; Exchange interaction; Stability diagram; Numerical simulation; Exact diagonalization 1. Introduction Laterally coupled quantum dots (QDs), where individ- ual dots are either formed by the depletion of the two- dimensional electron gas (2DEG) produced by the gates on the device surface [1,2] or by the vertical confinement in the quantum well [3], have emerged as promising candi- dates for the realization of a solid state quantum computer. In these systems entanglement between two-electron spin qubits can be manipulated by external electric and mag- netic fields. The interaction between the two qubits is quan- tified by the exchange energy J defined as the energy difference between the lowest singlet and triplet states. The understanding of the exchange energy properties is extremely important as J directly determines the period of Rabi oscillations [2], and hence the value of the ffiffiffiffiffiffiffiffiffiffiffiffiffiffi SWAP p operation time required for the exchange of infor- mation between the two qubits in a double-dot system [4]. In the double QD system the confinement potential in the lateral plane consists of the individual dot potentials and the electrostatic potential barrier separating them [5]. In general, tunneling through the barrier as well as Cou- lomb interaction between the two electrons control the magnitude of the exchange coupling. Earlier theoretical approaches based on the approximate Heitler–London method in a model double-dot potential [6] have shown that the exchange energy can be tuned with applied mag- netic fields all the way down to zero to become negative. Increasing magnetic field further causes exchange energy to go to zero as electrons localize in individual dots with vanishing overlap. More elaborate approaches such as Hund–Mullikan method [6,7] confirmed these results, albeit producing smaller values of the exchange coupling in the same conditions. The problem of two interacting 1359-0286/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.cossms.2006.11.004 * Corresponding author. Tel.: +1 217 333 6813. E-mail addresses: dmm3@uiuc.edu (D.V. Melnikov), lzhang7@uiuc. edu (L.-X. Zhang), leburton@ceg.uiuc.edu (J.-P. Leburton). 1 Tel.: +1 217 244 6913. 2 Tel.: +1 217 244 1964. Current Opinion in Solid State and Materials Science 10 (2006) 114–119