Metal-insulator transition in a two-dimensional electron system: the orbital effect of in-plane magnetic field

The conductance of an open quench-disordered two-dimensional (2D) electron system subject to an in-plane magnetic field is calculated within the framework of conventional Fermi liquid theory applied to actually a three-dimensional system of spinless electrons confined to a highly anisotropic (planar) near-surface potential well. Using the calculation method suggested in this paper, the magnetic field piercing a finite range of infinitely long system of carriers is treated as introducing the additional highly non-local scatterer which separates the circuit thus modelled into three parts -- the system as such and two perfect leads. The transverse quantization spectrum of the inner part of the electron waveguide thus constructed can be effectively tuned by means of the magnetic field, even though the least transverse dimension of the waveguide is small compared to the magnetic length. The initially finite (metallic) value of the conductance, which is attributed to the existence of extended modes of the transverse quantization, decreases rapidly as the magnetic field grows. This decrease is due to the mode number reduction effect produced by the magnetic field. The closing of the last current-carrying mode, which is slightly sensitive to the disorder level, is suggested as the origin of the magnetic-field-driven metal-to-insulator transition widely observed in 2D systems.Comment: 19 pages, 7 eps figures, the extension of cond-mat/040613

The longitudinal conductance of mesoscopic Hall samples with arbitrary disorder and periodic modulations

We use the Kubo-Landauer formalism to compute the longitudinal (two-terminal) conductance of a two dimensional electron system placed in a strong perpendicular magnetic field, and subjected to periodic modulations and/or disorder potentials. The scattering problem is recast as a set of inhomogeneous, coupled linear equations, allowing us to find the transmission probabilities from a finite-size system computation; the results are exact for non-interacting electrons. Our method fully accounts for the effects of the disorder and the periodic modulation, irrespective of their relative strength, as long as Landau level mixing is negligible. In particular, we focus on the interplay between the effects of the periodic modulation and those of the disorder. This appears to be the relevant regime to understand recent experiments [S. Melinte {\em et al}, Phys. Rev. Lett. {\bf 92}, 036802 (2004)], and our numerical results are in qualitative agreement with these experimental results. The numerical techniques we develop can be generalized straightforwardly to many-terminal geometries, as well as other multi-channel scattering problems.Comment: 13 pages, 11 figure

Chaos in Quantum Dots: Dynamical Modulation of Coulomb Blockade Peak Heights

The electrostatic energy of an additional electron on a conducting grain blocks the flow of current through the grain, an effect known as the Coulomb blockade. Current can flow only if two charge states of the grain have the same energy; in this case the conductance has a peak. In a small grain with quantized electron states, referred to as a quantum dot, the magnitude of the conductance peak is directly related to the magnitude of the wavefunction near the contacts to the dot. Since dots are generally irregular in shape, the dynamics of the electrons is chaotic, and the characteristics of Coulomb blockade peaks reflects those of wavefunctions in chaotic systems. Previously, a statistical theory for the peaks was derived by assuming these wavefunctions to be completely random. Here we show that the specific internal dynamics of the dot, even though it is chaotic, modulates the peaks: because all systems have short-time features, chaos is not equivalent to randomness. Semiclassical results are derived for both chaotic and integrable dots, which are surprisingly similar, and compared to numerical calculations. We argue that this modulation, though unappreciated, has already been seen in experiments.Comment: 4 pages, 3 postscript figs included (2 color), uses epsf.st

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

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

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

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

Implementation of the quantum walk step operator in lateral quantum dots

We propose a physical implementation of the step operator of the discrete quantum walk for an electron in a one-dimensional chain of quantum dots. The operating principle of the step operator is based on locally enhanced Zeeman splitting and the role of the quantum coin is played by the spin of the electron. We calculate the probability of successful transfer of the electron in the presence of decoherence due to quantum charge fluctuations, modeled as a bosonic bath. We then analyze two mechanisms for creating locally enhanced Zeeman splitting based on, respectively, locally applied electric and magnetic fields and slanting magnetic fields. Our results imply that a success probability of > 90% is feasible under realistic experimental conditions

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

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