Single-dot spectroscopy via elastic single-electron tunneling through a pair of coupled quantum dots

We study the electronic structure of a single self-assembled InAs quantum dot by probing elastic single-electron tunneling through a single pair of weakly coupled dots. In the region below pinch-off voltage, the non-linear threshold voltage behavior provides electronic addition energies exactly as the linear, Coulomb blockade oscillation does. By analyzing it, we identify the s and p shell addition spectrum for up to six electrons in the single InAs dot, i.e. one of the coupled dots. The evolution of shell addition spectrum with magnetic field provides Fock-Darwin spectra of s and p shell.Comment: 7 pages, 3 figures, Accepted for publication in Phys. Rev. Let

Addition Spectra of Chaotic Quantum Dots: Interplay between Interactions and Geometry

We investigate the influence of interactions and geometry on ground states of clean chaotic quantum dots using the self-consistent Hartree-Fock method. We find two distinct regimes of interaction strength: While capacitive energy fluctuations $\delta \chi$ follow approximately a random matrix prediction for weak interactions, there is a crossover to a regime where $\delta \chi$ is strongly enhanced and scales roughly with interaction strength. This enhancement is related to the rearrangement of charges into ordered states near the dot edge. This effect is non-universal depending on dot shape and size. It may provide additional insight into recent experiments on statistics of Coulomb blockade peak spacings.Comment: 4 pages, final version to appear in Phys. Rev. Let

Density Modulations and Addition Spectra of Interacting Electrons in Disordered Quantum Dots

We analyse the ground state of spinless fermions on a lattice in a weakly disordered potential, interacting via a nearest neighbour interaction, by applying the self-consistent Hartree-Fock approximation. We find that charge density modulations emerge progressively when r_s >1, even away from half-filling, with only short-range density correlations. Classical geometry dependent "magic numbers" can show up in the addition spectrum which are remarkably robust against quantum fluctuations and disorder averaging.Comment: 4 pages, 3 eps figure

Wigner Crystallization in a Quasi-3D Electronic System

When a strong magnetic field is applied perpendicularly (along z) to a sheet confining electrons to two dimensions (x-y), highly correlated states emerge as a result of the interplay between electron-electron interactions, confinement and disorder. These so-called fractional quantum Hall (FQH) liquids form a series of states which ultimately give way to a periodic electron solid that crystallizes at high magnetic fields. This quantum phase of electrons has been identified previously as a disorder-pinned two-dimensional Wigner crystal with broken translational symmetry in the x-y plane. Here, we report our discovery of a new insulating quantum phase of electrons when a very high magnetic field, up to 45T, is applied in a geometry parallel (y-direction) to the two-dimensional electron sheet. Our data point towards this new quantum phase being an electron solid in a "quasi-3D" configuration induced by orbital coupling with the parallel field

Towards an Explanation of the Mesoscopic Double-Slit Experiment: a new model for charging of a Quantum Dot

For a quantum dot (QD) in the intermediate regime between integrable and fully chaotic, the widths of single-particle levels naturally differ by orders of magnitude. In particular, the width of one strongly coupled level may be larger than the spacing between other, very narrow, levels. In this case many consecutive Coulomb blockade peaks are due to occupation of the same broad level. Between the peaks the electron jumps from this level to one of the narrow levels and the transmission through the dot at the next resonance essentially repeats that at the previous one. This offers a natural explanation to the recently observed behavior of the transmission phase in an interferometer with a QD.Comment: 4 pages, 2 figures, Journal versio

The Addition Spectrum and Koopmans' Theorem for Disordered Quantum Dots

We investigate the addition spectrum of disordered quantum dots containing spinless interacting fermions using the self-consistent Hartree-Fock approximation. We concentrate on the regime r_s >~1, with finite dimensionless conductance g. We find that in this approximation the peak spacing fluctuations do not scale with the mean single particle level spacing for either Coulomb or nearest neighbour interactions when r_s >~1. We also show that Koopmans' approximation to the addition spectrum can lead to errors that are of order the mean level spacing or larger, both in the mean addition spectrum peak spacings, and in the peak spacing fluctuations.Comment: 35 pages including 22 figures (eps

Unexpected features of branched flow through high-mobility two-dimensional electron gases

GaAs-based two-dimensional electron gases (2DEGs) show a wealth of remarkable electronic states, and serve as the basis for fast transistors, research on electrons in nanostructures, and prototypes of quantum-computing schemes. All these uses depend on the extremely low levels of disorder in GaAs 2DEGs, with low-temperature mean free paths ranging from microns to hundreds of microns. Here we study how disorder affects the spatial structure of electron transport by imaging electron flow in three different GaAs/AlGaAs 2DEGs, whose mobilities range over an order of magnitude. As expected, electrons flow along narrow branches that we find remain straight over a distance roughly proportional to the mean free path. We also observe two unanticipated phenomena in high-mobility samples. In our highest-mobility sample we observe an almost complete absence of sharp impurity or defect scattering, indicated by the complete suppression of quantum coherent interference fringes. Also, branched flow through the chaotic potential of a high-mobility sample remains stable to significant changes to the initial conditions of injected electrons.Comment: 22 pages, 4 figures, 1 tabl

Conductance Peak Distributions in Quantum Dots at Finite Temperature: Signatures of the Charging Energy

We derive the finite temperature conductance peak distributions and peak-to-peak correlations for quantum dots in the Coulomb blockade regime assuming the validity of random matrix theory. The distributions are universal, depending only on the symmetry class and the temperature measured in units of the mean level spacing, $\Delta$. When the temperature is comparable to $\Delta$ several resonances contribute to the same conductance peak and we find significant deviations from the previously known $T \ll \Delta$ distributions. In contrast to the $T \ll \Delta$ case, these distributions show a strong signature of the charging energy and charge quantization on the dot.Comment: 14 pages, 3 Postscript figures included, RevTex, to appear as a Rapid Communication in Physical Review

Ground-State Magnetization for Interacting Fermions in a Disordered Potential : Kinetic Energy, Exchange Interaction and Off-Diagonal Fluctuations

We study a model of interacting fermions in a disordered potential, which is assumed to generate uniformly fluctuating interaction matrix elements. We show that the ground state magnetization is systematically decreased by off-diagonal fluctuations of the interaction matrix elements. This effect is neglected in the Stoner picture of itinerant ferromagnetism in which the ground-state magnetization is simply determined by the balance between ferromagnetic exchange and kinetic energy, and increasing the interaction strength always favors ferromagnetism. The physical origin of the demagnetizing effect of interaction fluctuations is the larger number of final states available for interaction-induced scattering in the lower spin sectors of the Hilbert space. We analyze the energetic role played by these fluctuations in the limits of small and large interaction $U$. In the small $U$ limit we do second-order perturbation theory and identify explicitly transitions which are allowed for minimal spin and forbidden for higher spin. These transitions then on average lower the energy of the minimal spin ground state with respect to higher spin. For large interactions $U$ we amplify on our earlier work [Ph. Jacquod and A.D. Stone, Phys. Rev. Lett. 84, 3938 (2000)] which showed that minimal spin is favored due to a larger broadening of the many-body density of states in the low-spin sectors. Numerical results are presented in both limits.Comment: 35 pages, 24 figures - final, shortened version, to appear in Physical Review

Statistics of Coulomb Blockade Peak Spacings within the Hartree-Fock Approximation

We study the effect of electronic interactions on the addition spectra and on the energy level distributions of two-dimensional quantum dots with weak disorder using the self-consistent Hartree-Fock approximation for spinless electrons. We show that the distribution of the conductance peak spacings is Gaussian with large fluctuations that exceed, in agreement with experiments, the mean level spacing of the non-interacting system. We analyze this distribution on the basis of Koopmans' theorem. We show furthermore that the occupied and unoccupied Hartree-Fock levels exhibit Wigner-Dyson statistics.Comment: 5 pages, 2 figures, submitted for publicatio