Diffusive Conductors Research Articles

Low-Temperature Dephasing and Renormalization in Model Systems

We investigate low-temperature dephasing in several model systems, where a quantum degree of freedom is coupled to a bath. Dephasing, defined as the decay of the coherence of inital non-equilibrium states, also influences the dynamics of equilibrium correlation and response functions, as well as static interference effects. In particular in the latter case dephasing should be distinguished from renormalization effects. For illustration, and because of its relevance for quantum state engineering in dissipative environments, we first reconsider dephasing in spin-boson models. Next we review Caldeira–Leggett models, with applications, e.g., to persistent currents in mesoscopic rings. Then, we analyze the more general problem of a particle which interacts with a quantum field V ( t , r ( t )), the fluctuations of which are characterized by a dielectric function e(ω, k ). Finally, we compare this model, both the formulation as well as the results, to the problem of interacting electrons in a diffusive conductor.

Shot-noise anomalies in nondegenerate elastic diffusive conductors

We present a theoretical investigation of shot-noise properties in nondegenerate elastic diffusive conductors. Both Monte Carlo simulations and analytical approaches are used. Two new phenomena are found: (i) the display of enhanced shot noise for given energy dependences of the scattering time, and (ii) the recovery of full shot noise for asymptotic high applied bias. The first phenomenon is associated with the onset of negative differential conductivity in energy space that drives the system towards a dynamical electrical instability in excellent agreement with analytical predictions. The enhancement is found to be strongly amplified when the dimensionality in momentum space is lowered from 3 to 2 dimensions. The second phenomenon is due to the suppression of the effects of long range Coulomb correlations that takes place when the transit time becomes the shortest time scale in the system, and is common to both elastic and inelastic nondegenerate diffusive conductors. These phenomena shed new light in the understanding of the anomalous behavior of shot noise in mesoscopic conductors, which is a signature of correlations among different current pulses.

Electrical detection of spin accumulation and spin precession at room temperature in metallic spin valves

We have fabricated a multiterminal lateral mesoscopic metallic spin valve demonstrating spin precession at room temperature (RT), using tunnel barriers in combination with metallic ferromagnetic electrodes as a spin injector and detector. The observed modulation of the output signal due to the spin precession is discussed and explained in terms of a time-of-flight experiment of electrons in a diffusive conductor. The obtained spin relaxation length λsf=500 nm in an aluminum strip will make detailed studies of spin dependent transport phenomena possible and allow one to explore the possibilities of the electron spin for new electronic applications at RT.

Structure of quantum disordered wave functions: weak localization, far tails, and mesoscopic transport

We report on the comprehensive numerical study of the fluctuation and correlation properties of wave functions in three-dimensional mesoscopic diffusive conductors. Several large sets of nanoscale samples with finite metallic conductance, modeled by an Anderson model with different strengths of diagonal box disorder, have been generated in order to investigate both small and large deviations (as well as the connection between them) of the distribution function of eigenstate amplitudes from the universal prediction of random matrix theory. We find that small, weak localization-type, deviations contain both diffusive contributions (determined by the bulk and boundary conditions dependent terms) and ballistic ones which are generated by electron dynamics below the length scale set by the mean free path ℓ. By relating the extracted parameters of the functional form of nonperturbative deviations (“far tails”) to the exactly calculated transport properties of mesoscopic conductors, we compare our findings based on the full solution of the Schrödinger equation to different approximative analytical treatments. We find that statistics in the far tail can be explained by the exp-log-cube asymptotics (convincingly refuting the log-normal alternative), but with parameters whose dependence on ℓ is linear and, therefore, expected to be dominated by ballistic effects. It is demonstrated that both small deviations and far tails depend explicitly on the sample size--the remaining puzzle then is the evolution of the far tail parameters with the size of the conductor since short-scale physics is supposedly insensitive to the sample boundaries.

Scaling theory of phase-coherent metallic conductors

We present a scaling theory for describing the smooth crossover from ballistic to diffusive transport in phase-coherent metallic conductors. The theory confirms a recent conjecture by Beenakker [Rev. Mod. Phys. $69,$ 731 (1997)], and represents a substantial improvement in the two-terminal version of Nazarov's circuit theory [Phys. Rev. Lett. $73,$ 134 (1994); $73,$ 1420 (1994)]. In addition, our approach allows for the explicit inclusion of interfaces of arbitrary transparency, which are described using the supersymmetric nonlinear $\ensuremath{\sigma}$ model. The problem of two identical barriers separated by a diffusive conductor is solved exactly, and expressions for both the normal and Andreev conductances are presented.

Shot-noise statistics in diffusive conductors

We study the full probability distribution of the charge transmitted through a mesoscopic diffusive conductor during a measurement time Δ. We have considered a semi-classical model, with an exclusion principle in a discretized single-particle phase-space. In the large Δ limit, numerical simulations show a universal probability distribution which agrees very well with the quantum mechanical prediction of Lee et al. [Phys. Rev. B 51, 4079 (1995)] for the charge counting statistics. Special attention is given to its third cumulant, including an analysis of finite size effects and of some experimental constraints for its accurate measurement.

The theory of shot noise in the space-charge-limited diffusive conduction regime

As is well known, the fluctuations from a stable stationary nonequilibrium state are described by a linearized nonhomogeneous Boltzmann-Langevin equation. The stationary state itself may be described by a nonlinear Boltzmann equation. The ways of its linearization sometimes seem to be not unique. We argue that there is actually a unique way to obtain a linear equation for the fluctuations. In the present paper we treat as an example an analytical theory of nonequilibrium shot noise in a diffusive conductor under the space charge limited regime. Our approach is compared with that of Schomerus, Mishchenko and Beenakker [Phys. Rev. B 60, 5839 (1999)]. We find some difference between the present theory and the approach of their paper and discuss a possible origin of the difference. We believe that it is related to the fundamentals of the theory of fluctuation phenomena in a nonequilibrium electron gas.

Electrical detection of spin precession in a metallic mesoscopic spin valve.

To study and control the behaviour of the spins of electrons that are moving through a metal or semiconductor is an outstanding challenge in the field of 'spintronics', where possibilities for new electronic applications based on the spin degree of freedom are currently being explored. Recently, electrical control of spin coherence and coherent spin precession during transport was studied by optical techniques in semiconductors. Here we report controlled spin precession of electrically injected and detected electrons in a diffusive metallic conductor, using tunnel barriers in combination with metallic ferromagnetic electrodes as spin injector and detector. The output voltage of our device is sensitive to the spin degree of freedom only, and its sign can be switched from positive to negative, depending on the relative magnetization of the ferromagnetic electrodes. We show that the spin direction can be controlled by inducing a coherent spin precession caused by an applied perpendicular magnetic field. By inducing an average precession angle of 180 degrees, we are able to reverse the sign of the output voltage.

The characteristic potential method of noise calculation in multi-terminal homogeneous semiconductor resistors

Based on the characteristic potentials previously developed formulti-terminal diffusive mesoscopic conductors by Sukhorukov andLoss, the formulas are presented of both the short-circuit noisecurrents including thermal noise and excess noise (1/f noiseand generation-recombination noise) currents and the open-circuitnoise voltages of macroscopic multi-terminal homogeneous semiconductorresistors with arbitrary geometry under dc bias. The formulas areof neat volume integral form and they give the information abouthow much contribution a certain region of a device makes to theterminal noise currents or voltages. A comparison between thecharacteristic potential method and the impedance field methoddeveloped by Shockley and co-workers is presented. A direct experimental verification of the derived formulas has been provided by measuring thermal and 1/f noise of three-terminal homogeneous polycrystallinesilicon resistors and carbon resistors.

Numerical Investigation of Shot Noise between the Ballistic and the Diffusive Regime

We investigate shot noise suppression in several mesoscopic structures by means of a numerical approach based on the computation of the transmission matrix with the recursive Green's function method. We retrieve the “universal” values of the suppression factor obtained with random matrix theory for chaotic cavities and diffusive conductors. We then extend the investigation to more complex structures, such as multiple cascaded cavities and partially diffusive systems, and discuss the consequences on the shot noise suppression factor. Finally, we analyze the behavior of shot noise in an electron waveguide containing a large number of scatterers as the spatial position of the scatterers is changed from a regular array to a random distribution.

A novel device principle for nanoelectronics

We report on the results of our recent theoretical and experimental investigations of a novel, room temperature electrical property of three-terminal ballistic junctions (TBJs). For a symmetric TBJ device, it is found that when finite voltages V l and V r are applied in push–pull fashion, with V l= V and V r=− V, to the left and right branches, the voltage output V c from the central branch will always be negative. This property is in strong contrast to a symmetric three-terminal device made from conventional diffusive conductors, for which Ohm's law predicts a constant zero output of V c for all V l=− V r. This novel characteristic appears even when the device symmetry is broken, provided that | V| is greater than the threshold. It is also shown that the TBJ devices show a good parabolic behavior for V c vs. V in a large range of voltages V.

Poisson and Wigner-Dyson distributions of conductance fluctuations in quantum cavities

We investigate the statistical properties of conductance fluctuations in quantum cavities when the underlying classical dynamics is either regular or chaotic. Regardless of the dynamics, the correlation magnetic field of the conductance fluctuations in ballistic cavities increases linearly with the lead width, in contrast to its independence on the lead width in diffusive conductors. The linear increase is a consequence of electrons staying shorter in the cavity for wider leads. The probability distributions of the magnetic field and energy spacings between the nearest-neighbor peaks and dips in the conductance are found to be described by the Poisson distribution for regular quantum cavities and by the Wigner-Dyson distribution for chaotic quantum cavities. We also examine the influence of dephasing in the quantum cavities on the statistical behavior.

Quest for rare events in mesoscopic disordered metals

The study reports on the first large statistics numerical experiment searching for rare eigenstates of anomalously high amplitudes in three-dimensional diffusive metallic conductors. Only a small fraction of a huge number of investigated eigenfunctions generates the far asymptotic tail of their amplitude distribution function. The relevance of the relationship between disorder and spectral averaging, as well as of the quantum transport properties of the investigated mesoscopic samples, for the numerical exploration of eigenstate statistics is divulged. The quest provides exact results to serve as a reference point for understanding the limits of approximations employed in different analytical predictions and, therefore, the physics (quantum vs semiclassical) behind large deviations from the universal predictions of random matrix theory.

Mesoscopic physics on graphs

This report is a summary of recent work on theproperties of phase coherent diffusive conductors, especially inthe geometry of networks — also called graphs — made ofquasi-1D diffusive wires. These properties are written as afunction of the spectral determinant of the diffusion equation(the product of its eigenvalues). For a network with N nodes,this spectral determinant is related to the determinant of an N × N matrix which describes the connectivity of the network.I also consider the transmission through networks made of 1Dballistic wires and show how the transmission coefficient can bewritten in terms of an N × N matrix very similar to the aboveone. Finally I present a few considerations on the relationbetween the magnetism of noninteracting systems and themagnetism of interacting diffusive systems.

Full current statistics in diffusive normal-superconductor structures.

We study the current statistics in normal diffusive conductors in contact with a superconductor. Using an extension of the Keldysh Green's function method we are able to find the full distribution of charge transfers for all temperatures and voltages. For the non-Gaussian regime, we show that the equilibrium current fluctuations are enhanced by the presence of the superconductor. We predict an enhancement of the nonequilibrium current noise for temperatures below and voltages of the order of the Thouless energy E(Th) = D/L(2). Our calculation fully accounts for the proximity effect in the normal metal and agrees with experimental data.

Energy dependence of quasiparticle relaxation in a disordered fermi liquid.

A spectroscopic method is applied to measure the inelastic quasiparticle relaxation rate in a disordered Fermi liquid. The quasiparticle relaxation rate gamma is deduced from the magnitude of fluctuations in the local density of states, which are probed using resonant tunneling through a localized impurity state. We study its dependence on the excitation energy E measured from the Fermi level. In a disordered metal (heavily doped GaAs) we find that gamma~E3/2 within the experimentally accessible energy interval, in agreement with the Altshuler-Aronov theory for electron-electron interactions in diffusive conductors.

Weak charge quantization as an instanton of the interacting sigma model.

Coulomb blockade in a quantum dot attached to a diffusive conductor is considered in the framework of the nonlinear sigma model. It is shown that the weak charge quantization on the dot is associated with instanton configurations of the Q field in the conductor. The instantons have a finite action and are replica nonsymmetric. It is argued that such instantons may play a role in the transition regime to the interacting insulator.

Effect of dimensionality on shot-noise suppression in nondegenerate diffusive conductors

We present a theoretical investigation of shot-noise suppression due to long-range Coulomb interaction in nondegenerate diffusive conductors. Calculations make use of an ensemble Monte-Carlo simulator, self-consistently coupled with a one-dimensional Poisson solver. We analyze the noise in a lightly doped active region surrounded by two contacts acting as thermal reservoirs. The effect of momentum space dimensionality on shot-noise suppression is analyzed. Provided significant space-charge effects take place inside the active region, long-range Coulomb interaction is found to play an essential role in suppressing the shot noise at qU≫ k B T. In the elastic diffusive regime, dimensionality is found to modify the suppression factor γ, which within numerical uncertainty takes values of about 1/3, 1/2 and 0.7 in the cases of 3, 2 and 1 dimensions, respectively.

Conductance fluctuations in diffusive rings: Berry phase effects and criteria for adiabaticity

We study Berry phase effects on conductance properties of diffusive mesoscopic conductors, which are caused by an electron spin moving through an orientationally inhomogeneous magnetic field. Extending previous work, we start with an exact, i.e. not assuming adiabaticity, calculation of the universal conductance fluctuations in a diffusive ring within the weak localization regime, based on a differential equation which we derive for the diffuson in the presence of Zeeman coupling to a magnetic field texture. We calculate the field strength required for adiabaticity and show that this strength is reduced by the diffusive motion. We demonstrate that not only the phases but also the amplitudes of the h/2e Aharonov-Bohm oscillations are strongly affected by the Berry phase. In particular, we show that these amplitudes are completely suppressed at certain magic tilt angles of the external fields, and thereby provide a useful criterion for experimental searches. We also discuss Berry phase-like effects resulting from spin-orbit interaction in diffusive conductors and derive exact formulas for both magnetoconductance and conductance fluctuations. We discuss the power spectra of the magnetoconductance and the conductance fluctuations for inhomogeneous magnetic fields and for spin-orbit interaction.

Emittance fluctuations in a mesoscopic diffusive conductor

We report a first principles analysis of low frequency dynamic conductance fluctuations for disordered two-dimensional mesoscopic conductors. In the transport regime where dc conductance shows the familiar universal conductance fluctuations, we discovered that the low frequency emittance also fluctuates with an amplitude that is independent of the impurity scattering strength, showing a degree of generic behavior. When the impurity density is increased such that the dynamic response of the conductor changes from inductivelike to capacitivelike, the emittance distribution is found to cross over from Gaussian-like to non-Gaussian-like; the latter is qualitatively consistent with random matrix theory.