We analyze the frequency-dependent current fluctuations induced into a gate near a quantum point contact or a quantum chaotic cavity. We use a current-and charge-conserving effective scattering approach in which interactions are treated in the random-phase approximation. The current fluctuations measured at a nearby gate, coupled capacitively to the conductor, are determined by the screened charge fluctuations of the conductor. Both the equilibrium and nonequilibrium current noise at the gate can be expressed with the help of resistances which are related to the charge dynamics on the conductor. We evaluate these resistances for a point contact, and determine their distributions for an ensemble of chaotic cavities. For a quantum point contact these resistances exhibit pronounced oscillations with the opening of channels. For a chaotic cavity coupled to one-channel point contacts, the charge relaxation resistance shows a broad distribution between 1 4 and 1 2 of a resistance quantum. The nonequilibrium resistance exhibits a broad distribution between zero and 1 4 of a resistance quantum. ͓S0163-1829͑98͒03103-8͔
Quantum mechanics requires that identical particles are treated as indistinguishable. This requirement leads to correlations in the fluctuating properties of a system. Theoretical predictions are made for an experiment on a multi-lead chaotic quantum dot which can identify exchange effects in electronic current-current correlations. Interestingly, we find that the ensemble averaged exchange effects are of the order of the channel number, and are insensitive to dephasing.
The thermovoltage of a chaotic quantum dot is measured using a current heating technique. The fluctuations in the thermopower as a function of magnetic field and dot shape display a nonGaussian distribution, in agreement with simulations using Random Matrix Theory. We observe no contributions from weak localization or short trajectories in the thermopower. 72.20.Pa, 73.20.Dx, 05.45+b The electrical conductance of small -characteristic size much smaller than the electron mean free path -confined electron systems (usually denoted as quantum dots) shows distinct fluctuations. These fluctuations display correlations as a function of an external parameter such as shape or magnetic field, which can be described in a statistical manner. The electrons can, in fact, be viewed as billiard balls moving in a classically chaotic system where many random reflections at the system walls occur. Because of the wave-like nature of the electrons, quantum mechanics is needed to describe these systems fully. Chaos in quantum dots has been investigated [1][2][3] in conductance measurements but the analysis turns out to be difficult. So-called short trajectories [4] and weak localization effects [1,5] add up to the signature of chaotic motion. Moreover, current heating of the electrons in the dot appears to be unavoidable in conductance measurements. Electron heating effects in the dot smear out the underlying chaotic statistics and therefore the observed fluctuations exhibit mostly a Gaussian distribution, although theory predicts non-Gaussian distributions when a small number of electron modes is admitted to the dot [6]. Only when dephasing (modelled as extra modes coupling the dot to the environment) is included, Random Matrix Theory (RMT) [1,7] gives a Gaussian distribution. Very recently, Huibers et al. [8] observed small deviations from a Gaussian distribution in conductance measurements. However, other transport properties calculated from these data exhibit again Gaussian distributions in contrast to theoretical predictions.An alternative for the conductance measurements pursued so far (which inherently are accompanied by electron heating inside the dot) is to investigate the thermoelectric properties of a system. Thermopower measurements have already been used to study semiconductor nanostructures like quantum point-contacts [9] and quantum dots in the Coulomb blockade regime [10,11]. The thermopower S measures directly the parametric derivative of the conductance, S ∝ G −1 ∂G/∂X with X = E (energy), and thus yields both similar and additional information on the electron transport processes as can be obtained from conductance measurements. The distribution of parametric derivatives (X = E, B, shape, . . .) of the conductance of a quantum dot is the subject of recent 13]. The probability distribution for the thermopower is again expected to be non-Gaussian for chaotic conductors, exhibiting cusps at zero amplitude and non-exponential tails [13,14].In this paper, we present magneto-thermopower measurements of a statistical en...
The conductance G of a quantum dot with single-mode ballistic pomt contacts depends sensitively on external parameters X such äs gate voltage and magnetic field We calculate the jomt distnbution of G and dG/dX by relating it to the distnbution of the Wigner Smith time delay matnx of a chaotic System The distnbution of dG/dX has a smgularity at zero and algebraic tails While G and dG/dX are correlated, the ratio of dG/dX and -jG(l -G) is independent of G Coulomb interactions change the distnbution of dG/dX by mducing a transition from the grand canonical to the canonical ensemble All these piedictions can be tested in semiconductor microstiuctures or microwave cavities [S0031 9007(97) The mterest m this problem was stimulated by expenments on semiconductor microstructures known äs quantum dots, m which the election motion is ballistic and chaotic [5] A typical quantum dot is confined by gate electrodes, and connected to two election reservoirs by bal hstic pomt contacts, thiough which only a few modes can propagate at the Fermi level The parametnc dependence of the conductance has been measured by several groups [6][7][8] In the single-mode hmit, parametnc fluctuations are of the same ordei äs the aveiage, so that one needs the complete distnbution of G and dG/dX to character ize the System Knowing the average and vanance is not sufficient Analytical results are available for pomt con tacts with a large number of modes [9][10][11][12][13][14][15] In this paper, we present the complete distnbution in the opposite hmit of two single-mode pomt contacts and show that it differs stnkmgly from the multimode case consideied previouslyThe mam differences which we have found are the following We consider the jomt distnbution of the conductance G and the derivatives 3G/3V, dG/dX with respect to the gate voltage V and an external parameter X (typically the magnetic field) If the pomt contacts contain a large number of modes, P(G, 3G/3V, dG/dX) factonzes mto three independent Gaussian distnbutions [9][10][11][12] In the single-mode case, in contrast, we find that this distnbution does not factonze and decays algebraically rather than exponentially By integratmg out G and one of the two derivatives, we obtain the conductance velocity distnbutions P(dG/dV) and P(dG/dX) plotted m Fig l Both distubutions have a smgularity at zero velocity, and alge braic tails A remaikable piediction of our theory is that the correlations between G, on the one hand, and dG/dV and dG/dX, on the other hand, can be transformed away by the change of variables G = (2e 2 /h) sin 2 Θ, where θ is the polar coordmate mtroduced in Ref [13] The derivatives dO/dV and 3Θ/ΘΧ are statistically independent of θ Theie exists no change of variables that transforms away the correlations between dG/dV and 3G/dX Anothei new feature of the smgle mode case concerns the effect of Coulomb mtei actions [16,17] In the simplest model, the strength of the Coulomb repulsion is measured by the ratio of the chaiging eneigy e 1 /C (with C the capacitance of the quantum dot) and...
We show (analytically and by numerical simulation) that the zerotemperature limit of the distribution of the thermopower S of a onedimensional disordered wire in the localized regime is a Lorentzian, with a disorder-independent width of 4π 3 k 2 B T /3e∆ (where T is the temperature and ∆ the mean level spacing). Upon raising the temperature the distribution crosses over to an exponential form ∝ exp (−2|S|eT /∆). We also consider the case of a chaotic quantum dot with two single-channel ballistic point contacts. The distribution of S then has a cusp at S = 0 and a tail ∝ |S| −1−β ln |S| for large S (with β = 1, 2 depending on the presence or absence of time-reversal symmetry). I. INTRODUCTIONThermo-electric transport properties of conductors probe the energy dependence of the scattering processes limiting conduction. At low temperatures and in small (mesoscopic) systems, elastic impurity scattering is the dominant scattering process. The energy dependence of the conductance is then a quantum interference effect.1 The derivative dG/dE of the conductance with respect to the Fermi energy is measured by the thermopower S, defined as the ratio −∆V /∆T of a (small) voltage and temperature difference applied over the sample at zero electrical current. Experimental and theoretical studies of the thermopower exist for several mesoscopic devices. One finds a series of sharp peaks in the thermopower of quantum point contacts, 2 aperiodic fluctuations in diffusive conductors, 3 sawtooth oscillations in quantum dots in the Coulomb blockade regime, 4 and Aharonov-Bohm oscillations in metal rings. 5Here we study the statistical distribution of the thermopower in two different systems, not considered previously: A disordered wire in the localized regime and a chaotic quantum dot with ballistic point contacts. A single transmitted mode is assumed in both cases. In the disordered wire, conduction takes place by resonant tunneling through localized states. The resonances are very narrow and appear at uncorrelated energies. The distributions of the thermopower and the conductance are both broad, but otherwise quite different: Instead of the log-normal distribution of the conductance 1 we find a Lorentzian distribution for the thermopower. In the quantum dot, the resonances are correlated and the widths 1 are of the same order as the spacings. The correlations are described by random-matrix theory, 6,7 under the assumption that the classical dynamics in the dot is chaotic. The thermopower distribution in this case follows from the distribution of the time-delay matrix found recently. 8The thermopower (at temperature T and Fermi energy E F ) is given by the Cutler-Mott formula 9,10where G is the zero-temperature conductance and f is the Fermi-Dirac distribution function. In the limit T → 0 Eq. (1.1) simplifies towhere G and dG/dE are to be evaluated at E = E F . We consider mainly the zerotemperature limit of the thermopower, by studying the dimensionless quantityHere ∆ is the mean level spacing near the Fermi energy. Since we...
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