Dissociation of vertical semiconductor diatomic artificial molecules

We investigate the dissociation of few-electron circular vertical semiconductor double quantum dot artificial molecules at 0 T as a function of interdot distance. Slight mismatch introduced in the fabrication of the artificial molecules from nominally identical constituent quantum wells induces localization by offsetting the energy levels in the quantum dots by up to 2 meV, and this plays a crucial role in the appearance of the addition energy spectra as a function of coupling strength particularly in the weak coupling limit.Comment: Accepted for publication in Phys. Rev. Let

Yang-Mills Integrals

Two results are presented for reduced Yang-Mills integrals with different symmetry groups and dimensions: the first is a compact integral representation in terms of the relevant variables of the integral, the second is a method to analytically evaluate the integrals in cases of low order. This is exhibited by evaluating a Yang-Mills integral over real symmetric matrices of order 3.Comment: LaTeX, 10 pages, references added and minimal change

Dynamical aspects of the fuzzy CP2^{2} in the large NN reduced model with a cubic term

``Fuzzy CP^2'', which is a four-dimensional fuzzy manifold extension of the well-known fuzzy analogous to the fuzzy 2-sphere (S^2), appears as a classical solution in the dimensionally reduced 8d Yang-Mills model with a cubic term involving the structure constant of the SU(3) Lie algebra. Although the fuzzy S^2, which is also a classical solution of the same model, has actually smaller free energy than the fuzzy CP^2, Monte Carlo simulation shows that the fuzzy CP^2 is stable even nonperturbatively due to the suppression of tunneling effects at large N as far as the coefficient of the cubic term ($\alpha$) is sufficiently large. As \alpha is decreased, both the fuzzy CP$^2$ and the fuzzy S^2 collapse to a solid ball and the system is essentially described by the pure Yang-Mills model (\alpha = 0). The corresponding transitions are of first order and the critical points can be understood analytically. The gauge group generated dynamically above the critical point turns out to be of rank one for both CP^2 and S^2 cases. Above the critical point, we also perform perturbative calculations for various quantities to all orders, taking advantage of the one-loop saturation of the effective action in the large-N limit. By extrapolating our Monte Carlo results to N=\infty, we find excellent agreement with the all order results.Comment: 27 pages, 7 figures, (v2) References added (v3) all order analyses added, some typos correcte

Direct Coulomb and Exchange Interaction in Artificial Atoms

We determine the contributions from the direct Coulomb and exchange interactions to the total interaction in semiconductor artificial atoms. We tune the relative strengths of the two interactions and measure them as a function of the number of confined electrons. We find that electrons tend to have parallel spins when they occupy nearly degenerate single-particle states. We use a magnetic field to adjust the single-particle state degeneracy, and find that the spin-configurations in an arbitrary magnetic field are well explained in terms of two-electron singlet and triplet states.Comment: 4 pages, 5 figure

A vertical diatomic artificial molecule in the intermediate coupling regime in a parallel and perpendicular magnetic field

We present experimental results for the ground state electrochemical potentials of a few electron semiconductor artificial molecule made by vertically coupling two quantum dots, in the intermediate coupling regime, in perpendicular and parallel magnetic fields up to 5 T. We perform a quantitative analysis based on local-spin density functional theory. The agreement between theoretical and experimental results is good, and the phase transitions are well reproduced.Comment: Typeset using Revtex, 13 pages and 8 Postscript figure

Energy levels and magneto-optical transitions in parabolic quantum dots with spin-orbit coupling

We report on the electronic properties of few interacting electrons confined in a parabolic quantum dot based on a theoretical approach developed to investigate the influence of Bychkov-Rashba spin-orbit (SO) interaction on such a system. We note that the spin-orbit coupling profoundly influences the energy spectrum of interacting electrons in a quantum dot. Here we present accurate results for the energy levels and optical-absorption spectra for parabolic quantum dots containing upto four interacting electrons, in the presence of spin-orbit coupling and under the influence of an externally applied, perpendicular magnetic field. We have described in detail about a very accurate numerical scheme to evaluate these quantities. We have evaluated the effects of SO coupling on the Fock-Darwin spectra for quantum dots made out of three different semiconductor systems, InAs, InSb, and GaAs.Comment: expanded version of cond-mat/0501642 to be published in Phys. Rev. Let

Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings

We study the properties of the space-time that emerges dynamically from the matrix model for type IIB superstrings in ten dimensions. We calculate the free energy and the extent of space-time using the Gaussian expansion method up to the third order. Unlike previous works, we study the SO(d) symmetric vacua with all possible values of d within the range $2 \le d \le 7$, and observe clear indication of plateaus in the parameter space of the Gaussian action, which is crucial for the results to be reliable. The obtained results indeed exhibit systematic dependence on d, which turns out to be surprisingly similar to what was observed recently in an analogous work on the six-dimensional version of the model. In particular, we find the following properties: i) the extent in the shrunken directions is given by a constant, which does not depend on d; ii) the ten-dimensional volume of the Euclidean space-time is given by a constant, which does not depend on d except for d = 2; iii) The free energy takes the minimum value at d = 3. Intuitive understanding of these results is given by using the low-energy effective theory and some Monte Carlo results.Comment: 33 pages, 10 figures; minor corrections, reference added. arXiv admin note: substantial text overlap with arXiv:1007.088

Absence of a fuzzy S4S^4 phase in the dimensionally reduced 5d Yang-Mills-Chern-Simons model

We perform nonperturbative studies of the dimensionally reduced 5d Yang-Mills-Chern-Simons model, in which a four-dimensional fuzzy manifold, ``fuzzy S$^{4}$'', is known to exist as a classical solution. Although the action is unbounded from below, Monte Carlo simulations provide an evidence for a well-defined vacuum, which stabilizes at large $N$, when the coefficient of the Chern-Simons term is sufficiently small. The fuzzy S$^{4}$ prepared as an initial configuration decays rapidly into this vacuum in the process of thermalization. Thus we find that the model does not possess a ``fuzzy S$^{4}$ phase'' in contrast to our previous results on the fuzzy S$^{2}$.Comment: 11 pages, 2 figures, (v2) typos correcte

A note on instanton counting for N=2 gauge theories with classical gauge groups

We study the prepotential of N=2 gauge theories using the instanton counting techniques introduced by Nekrasov. For the SO theories without matter we find a closed expression for the full prepotential and its string theory gravitational corrections. For the more subtle case of Sp theories without matter we discuss general features and compute the prepotential up to instanton number three. We also briefly discuss SU theories with matter in the symmetric and antisymmetric representations. We check all our results against the predictions of the corresponding Seiberg-Witten geometries.Comment: 24 pages, LaTeX. v2: refs added. v3: typos correcte

Electron transport through double quantum dots

Electron transport experiments on two lateral quantum dots coupled in series are reviewed. An introduction to the charge stability diagram is given in terms of the electrochemical potentials of both dots. Resonant tunneling experiments show that the double dot geometry allows for an accurate determination of the intrinsic lifetime of discrete energy states in quantum dots. The evolution of discrete energy levels in magnetic field is studied. The resolution allows to resolve avoided crossings in the spectrum of a quantum dot. With microwave spectroscopy it is possible to probe the transition from ionic bonding (for weak inter-dot tunnel coupling) to covalent bonding (for strong inter-dot tunnel coupling) in a double dot artificial molecule. This review on the present experimental status of double quantum dot studies is motivated by their relevance for realizing solid state quantum bits.Comment: 32 pages, 31 figure