Semiclassical Approach to Orbital Magnetism of Interacting Diffusive Quantum Systems

We study interaction effects on the orbital magnetism of diffusive mesoscopic quantum systems. By combining many-body perturbation theory with semiclassical techniques, we show that the interaction contribution to the ensemble averaged quantum thermodynamic potential can be reduced to an essentially classical operator. We compute the magnetic response of disordered rings and dots for diffusive classical dynamics. Our semiclassical approach reproduces the results of previous diagrammatic quantum calculations.Comment: 8 pages, revtex, includes 1 postscript fi

Incipient Wigner Localization in Circular Quantum Dots

We study the development of electron-electron correlations in circular quantum dots as the density is decreased. We consider a wide range of both electron number, N<=20, and electron gas parameter, r_s<18, using the diffusion quantum Monte Carlo technique. Features associated with correlation appear to develop very differently in quantum dots than in bulk. The main reason is that translational symmetry is necessarily broken in a dot, leading to density modulation and inhomogeneity. Electron-electron interactions act to enhance this modulation ultimately leading to localization. This process appears to be completely smooth and occurs over a wide range of density. Thus there is a broad regime of ``incipient'' Wigner crystallization in these quantum dots. Our specific conclusions are: (i) The density develops sharp rings while the pair density shows both radial and angular inhomogeneity. (ii) The spin of the ground state is consistent with Hund's (first) rule throughout our entire range of r_s for all 4<N<20. (iii) The addition energy curve first becomes smoother as interactions strengthen -- the mesoscopic fluctuations are damped by correlation -- and then starts to show features characteristic of the classical addition energy. (iv) Localization effects are stronger for a smaller number of electrons. (v) Finally, the gap to certain spin excitations becomes small at the strong interaction (large r_s) side of our regime.Comment: 14 pages, 12 figure

Chaos and Interacting Electrons in Ballistic Quantum Dots

We show that the classical dynamics of independent particles can determine the quantum properties of interacting electrons in the ballistic regime. This connection is established using diagrammatic perturbation theory and semiclassical finite-temperature Green functions. Specifically, the orbital magnetism is greatly enhanced over the Landau susceptibility by the combined effects of interactions and finite size. The presence of families of periodic orbits in regular systems makes their susceptibility parametrically larger than that of chaotic systems, a difference which emerges from correlation terms.Comment: 4 pages, revtex, includes 3 postscript fig

Far-from-equilibrium noise heating and laser cooling dynamics in radio-frequency Paul traps

We study the stochastic dynamics of a particle in a periodically driven potential. For atomic ions trapped in radio-frequency Paul traps, noise heating and laser cooling typically act slowly in comparison with the unperturbed motion. These stochastic processes can be accounted for in terms of a probability distribution defined over the action variables, which would otherwise be conserved within the regular regions of the Hamiltonian phase space. We present a semiclassical theory of low-saturation laser cooling applicable from the limit of low-amplitude motion to large-amplitude motion, accounting fully for the time-dependent and anharmonic trap. We employ our approach to a detailed study of the stochastic dynamics of a single ion, drawing general conclusions regarding the nonequilibrium dynamics of laser-cooled trapped ions. We predict a regime of anharmonic motion in which laser cooling becomes diffusive (i.e., it is equally likely to cool the ion as it is to heat it), and can also turn into effective heating. This implies that a high-energy ion could be easily lost from the trap despite being laser cooled; however, we find that this loss can be counteracted using a laser detuning much larger than Doppler detuning.Comment: 23 pages, 7 figure

Interaction-Induced Magnetization of the Two-Dimensional Electron Gas

We consider the contribution of electron-electron interactions to the orbital magnetization of a two-dimensional electron gas, focusing on the ballistic limit in the regime of negligible Landau-level spacing. This regime can be described by combining diagrammatic perturbation theory with semiclassical techniques. At sufficiently low temperatures, the interaction-induced magnetization overwhelms the Landau and Pauli contributions. Curiously, the interaction-induced magnetization is third-order in the (renormalized) Coulomb interaction. We give a simple interpretation of this effect in terms of classical paths using a renormalization argument: a polygon must have at least three sides in order to enclose area. To leading order in the renormalized interaction, the renormalization argument gives exactly the same result as the full treatment.Comment: 11 pages including 4 ps figures; uses revtex and epsf.st

Marginal topological properties of graphene: a comparison with topological insulators

The electronic structures of graphene systems and topological insulators have closely-related features, such as quantized Berry phase and zero-energy edge states. The reason for these analogies is that in both systems there are two relevant orbital bands, which generate the pseudo-spin degree of freedom, and, less obviously, there is a correspondence between the valley degree of freedom in graphene and electron spin in topological insulators. Despite the similarities, there are also several important distinctions, both for the bulk topological properties and for their implications for the edge states -- primarily due to the fundamental difference between valley and spin. In view of their peculiar band structure features, gapped graphene systems should be properly characterized as marginal topological insulators, distinct from either the trivial insulators or the true topological insulators.Comment: This manuscript will be published on the Proceedings of the 2010 Nobel Symposium on Graphene and Quantum Matte

Regular Tunnelling Sequences in Mixed Systems

We show that the pattern of tunnelling rates can display a vivid and regular pattern when the classical dynamics is of mixed chaotic/regular type. We consider the situation in which the dominant tunnelling route connects to a stable periodic orbit and this orbit is surrounded by a regular island which supports a number of quantum states. We derive an explicit semiclassical expression for the positions and tunnelling rates of these states by use of a complexified trace formula.Comment: submitted to Physica E as a contribution to the workshop proceedings of "Dynamics of Complex Systems" held at the Max Planck Institute for the Physics of Complex Systems in Dresden from March 30 to June 15, 199

Spin Qubits in Multi-Electron Quantum Dots

We study the effect of mesoscopic fluctuations on the magnitude of errors that can occur in exchange operations on quantum dot spin-qubits. Mid-size double quantum dots, with an odd number of electrons in the range of a few tens in each dot, are investigated through the constant interaction model using realistic parameters. It is found that the constraint of having short pulses and small errors implies keeping accurate control, at the few percent level, of several electrode voltages. In practice, the number of independent parameters per dot that one should tune depends on the configuration and ranges from one to four.Comment: RevTex, 6 pages, 5 figures. v3: two figures added, more details provided. Accepted for publication in PR

Orbital Magnetism in Ensembles of Parabolic Potentials

We study the magnetic susceptibility of an ensemble of non-interacting electrons confined by parabolic potentials and subjected to a perpendicular magnetic field at finite temperatures. We show that the behavior of the average susceptibility is qualitatively different from that of billiards. When averaged over the Fermi energy the susceptibility exhibits a large paramagnetic response only at certain special field values, corresponding to comensurate classical frequencies, being negligible elsewhere. We derive approximate analytical formulae for the susceptibility and compare the results with numerical calculations.Comment: 4 pages, 4 figures, REVTE