Magnetization for the spin-orbit strength evaluation in laterally coupled double quantum dots

In this work, we present a theoretical study of the problem of spin-orbit coupling in semi-conductor quantum dots. We calculate the energy spectrum of two electrons confined in two laterally coupled quantum dots, under the influence of an applied perpendicular magnetic field. We analyze the effects of the Zeeman and the spin-orbit coupling on the energy levels. Zeeman splitting causes a level crossing in the low states, namely the singlet and triplet states and a jump of the magnetization at a certain magnetic field B-C. The spin-orbit coupling deeply influences the energy spectrum of the interacting electrons in the coupled quantum dots. The levels crossing caused by the Zeeman splitting is lifted. A level anti-crossing in the ground states occurs and is observed in the values of magnetic field lying in the range of [B-min, B-max]. where B-min< B-C < B-max. The gap Delta B = B-max - B-min increases with the spin-orbit coupling strength. B-min and B-max can be determined, experimentally by detecting respectively the minimum and the maximum of the magnetization. We plot the gap Delta B as a function of the spin orbit coupling, for different temperature. Magnetization will therefore provide a direct probe of the spin-orbit coupling strength. (C) 2008 Elsevier B.V. All rights reserved.