Rate of equilibration of a one-dimensional Wigner crystal

We consider a system of one-dimensional spinless particles interacting via long-range repulsion. In the limit of strong interactions the system is a Wigner crystal, with excitations analogous to phonons in solids. In a harmonic crystal the phonons do not interact, and the system never reaches thermal equilibrium. We account for the anharmonism of the Wigner crystal and find the rate at which it approaches equilibrium. The full equilibration of the system requires umklapp scattering of phonons, resulting in exponential suppression of the equilibration rate at low temperatures.Comment: Prepared for the proceedings of the International School and Workshop on Electronic Crystals, ECRYS-201

Fractional plateaus in the Coulomb blockade of coupled quantum dots

Ground-state properties of a double-large-dot sample connected to a reservoir via a single-mode point contact are investigated. When the interdot transmission is perfect and the dots controlled by the same dimensionless gate voltage, we find that for any finite backscattering from the barrier between the lead and the left dot, the average dot charge exhibits a Coulomb-staircase behavior with steps of size e/2 and the capacitance peak period is halved. The interdot electrostatic coupling here is weak. For strong tunneling between the left dot and the lead, we report a conspicuous intermediate phase in which the fractional plateaus get substantially altered by an increasing slope.Comment: 6 pages, 4 figures, final versio

Effective action and interaction energy of coupled quantum dots

We obtain the effective action of tunnel-coupled quantum dots, by modeling the system as a Luttinger liquid with multiple barriers. For a double dot system, we find that the resonance conditions for perfect conductance form a hexagon in the plane of the two gate voltages controlling the density of electrons in each dot. We also explicitly obtain the functional dependence of the interaction energy and peak-splitting on the gate voltage controlling tunneling between the dots and their charging energies. Our results are in good agreement with recent experimental results, from which we obtain the Luttinger interaction parameter $K=0.74$.Comment: 5 pgs,latex,3 figs,revised version to be publshed in Phys.Rev.

Scaling Of The Coulomb Energy Due To Quantum Fluctuations In The Charge Of A Quantum Dot

The charging energy of a quantum dot is measured through the effect of its potential on the conductance of a second dot. This technique allows a measurement of the scaling of the dot's charging energy with the conductance of the tunnel barriers leading to the dot. We find that the charging energy scales quadratically with the reflection probability of the barriers. In a second experiment we study the transition from a single to a double-dot which exhibits a scaling behavior linear in the reflection probability. The observed power-laws agree with a recent theory.Comment: 5 pages, uuencoded and compressed postscript file, with figure

Strong Tunneling in Double-Island Structures

We study the electron transport through a system of two low-capacitance metal islands connected in series between two electrodes. The work is motivated in part by experiments on semiconducting double-dots, which show intriguing effects arising from coherent tunneling of electrons and mixing of the single-electron states across tunneling barriers. In this article, we show how coherent tunneling affects metallic systems and leads to a mixing of the macroscopic charge states across the barriers. We apply a recently formulated RG approach to examine the linear response of the system with high tunnel conductances (up to 8e^2/h). In addition we calculate the (second order) cotunneling contributions to the non-linear conductance. Our main results are that the peaks in the linear and nonlinear conductance as a function of the gate voltage are reduced and broadened in an asymmetric way, as well as shifted in their positions. In the limit where the two islands are coupled weakly to the electrodes, we compare to theoretical results obtained by Golden and Halperin and Matveev et al. In the opposite case when the two islands are coupled more strongly to the leads than to each other, the peaks are found to shift, in qualitative agreement with the recent prediction of Andrei et al. for a similar double-dot system which exhibits a phase transition.Comment: 12 page

Weak Charge Quantization on Superconducting Islands

We consider the Coulomb blockade on a superconductive quantum dot strongly coupled to a lead through a tunnelling barrier and/or normal diffusive metal. Andreev transport of the correlated pairs leads to quantum fluctuations of the charge on the dot. These fluctuations result in exponential renormalization of the effective charging energy. We employ two complimentary ways to approach the problem, leading to the coinciding results: the instanton and the functional RG treatment of the non-linear sigma model. We also derive the charging energy renormalization in terms of arbitrary transmission matrix of the multi-channel interface.Comment: 21 pages, 4 eps figures, RevTe

Coulomb blockade of strongly coupled quantum dots studied via bosonization of a channel with a finite barrier

A pair of quantum dots, coupled through a point contact, can exhibit Coulomb blockade effects that reflect an oscillatory term in the dots' total energy whose value depends on whether the total number of electrons on the dots is even or odd. The effective energy associated with this even-odd alternation is reduced, relative to the bare Coulomb blockade energy for uncoupled dots, by a factor (1-f) that decreases as the interdot coupling is increased. When the transmission coefficient for interdot electronic motion is independent of energy and the same for all channels within the point contact (which are assumed uncoupled), the factor (1-f) takes on a universal value determined solely by the number of channels and the dimensionless conductance g of each individual channel. This paper studies corrections to the universal value of (1-f) that result when the transmission coefficent varies over energy scales of the size of the bare Coulomb blockade energy. We consider a model in which the point contact is described by a single orbital channel containing a parabolic barrier potential, and we calculate the leading correction to (1-f) for one-channel (spin-split) and two-channel (spin-degenerate) point contacts in the limit where the single orbital channel is almost completely open. By generalizing a previously used bosonization technique, we find that, for a given value of the dimensionless conductance g, the value of (1-f) is increased relative to its value for a zero-thickness barrier, but the absolute value of the increase is small in the region where our calculations apply.Comment: 13 pages, 3 Postscript figure

Coulomb Blockade of Tunneling Through a Double Quantum Dot

We study the Coulomb blockade of tunneling through a double quantum dot. The temperature dependence of the linear conductance is strongly affected by the inter-dot tunneling. As the tunneling grows, a crossover from temperature-independent peak conductance to a power-law suppression of conductance at low temperatures is predicted. This suppression is a manifestation of the Anderson orthogonality catastrophe associated with the charge re-distribution between the dots, which accompanies the tunneling of an electron into a dot. We find analytically the shapes of the Coulomb blockade peaks in conductance as a function of gate voltage.Comment: 11 pages, revtex3.0 and multicols.sty, 4 figures uuencode

Resonant tunneling and the multichannel Kondo problem: the quantum Brownian motion description

We study mesoscopic resonant tunneling as well as multichannel Kondo problems by mapping them to a first-quantized quantum mechanical model of a particle moving in a multi-dimensional periodic potential with Ohmic dissipation. From a renormalization group analysis, we obtain phase diagrams of the quantum Brownian motion model with various lattice symmetries. For a symmorphic lattice, there are two phases at T=0: a localized phase in which the particle is trapped in a potential minimum, and a free phase in which the particle is unaffected by the periodic potential. For a non-symmorphic lattice, however, there may be an additional intermediate phase in which the particle is neither localized nor completely free. The fixed point governing the intermediate phase is shown to be identical to the well-known multichannel Kondo fixed point in the Toulouse limit as well as the resonance fixed point of a quantum dot model and a double-barrier Luttinger liquid model. The mapping allows us to compute the fixed-poing mobility $\mu^*$ of the quantum Brownian motion model exactly, using known conformal-field-theory results of the Kondo problem. From the mobility, we find that the peak value of the conductance resonance of a spin-1/2 quantum dot problem is given by $e^2/2h$. The scaling form of the resonance line shape is predicted

Thermopower of a single electron transistor in the regime of strong inelastic cotunneling

We study Coulomb blockade oscillations of thermoelectric coefficients of a single electron transistor based on a quantum dot strongly coupled to one of the leads by a quantum point contact. At temperatures below the charging energy E_C the transport of electrons is dominated by strong inelastic cotunneling. In this regime we find analytic expressions for the thermopower as a function of temperature T and the reflection amplitude $r$ in the contact. In the case when the electron spins are polarized by a strong external magnetic field, the thermopower shows sinusoidal oscillations as a function of the gate voltage with the amplitude of the order of $e^{-1}|r|\frac{T}{E_C}$. We obtain qualitatively different results in the absence of the magnetic field. At temperatures between $E_C$ and $E_C|r|^2$ the thermopower oscillations are sinusoidal with the amplitude of order $e^{-1}|r|^2 \ln \frac{E_C}{T}$. On the other hand, at $T\ll E_C|r|^2$ we find non-sinusoidal oscillations of the thermopower with the amplitude $\sim e^{-1} |r| \sqrt{T/E_C} \ln(E_C/T)$.Comment: 14 pages, 3 figure