Electronic properties and spin polarization in coupled quantum dots Satyadev Nagaraja and Jean-Pierre Leburton Beckman Institute for Advanced Science & Technology, 405 N. Mathews Avenue, Urbana, Illinois 61820 and Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61820 Richard M. Martin Beckman Institute for Advanced Science & Technology, 405 N. Mathews Avenue, Urbana, Illinois 61820 and Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 ~Received 14 December 1998; revised manuscript received 28 April 1999! Electronic structure and charging properties of an electrostatically defined double quantum dot system are investigated within the local spin density approximation under the density functional theory. Characteristics of electron charging of the double dot system is influenced by quantum-mechanical as well as electrostatic coupling between the individual dots. In the case of weak coupling, the double dot system is shown to exhibit double electron charging in agreement with the observations of Waugh et al. @Phys. Rev. Lett. 75, 705 ~1995!#. Also, the coupled dot system shows spin polarization for higher number of electrons in the dot N due to Hund’s rule. For strong coupling, we show that coherent bonding and antibonding states are formed which produce a reordering of the single-particle energy levels and revert the double dot system into a spin unpolarized state for same N. @S0163-1829~99!05435-1# I. INTRODUCTION Physical properties such as three-dimensional electron confinement, energy quantization, and shell structures, typi- cal of atoms, can now be realized in ultrasmall semiconduc- tor structures called quantum dots ~QD’s!. The ability to ob- serve such atomic phenomena that occur naturally on the scale of a few Å in manmade nanostructures with feature size of a few hundreds or thousands of angstroms has resulted in a flurry of experimental and theoretical investigations of QDs in recent years. Motivation for such studies has risen largely from a need to study fundamental electronic proper- ties, but also increasingly from the possibility of making ul- trasmall memories 1 and high efficiency lasers. 2 Lately, atten- tion has been focussed on arrays of quantum dots coupled through tunnel junctions. 3–5 Their appeal stems form the many features they share with molecules. Just as in mol- ecules electron states can couple forming covalent states that are delocalized over the entire array making possible for an occupying electron to tunnel between the various dots with- out being localized to any. 6,7 These bonding states are lower in energy than the constituent dot states by an amount that is equivalent to the binding energy of the molecule. Hence a two-dot system may be compared to a diatomic molecule. Such artificial molecules provide an advantage in that the number of electrons in the coupled dot, equivalently the con- stituent ‘‘atoms’’ in the periodic table, may be varied by varying an external potential. Different molecular analogs can be realized by varying the size of the dots, simulta- neously or independently, and their number of electrons. Furthermore, the vibrational motion of a molecule may be simulated by driving such an array between weak and strong tunneling regimes. The volume of experimental 8,9,4 and theoretical work 3,10–14 on coupled dots has been growing in recent times. In particular, Ruzin et al. 11 studied the Coulomb blockade structure for two nonidentical dots using the activation-energy approach. Stafford et al. 12 and Klimeck et al. 13 have used a Mott-Hubbard approach with and with- out interdot capacitances to determine the many-body wave function for an array of dots. More recently Golden et al. 14 have studied the problem of Coulomb blockade peak split- ting in the weak and strong coupling limits to explain the experimental data in Ref. 5. The present work is motivated by the following factors. ~1! The need to treat the problem self-consistently since the distortion of the confining potential and the weakening of confinement are both significant as the charge in the dot increases. 15,16 The latter effect is particularly critical in elec- trostatically confined dots. ~2! The need to consider explicitly the electron spin. This is necessitated by the findings of Tarucha et al. in gated ver- tical quantum dots which established that shell filling in QDs is governed by Hund’s rules just as in atoms. Some recent theoritical investigations of Lee et al., 17 Fonseca et al., 18 Wojs et al., 19 and Koskinen et al. 20 have studied spin effects in LSDA in single QDs. To our knowledge, rigorous calcu- lations based on a spin dependent model of double QDs have not been done so far. ~3! The experimental results of Waugh et al. 5 on the con- ductance of electrostatically confined double and triple dots in the weak and strong tunneling regimes. The splitting of conductance peaks that increased with the interdot tunneling strength coupling, establishes the fact that the splitting is proportional to the energy of interaction between the dots. Another feature though weak but clearly visible in their re- sults @Figs. 2~a!,2~b!, and 2~c! in Ref. 5# is the increase in the separation of the successive split peaks for a constant tunnel conductance. In the present work, we focus on a system of two similar dots whose dimensions are such that the electron-electron interaction energy is comparable to the single-particle energy level spacing D E . The number of electrons in the dot, N, is PHYSICAL REVIEW B 15 SEPTEMBER 1999-II VOLUME 60, NUMBER 12 PRB 60 0163-1829/99/60~12!/8759~8!/$15.00 8759 ©1999 The American Physical Society