Reversing the sign of current-current correlations

Current-correlations are a very sensitive probe of the fluctuations of small conductors. For non-interacting particles injected from thermal sources there is a simple connection between the sign of correlations and statistics: current-current correlations of Fermions are negative, intensity-intensity correlations of Bosons can be positive. In contrast to photons, electrons are interacting entities, and we can expect the simple connection between statistics and the sign of current-current correlations to be broken, if interactions play a crucial role. We present a number of examples in which interactions are important. At a voltage probe the potential fluctuates to maintain zero current. It is shown that there are geometries for which these fluctuations lead to positive correlations. Displacement currents at capacitively coupled contacts are also positively correlated if both contacts contribute to screening of the same excess charge fluctuation. Hybrid normal superconducting systems provide another example which permits positive correlations. The conditions for positive correlations differ strongly depending on whether the normal conductor is open and well coupled to the superconductor or is only weakly coupled via a barrier to the superconductor. In latter case, positive correlations result if the partition noise generated by Cooper pairs is overcome by pairs which are broken up and emit one electron into the contacts of interest.Comment: 30 pages, 9 figures, for "Quantum Noise", edited by Yu. V. Nazarov and Ya. M. Blanter (Kluwer

Time-Dependent Transport in Mesoscopic Structures

A discussion of recent work on time-dependent transport in mesoscopic structures is presented. The discussion emphasizes the use of time-dependent transport to gain information on the charge distribution and its collective dynamics. We discuss the RC-time of mesoscopic capacitors, the dynamic conductance of quantum point contacts and dynamic weak localization effects in chaotic cavities. We review work on adiabatic quantum pumping and photon-assisted transport, and conclude with a list which demonstrates the wide range of problems which are of interest

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

The local Larmor clock is used to derive a hierarchy of local densities of states. At the bottom of this hierarchy are the partial density of states for which represent the contribution to the local density of states if both the incident and outgoing scattering channel are prescribed. On the next higher level is the injectivity which represents the contribution to the local density of states if only the incident channel is prescribed regardless of the final scattering channel. The injectivity is related by reciprocity to the emissivity of a point into a quantum channel. The sum of all partial density of states or the sum of all injectivities or the sum of all emissivities is equal to the local density of states. The use of the partial density of states is illustrated for a number of different electron transport problems in mesoscopic physics: The transmission from a tunneling tip into a mesoscopic conductor, the discussion of inelastic or phase breaking scattering with a voltage probe, and the ac-conductance of mesoscopic conductors. The transition from a capacitive response (positive time-delay) to an inductive response (negative time-delay) for a quantum point contact is used to illustrate the difficulty in associating time-scales with a linear response analysis. A brief discussion of the off-diagonal elements of a partial density of states matrix is presented. The off-diagonal elements permit to investigate carrier fluctuations away from the average carrier density. The work concludes with a discussion of the relation between the partial density of states matrix and the Wigner-Smith delay time matrix

Charge Relaxation Resistances and Charge Fluctuations in Mesoscopic Conductors

A brief overview is presented of recent work which investigates the time-dependent relaxation of charge and its spontaneous fluctuations on mesoscopic conductors in the proximity of gates. The leading terms of the low frequency conductance are determined by a capacitive or inductive emittance and a dissipative charge relaxation resistance. The charge relaxation resistance is determined by the ratio of the mean square dwell time of the carriers in the conductor and the square of the mean dwell time. The contribution of each scattering channel is proportional to half a resistance quantum. We discuss the charge relaxation resistance for mesoscopic capacitors, quantum point contacts, chaotic cavities, ballistic wires and for transport along edge channels in the quantized Hall regime. At equilibrium the charge relaxation resistance also determines via the fluctuation-dissipation theorem the spontaneous fluctuations of charge on the conductor. Of particular interest are the charge fluctuations in the presence of transport in a regime where the conductor exhibits shot noise. At low frequencies and voltages charge relaxation is determined by a nonequilibrium charge relaxation resistance

Hidden quantum pump effects in quantum coherent rings

Time periodic perturbations of an electron system on a ring are examined. For small frequencies periodic small amplitude perturbations give rise to side band currents which in leading order are inversely proportional to the frequency. These side band currents compensate the current of the central band such that to leading order no net pumped current is generated. In the non-adiabatic limit, larger pump frequencies can lead to resonant excitations: as a consequence a net pumped current arises. We illustrate our results for a one channel ring with a quantum dot whose barriers are modulated parametrically.Comment: 8 pages, 5 figure

Quantum capacitance: a microscopic derivation

We start from microscopic approach to many body physics and show the analytical steps and approximations required to arrive at the concept of quantum capacitance. These approximations are valid only in the semi-classical limit and the quantum capacitance in that case is determined by Lindhard function. The effective capacitance is the geometrical capacitance and the quantum capacitance in series, and this too is established starting from a microscopic theory.Comment: 7 fig

Gauge invariant nonlinear electric transport in mesoscopic conductors

We use the scattering approach to investigate the nonlinear current-voltage characteristic of mesoscopic conductors. We discuss the leading nonlinearity by taking into account the self-consistent nonequilibrium potential. We emphasize conservation of the overall charge and current which are connected to the invariance under a global voltage shift (gauge invariance). As examples, we discuss the rectification coefficient of a quantum point contact and the nonlinear current-voltage characteristic of a resonant level in a double barrier structure.Comment: (Replaced version, with corrected Eq.(4)); 5 pages, RevTeX, 1 figure, uuencode

Chaotic dot-superconductor analog of the Hanbury Brown Twiss effect

As an electrical analog of the optical Hanbury Brown Twiss effect, we study current cross-correlations in a chaotic quantum dot-superconductor junction. One superconducting and two normal reservoirs are connected via point contacts to a chaotic quantum dot. For a wide range of contact widths and transparencies, we find large positive current correlations. The positive correlations are generally enhanced by normal backscattering in the contacts. Moreover, for normal backscattering in the contacts, the positive correlations survive when suppressing the proximity effect in the dot with a weak magnetic field.Comment: 4 pages, 3 figure