Distribution of Parametric Conductance Derivatives of a Quantum Dot

Abstract

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...

Statistical fluctuations of pumping and rectification currents in quantum dots

“…This appendix serves to remedy the discrepancy between the theoretical 30 and experimental 26 distributions of parametric dimensionless velocities ∂g 0 /∂X. This discussion gives further support to the statistical theory employed in this paper, and provides a further illustration of the important role of temperature in the statistical fluctuations of conductance-related quantities.…”

“…The statistical fluctuations of this quantity were investigated in Ref. 30, where the distributions of ∂G/∂X were presented for the N = 2 case. Recall that the linear conductance G is given by the Landauer formula…”

“…C, we study a very closely related issue and show how thermal smearing explains the discrepancy between the recently experimental measured parametric conductance velocity distribution 26 and the analytical predictions at zero temperature. 30 A simple inspection of Eqs. (6) and (7) shows that ∂g 0 /∂X i = 0, since it is proportional to ∂H/∂X i .…”

Excess conductance of a spin-filtering quantum dot

“…In the opposite, more realistic, regime e 2 / C ӷ⌬ the charging energy introduces a weight factor equal to the density of states in the ensemble averages. 19 This weight factor converts the grand-canonical average ͗¯͘ ͑considered so far͒ into a canonical average,…”

The Local Larmor Clock, Partial Densities of States, and Mesoscopic Physics

“…If carriers in the transmitted beam acquire a polarization in the direction of the magnetic field then carriers in the reflected beam must have a corresponding polarization opposite to the direction of the magnetic field. In mesoscopic physics, in electrical transport problems, the sensitivity plays a role in the discussion of non-linear current-voltage characteristics and plays a role if we ask about the change of the conductance in response to the variation of a gate voltage [24]. Below, we will not further discuss the sensitivity, but we will present a number of examples in which the partial densities of states play a role.…”