Charge Fluctuations in the Edge States of N-S hybrid Nano-Structures

In this work we show how to calculate the equilibrium and non-equilibrium charge fluctuations in a gated normal mesoscopic conductor which is attached to one normal lead and one superconducting lead. We then consider an example where the structure is placed in a high magnetic field, such that the transport is dominated by edge states. We calculate the equilibrium and non-equilibrium charge fluctuations in the gate, for a single edge state, comparing our results to those for the same system, but with two normal leads. We then consider the specific example of a quantum point contact and calculate the charge fluctuations in the gate for more than one edge state.Comment: 4 pages with 1 figure. In published version the high magnetic field dynamics of the holes is treated incorrectly. An erratum is in preparatio

Local densities, distribution functions, and wave function correlations for spatially resolved shot noise at nanocontacts

We consider a current-carrying, phase-coherent multi-probe conductor to which a small tunneling contact is attached. We treat the conductor and the tunneling contact as a phase-coherent entity and use a Green's function formulation of the scattering approach. We show that the average current and the current fluctuations at the tunneling contact are determined by an effective local non-equilibrium distribution function. This function characterizes the distribution of charge-carriers (or quasi-particles) inside the conductor. It is an exact quantum-mechanical expression and contains the phase-coherence of the particles via local partial densities of states, called injectivities. The distribution function is analyzed for different systems in the zero-temperature limit as well as at finite temperature. Furthermore, we investigate in detail the correlations of the currents measured at two different contacts of a four-probe sample, where two of the probes are only weakly coupled contacts. In particular, we show that the correlations of the currents are at zero-temperature given by spatially non-diagonal injectivities and emissivities. These non-diagonal densities are sensitive to correlations of wave functions and the phase of the wave functions. We consider ballistic conductors and metallic diffusive conductors. We also analyze the Aharonov-Bohm oscillations in the shot noise correlations of a conductor which in the absence of the nano-contacts exhibits no flux-sensitivity in the conductance.Comment: 17 pages, 8 figure

Nonlocal effects in the shot noise of diffusive superconductor - normal-metal systems

A cross-shaped diffusive system with two superconducting and two normal electrodes is considered. A voltage $eV < \Delta$ is applied between the normal leads. Even in the absence of average current through the superconducting electrodes their presence increases the shot noise at the normal electrodes and doubles it in the case of a strong coupling to the superconductors. The nonequilibrium noise at the superconducting electrodes remains finite even in the case of a vanishingly small transport current due to the absence of energy transfer into the superconductors. This noise is suppressed by electron-electron scattering at sufficiently high voltages.Comment: 4 pages, RevTeX, 2 eps figure

Quantum shot-noise at local tunneling contacts on mesoscopic multiprobe conductors

New experiments that measure the low-frequency shot-noise spectrum at local tunneling contacts on mesoscopic structures are proposed. The current fluctuation spectrum at a single tunneling tip is determined by local partial densities of states. The current-correlation spectrum between two tunneling tips is sensitive to non-diagonal density of states elements which are expressed in terms of products of scattering states of the conductor. Thus such an experiment permits to investigate correlations of electronic wave functions. We present specific results for a clean wire with a single barrier and for metallic diffusive conductors.Comment: 4 pages REVTeX, 2 figure

Smearing of charge fluctuations in a grain by spin-flip assisted tunneling

We investigate the charge fluctuations of a grain (large dot) coupled to a lead via a small quantum dot in the Kondo regime. We show that the strong entanglement of charge and spin flips in this setup can result in a stable SU(4) Kondo fixed point, which considerably smears out the Coulomb staircase behavior already in the weak tunneling limit. This behavior is robust enough to be experimentally observable.Comment: 4 pages, 1 figure, final version for PRB Rapid Com

Positive cross-correlations induced by ferromagnetic contacts

Due to the Fermionic nature of carriers, correlations between electric currents flowing through two different contacts attached to a conductor present a negative sign. Possibility for positive cross-correlations has been demonstrated in hybrid normal/superconductor structures under certain conditions. In this paper we show that positive cross-correlations can be induced, if not already present, in such structures by employing ferromagnetic leads with magnetizations aligned anti-parallel to each other. We consider three-terminal hybrid structures and calculate the mean-square correlations of current fluctuations as a function of the bias voltage at finite temperature.Comment: 6 pages, 5 figures; accepted version by PRB, figures replace

Lifetime of metastable states in resonant tunneling structures

We investigate the transport of electrons through a double-barrier resonant-tunneling structure in the regime where the current-voltage characteristics exhibit bistability. In this regime one of the states is metastable, and the system eventually switches from it to the stable state. We show that the mean switching time grows exponentially as the voltage across the device is tuned from the its boundary value into the bistable region. In samples of small area we find that the logarithm of the lifetime is proportional to the voltage (measured from its boundary value) to the 3/2 power, while in larger samples the logarithm of the lifetime is linearly proportional to the voltage.Comment: REVTeX 4, 5 pages, 3 EPS-figure

The Hanbury Brown and Twiss Experiment with Fermions

We realized an equivalent Hanbury Brown and Twiss experiment for a beam of electrons in a two dimensional electron gas in the quantum Hall regime. A metallic split gate serves as a tunable beam splitter which is used to partition the incident beam into transmitted and reflected partial beams. The current fluctuations in the reflected and transmitted beam are fully anticorrelated demonstrating that fermions tend to exclude each other (anti-bunching). If the occupation probability of the incident beam is lowered by an additional gate, the anticorrelation is reduced and disappears in the classical limit of a highly diluted beam

Nonlinear voltage dependence of shot noise

The current noise in a multi-probe mesoscopic conductor can have a nonlinear dependence on the strength of driving bias voltage. This paper presents a theoretical formulation for the nonlinear noise spectra. We pay special attention to maintain gauge invariance at the nonlinear level. At small but finite voltages, explicit expressions for nonlinear noise spectra, expanded order by order in the bias, have been derived. In the wideband limit, a closed form solution of the noise spectra for finite voltages is obtained

Coulomb induced positive current-current correlations in normal conductors

In the white-noise limit current correlations measured at different contacts of a mesoscopic conductor are negative due to the antisymmetry of the wave function (Pauli principle). We show that current fluctuations at capacitive contacts induced via the long range Coulomb interaction as consequence of charge fluctuations in the mesoscopic sample can be {\it positively} correlated. The positive correlations are a consequence of the extension of the wave-functions into areas near both contacts. As an example we investigate in detail a quantum point contact in a high magnetic field under conditions in which transport is along an edge state.Comment: Revtex, 4 pages includes 2 figure