Interactions and Disorder in Quantum Dots: Instabilities and Phase Transitions

Using a fermionic renormalization group approach we analyse a model where the electrons diffusing on a quantum dot interact via Fermi-liquid interactions. Describing the single-particle states by Random Matrix Theory, we find that interactions can induce phase transitions (or crossovers for finite systems) to regimes where fluctuations and collective effects dominate at low energies. Implications for experiments and numerical work on quantum dots are discussed.Comment: 4 pages, 1 figure; version to appear in Phys Rev Letter

Quantum Dots with Disorder and Interactions: A Solvable Large-g Limit

We show that problem of interacting electrons in a quantum dot with chaotic boundary conditions is solvable in the large-g limit, where g is the dimensionless conductance of the dot. The critical point of the $g=\infty$ theory (whose location and exponent are known exactly) that separates strong and weak-coupling phases also controls a wider fan-shaped region in the coupling-1/g plane, just as a quantum critical point controls the fan in at T>0. The weak-coupling phase is governed by the Universal Hamiltonian and the strong-coupling phase is a disordered version of the Pomeranchuk transition in a clean Fermi liquid. Predictions are made in the various regimes for the Coulomb Blockade peak spacing distributions and Fock-space delocalization (reflected in the quasiparticle width and ground state wavefunction).Comment: 4 pages, 2 figure

Diamagnetic Persistent Currents and Spontaneous Time-Reversal Symmetry Breaking in Mesoscopic Structures

Recently, new strongly interacting phases have been uncovered in mesoscopic systems with chaotic scattering at the boundaries by two of the present authors and R. Shankar. This analysis is reliable when the dimensionless conductance of the system is large, and is nonperturbative in both disorder and interactions. The new phases are the mesoscopic analogue of spontaneous distortions of the Fermi surface induced by interactions in bulk systems and can occur in any Fermi liquid channel with angular momentum $m$. Here we show that the phase with $m$ even has a diamagnetic persistent current (seen experimentally but mysterious theoretically), while that with $m$ odd can be driven through a transition which spontaneously breaks time-reversal symmetry by increasing the coupling to dissipative leads.Comment: 4 pages, three eps figure

Spin and e-e interactions in quantum dots: Leading order corrections to universality and temperature effects

We study the statistics of the spacing between Coulomb blockade conductance peaks in quantum dots with large dimensionless conductance g. Our starting point is the ``universal Hamiltonian''--valid in the g->oo limit--which includes the charging energy, the single-electron energies (described by random matrix theory), and the average exchange interaction. We then calculate the magnitude of the most relevant finite g corrections, namely, the effect of surface charge, the ``gate'' effect, and the fluctuation of the residual e-e interaction. The resulting zero-temperature peak spacing distribution has corrections of order Delta/sqrt(g). For typical values of the e-e interaction (r_s ~ 1) and simple geometries, theory does indeed predict an asymmetric distribution with a significant even/odd effect. The width of the distribution is of order 0.3 Delta, and its dominant feature is a large peak for the odd case, reminiscent of the delta-function in the g->oo limit. We consider finite temperature effects next. Only after their inclusion is good agreement with the experimental results obtained. Even relatively low temperature causes large modifications in the peak spacing distribution: (a) its peak is dominated by the even distribution at kT ~ 0.3 Delta (at lower T a double peak appears); (b) it becomes more symmetric; (c) the even/odd effect is considerably weaker; (d) the delta-function is completely washed-out; and (e) fluctuation of the coupling to the leads becomes relevant. Experiments aimed at observing the T=0 peak spacing distribution should therefore be done at kT<0.1 Delta for typical values of the e-e interaction.Comment: 15 pages, 4 figure

A Solvable Regime of Disorder and Interactions in Ballistic Nanostructures, Part I: Consequences for Coulomb Blockade

We provide a framework for analyzing the problem of interacting electrons in a ballistic quantum dot with chaotic boundary conditions within an energy $E_T$ (the Thouless energy) of the Fermi energy. Within this window we show that the interactions can be characterized by Landau Fermi liquid parameters. When $g$, the dimensionless conductance of the dot, is large, we find that the disordered interacting problem can be solved in a saddle-point approximation which becomes exact as $g\to\infty$ (as in a large-N theory). The infinite $g$ theory shows a transition to a strong-coupling phase characterized by the same order parameter as in the Pomeranchuk transition in clean systems (a spontaneous interaction-induced Fermi surface distortion), but smeared and pinned by disorder. At finite $g$, the two phases and critical point evolve into three regimes in the $u_m-1/g$ plane -- weak- and strong-coupling regimes separated by crossover lines from a quantum-critical regime controlled by the quantum critical point. In the strong-coupling and quantum-critical regions, the quasiparticle acquires a width of the same order as the level spacing $\Delta$ within a few $\Delta$'s of the Fermi energy due to coupling to collective excitations. In the strong coupling regime if $m$ is odd, the dot will (if isolated) cross over from the orthogonal to unitary ensemble for an exponentially small external flux, or will (if strongly coupled to leads) break time-reversal symmetry spontaneously.Comment: 33 pages, 14 figures. Very minor changes. We have clarified that we are treating charge-channel instabilities in spinful systems, leaving spin-channel instabilities for future work. No substantive results are change

The renormalization group for interacting fermions: from Fermi liquids to quantum dots

The renormalization group approach as developed by the author for Fermi liquids is applied to clean Fermi liquids and ballistic quantum dots. In the former case Landau theory is shown to be a fixed point and in the latter the Universal Hamiltonian is shown to be a fixed point for weak coupling. The strong coupling phase is analyzed using large N and Random Matrix methods.Comment: Lectures given at the Fifteenth Chris Engelbrecht Summer School South Africa, January 2004. 6 eps figs and springer style file (svmult

Advances in Vehicular Ad-hoc Networks (VANETs): challenges and road-map for future development

Recent advances in wireless communication technologies and auto-mobile industry have triggered a significant research interest in the field of vehicular ad-hoc networks (VANETs) over the past few years. A vehicular network consists of vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communications supported by wireless access technologies such as IEEE 802.11p. This innovation in wireless communication has been envisaged to improve road safety and motor traffic efficiency in near future through the development of intelligent transportation system (ITS). Hence, governments, auto-mobile industries and academia are heavily partnering through several ongoing research projects to establish standards for VANETs. The typical set of VANET application areas, such as vehicle collision warning and traffic information dissemination have made VANET an interesting field of mobile wireless communication. This paper provides an overview on current research state, challenges, potentials of VANETs as well as the ways forward to achieving the long awaited ITS