arXiv subjects

M. Buttiker

Publications and source records attributed to M. Buttiker.

85 records · Page 5Linked to original sources

arXiv1997

Shot Noise Current-Current Correlations in Multi-Terminal Diffusive Conductors

We investigate the correlations in the current fluctuations at different terminals of metallic diffusive conductors. We start from scattering matrix expressions for the shot noise and use the Fisher-Lee relation in combination with diagram technique to evaluate the noise correlations. Of particular interest are exchange (interference) effects analogous to the Hanbury Brown--Twiss effect in optics. We find that the exchange effect exists in the ensemble averaged current correlations. Depending on the geometry, it might have the same magnitude as the mean square current fluctuations of the shot noise. The approach which we use is first applied to present a novel derivation of the 1/3-suppression of shot noise in a two-terminal geometry, valid for an arbitrary relation between the length and wire width. We find that in all geometries correlations are insensitive to dephasing.

cond-mat.mes-hall↗

arXiv1996

Charge-Relaxation and Dwell Time in the fluctuating Admittance of a Chaotic Cavity

We consider the admittance of a chaotic quantum dot, capacitively coupled to a gate and connected to two electron reservoirs by multichannel ballistic point contacts. For a dot in the regime of weak-localization and universal conductance fluctuations, we calculate the average and variance of the admittance using random-matrix theory. We find that the admittance is governed by two time-scales: the classical admittance depends on the RC-time of the quantum dot, but the relevant time scale for the weak-localization correction and the admittance fluctuations is the dwell time. An extension of the circular ensemble is used for a statistical description of the energy dependence of the scattering matrix.

cond-mat.mes-hall↗

arXiv1996

Admittance and Nonlinear Transport in Quantum Wires, Point Contacts, and Resonant Tunneling Barriers

We present a discussion of the admittance (ac-conductance) and nonlinear I-V-characteristic for a number of mesoscopic conductors. Our approach is based on a generalization of the scattering approach which now includes the effects of the (long-range) Coulomb interaction. We discuss the admittance of a wire with an impurity and with a nearby gate. We extend a discussion of the low-frequency admittance of a quantum point contact to investigate the effects of the gates used to form the contact. We discuss the nonlinear I-V characteristic of a resonant double barrier structure and discuss the admittance for the double barrier for a large range of frequencies. Our approach emphasizes the overall conservation of charge (gauge invariance) and current conservation and the resulting sum rules for the admittance matrix and nonlinear transport coefficients.

cond-mat.mes-hall↗

arXiv1996

Magnetic Field Symmetry of Dynamic Capacitances

While the static capacitance matrix is always symmetric and thus an even function of the magnetic field, the dynamic capacitance matrix of multi-terminal samples obeys in general only the weaker Onsager-Casimir symmetry relations. Our results are in accordance with recent experimental observations of asymmetric dynamic capacitances in quantized Hall systems. We predict quantization of the four-terminal resistances of an insulating Hall sample.

cond-mat↗

arXiv1996

Dynamic Conductance in Quantum Hall Systems

In the framework of the edge-channel picture and the scattering approach to conduction, we discuss the low frequency admittance of quantized Hall samples up to second order in frequency. The first-order term gives the leading order phase-shift between current and voltage and is associated with the displacement current. It is determined by the emittance which is a capacitance in a capacitive arrangement of edge channels but which is inductive-like if edge channels predominate which transmit charge between different reservoirs. The second-order term is associated with the charge relaxation. We apply our results to a Corbino disc and to two- and four-terminal quantum Hall bars, and we discuss the symmetry properties of the current response. In particular, we calculate the longitudinal resistance and the Hall resistance as a function of frequency.

cond-mat↗

arXiv1996

Low-frequency admittance of quantized Hall conductors

We present a current and charge conserving theory for the low frequency admittance of a two-dimensional electron gas connected to ideal metallic contacts and subject to a quantizing magnetic field. In the framework of the edge-channel picture, we calculate the admittance up to first order with respect to frequency. The transport coefficients in first order with respect to frequency, which are called emittances, determine the charge emitted into a contact of the sample or a gate in response to an oscillating voltage applied to a contact of the sample or a nearby gate. The emittances depend on the potential distribution inside the sample which is established in response to the oscillation of the potential at a contact. We show that the emittances can be related to the elements of an electro-chemical capacitance matrix which describes a (fictitious) geometry in which each edge channel is coupled to its own reservoir. The particular relation of the emittance matrix to this electro-chemical capacitance matrix depends strongly on the topology of the edge channels: We show that edge channels which connect different reservoirs contribute with a negative capacitance to the emittance. For example, while the emittance of a two-terminal Corbino disc is a capacitance, the emittance of a two-terminal quantum Hall bar is a negative capacitance. The geometry of the edge-channel arrangement in a many-terminal setup is reflected by symmetry properties of the emittance matrix. We investigate the effect of voltage probes and calculate the longitudinal and the Hall resistances of an ideal four-terminal Hall bar for low frequencies.

cond-mat↗

arXiv1996

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.

cond-mat↗

arXiv1996

Partial Densities of States, Scattering Matrices, and Green's Functions

The response of an arbitrary scattering problem to quasi-static perturbations in the scattering potential is naturally expressed in terms of a set of local partial densities of states and a set of sensitivities each associated with one element of the scattering matrix. We define the local partial densities of states and the sensitivities in terms of functional derivatives of the scattering matrix and discuss their relation to the Green's function. Certain combinations of the local partial densities of states represent the injectivity of a scattering channel into the system and the emissivity into a scattering channel. It is shown that the injectivities and emissivities are simply related to the absolute square of the scattering wave-function. We discuss also the connection of the partial densities of states and the sensitivities to characteristic times. We apply these concepts to a delta-barrier and to the local Larmor clock.

cond-mat↗

arXiv1996

Basic elements of electrical conduction

A theory of the dynamical conductance of mesoscopic conductors is presented. It is applied to mesoscopic capacitors, resonant double barriers, ballistic wires, metallic diffusive wires, and to the Corbino disk and the Hall bar in quantizing magnetic fields. Central to this approach is a discussion of the charge and potential distribution in mesoscopic conductors. It is necessary to take into account the implications of the long-range Coulomb interaction in order to obtain a charge and current conserving theory. We emphasize the low-frequency response. This has the advantage that the approach is of considerable generality. The theory can be used to discuss the self-consistency of the dc-conductance formula. The theory can also be applied to discuss the rectifying (nonlinear) behavior of mesoscopic conductors.

cond-mat↗

arXiv1996

Low frequency admittance of a quantum point contact

We present a current and charge conserving theory for the low frequency admittance of a quantum point contact. We derive expressions for the electrochemical capacitance and the displacement current. The latter is determined by the {\em emittance} which equals the capacitance only in the limit of vanishing transmission. With the opening of channels the capacitance and the emittance decrease in a step-like manner in synchronism with the conductance steps. For vanishing reflection, the capacitance vanishes and the emittance is negative.

cond-mat↗

arXiv1995

Aharonov-Bohm oscillations in a mesoscopic ring with a quantum dot

We present an analysis of the Aharonov-Bohm oscillations for a mesoscopic ring with a quantum dot inserted in one of its arms. It is shown that microreversibility demands that the phase of the Aharonov-Bohm oscillations changes {\it abruptly} when a resonant level crosses the Fermi energy. We use the Friedel sum rule to discuss the conservation of the parity of the oscillations at different conductance peaks. Our predictions are illustrated with the help of a simple one channel model that permits the variation of the potential landscape along the ring.

cond-mat↗

arXiv1994

Time-Dependent Current Partition in Mesoscopic Conductors

The currents at the terminals of a mesoscopic conductor are evaluated in the presence of slowly oscillating potentials applied to the contacts of the sample. The need to find a charge and current conserving solution to this dynamic current partition problem is emphasized. We present results for the electro-chemical admittance describing the long range Coulomb interaction in a Hartree approach. For multiply connected samples we discuss the symmetry of the admittance under reversal of an Aharonov-Bohm flux.

cond-mat↗

arXiv1994

Characteristic Potentials for Mesoscopic Rings Threaded by an Aharonov-Bohm Flux

Electro-static potentials for samples with the topology of a ring and penetrated by an Aharonov-Bohm flux are discussed. The sensitivity of the electron-density distribution to small variations in the flux generates an effective electro-static potential which is itself a periodic function of flux. We investigate a simple model in which the flux sensitive potential leads to a persistent current which is enhanced compared to that of a loop of non-interacting electrons. For sample geometries with contacts the sensitivity of the electro-static potential to flux leads to a flux-induced capacitance. This capacitance gives the variation in charge due to an increment in flux. The flux-induced capacitance is contrasted with the electro-chemical capacitance which gives the variation in charge due to an increment in an electro-chemical potential. The discussion is formulated in terms of characteristic functions which give the variation of the electro-static potential in the interior of the conductor due to an increment in the external control parameters (flux, electro-chemical potentials). Paper submitted to the 16th Nordic Semiconductor Meeting, Laugarvatan, Iceland, June 12-15, 1994. The proceedings will be published in Physica Scripta.

cond-mat↗