Mesoscopic Transport Research Articles

Observation of intensity statistics of light transmitted through 3D random media.

We experimentally observe the spatial intensity statistics of light transmitted through three-dimensional (3D) isotropic scattering media. The intensity distributions measured through layers consisting of zinc oxide nanoparticles differ significantly from the usual Rayleigh statistics associated with speckle and instead are in agreement with the predictions of mesoscopic transport theory, taking into account the known material parameters of the samples. Consistent with the measured spatial intensity fluctuations, the total transmission fluctuates. The magnitude of the fluctuations in the total transmission is smaller than expected on the basis of quasi-one-dimensional (1D) transport theory, which indicates that quasi-1D theories cannot fully describe these open 3D media.

Current patterns and orbital magnetism in mesoscopic dc transport.

We present ab initio calculations of the local current density j(r) as it arises in dc-transport measurements. We discover pronounced patterns in the local current density, ring currents ("eddies"), that go along with orbital magnetism. Importantly, the magnitude of the ring currents can exceed the (average) transport current by orders of magnitude. We find associated magnetic fields that exhibit drastic fluctuations with field gradients reaching 1 T nm⁻¹ V⁻¹. The relevance of our observations for spin relaxation in systems with very weak spin-orbit interaction, such as organic semiconductors, is discussed. In such systems, spin relaxation induced by bias driven orbital magnetism competes with relaxation induced by the hyperfine interaction and appears to be of similar strength. We propose a NMR-type experiment in the presence of dc-current flow to observe the spatial fluctuations of the induced magnetic fields.

Mean free paths in single-walled carbon nanotubes measured by Kelvin probe force microscopy

The inelastic mean free path ${\ensuremath{\lambda}}_{\mathrm{MFP}}$ is a critical parameter for electronic devices. Here, we demonstrate Kelvin probe force microscopy (KPFM) as a technique for studying ${\ensuremath{\lambda}}_{\mathrm{MFP}}$ in biased, semi-metallic single-walled carbon nanotubes (SWNTs). Having one of the longest room-temperature ${\ensuremath{\lambda}}_{\mathrm{MFP}}$ values of any known material, SWNTs provide a unique platform for probing mesoscopic transport. KPFM directly determined ${\ensuremath{\lambda}}_{\mathrm{MFP}}$ as a function of bias, quantitatively determined the contributions of different scattering mechanisms, and enabled comparative study of individual SWNTs with and without disorder. The room-temperature mean free paths for optical phonon and surface plasmon-polariton scattering were measured to be 62 \ifmmode\pm\else\textpm\fi{} 20 nm and 260 \ifmmode\pm\else\textpm\fi{} 50 nm, respectively. The optical phonon scattering length is significantly longer than inferred from previous measurements, and it resolves a longstanding discrepancy between SWNT theory and experiment, suggesting that KPFM could become a preferred quantitative technique for studying transport in nanoscale systems.

Conditional spin counting statistics as a probe of Coulomb interaction and spin-resolved bunching

Full counting statistics is a powerful tool to characterize the noise and correlations in transport through mesoscopic systems. In this work, we propose the theory of conditional spin counting statistics, i.e., the statistical fluctuations of spin-up (down) current given the observation of the spin-down (up) current. In the context of transport through a single quantum dot, it is demonstrated that a strong Coulomb interaction leads to a conditional spin counting statistics that exhibits a substantial change in comparison to that without Coulomb repulsion. It thus can be served as an effective way to probe the Coulomb interactions in mesoscopic transport systems. In case of spin polarized transport, it is further shown that the conditional spin counting statistics offers a transparent tool to reveal the spin-resolved bunching behavior.

Memory Effects in Non-Interacting Mesoscopic Transport

Consider a quantum dot coupled to two semi-infinite one-dimensional leads at thermal equilibrium. We turn on adiabatically a bias between the leads such that there exists exactly one discrete eigenvalue both at the beginning and at the end of the switching procedure. For a specific adiabatic limit scenario, it is shown that the expectation in the final bound state strongly depends on the history of the switching procedure. On the contrary, the contribution to the final steady-state corresponding to the continuous spectrum has no memory, and only depends on the initial and final values of the bias.

Finite-element methods for spatially resolved mesoscopic electron transport

A finite-element method is presented for calculating the quantum conductance of mesoscopic two-dimensional electron devices of complex geometry attached to semi-infinite leads. For computational purposes, the leads must be cut off at some finite length. To avoid spurious, unphysical reflections, this is modeled by transparent boundary conditions. We introduce the Hardy space infinite-element technique from acoustic scattering as a way of setting up transparent boundary conditions for transport computations spanning the range from the quantum mechanical to the quasiclassical regime. These boundary conditions are exact even for wave packets and thus are especially useful in the limit of high energies with many excited modes. Yet, they possess a memory-friendly sparse matrix representation. In addition to unbounded domains, Hardy space elements allow us to truncate those parts of the computational domain which are irrelevant for the calculation of the transport properties. Thus, the computation can be done only on the region that is essential for a physically meaningful simulation of the scattering states. The benefits of the method are demonstrated by three examples. The convergence properties are tested on the transport through a quasi-one-dimensional quantum wire. It is shown that higher-order finite elements considerably improve current conservation and establish the correct phase shift between the real and the imaginary parts of the electron wave function. The Aharonov-Bohm effect demonstrates that characteristic features of quantum interference can be assessed. A simulation of electron magnetic focusing exemplifies the capability of the computational framework to study the crossover from quantum to quasiclassical behavior.

Anticorrelation for conductance fluctuations in chaotic quantum dots

We investigate the correlation functions of mesoscopic electronic transport in open chaotic quantum dots with finite tunnel barriers in the crossover between Wigner-Dyson ensembles. Using an analytical stub formalism, we show the emergence of a depletion and amplification of conductance fluctuations as a function of tunnel barriers for both parametric variations of electron energy and magnetoconductance fields. Furthermore, even for pure Dyson ensembles, correlation functions of conductance fluctuations in chaotic quantum dots can exhibit anticorrelation. Experimental support to our findings is pointed out.

Broken Symmetries, Zero-Energy Modes, and Quantum Transport in Disordered Graphene: From Supermetallic to Insulating Regimes

The role of defect-induced zero-energy modes on charge transport in graphene is investigated using Kubo and Landauer transport calculations. By tuning the density of random distributions of monovacancies either equally populating the two sublattices or exclusively located on a single sublattice, all conduction regimes are covered from direct tunneling through evanescent modes to mesoscopic transport in bulk disordered graphene. Depending on the transport measurement geometry, defect density, and broken sublattice symmetry, the Dirac-point conductivity is either exceptionally robust against disorder (supermetallic state) or suppressed through a gap opening or by algebraic localization of zero-energy modes, whereas weak localization and the Anderson insulating regime are obtained for higher energies. These findings clarify the contribution of zero-energy modes to transport at the Dirac point, hitherto controversial.

Mesoscopic thermoelectric transport near zero transmission energies

We study the thermoelectric transport coefficients of a one-dimensional (1D) electron waveguide connected to one and then two off-channel cavities, in the presence of dephasing phonons. The model system is that of a linear chain described as a 1D lattice. For simplicity we consider single-mode cavities, which may be tuned with external gates. While the presence of only one off-channel cavity yields a nearly symmetric transmission profile, which is canceled around the cavity mode, an additional cavity modifies this profile strongly and results in an asymmetric shape characterized by oscillations. In both cases, we consider electron-phonon interactions in our calculations and analyze their effects on the transmission function around the Fermi energy. Knowledge of the energy-dependent transmission function allows the numerical computation of thermoelectric transport coefficients, including the thermopower. In the presence of a second off-channel cavity, the sign of the thermopower depends on the relative position of this cavity energy level with respect to the Fermi energy: the thermopower is positive when low-energy electrons in the vicinity of the Fermi level are not transmitted, and becomes negative when the higher-energy electrons are not transmitted.

Mesoscopic light transport by very strong collective multiple scattering in nanowire mats

Under the extreme condition of the scattering length being much shorter than the wavelength, light transport in random media is strongly modified by mesoscopic interference, and can even be halted in an effect known as Anderson localization. Anderson localization in three dimensions has recently been realized for acoustic waves and for cold atoms. Mats of disordered, high-refractive-index semiconductor nanowires are one of the strongest three-dimensional scattering materials for light, but localization has not been shown. Here, we use statistical methods originally developed for microwave waveguides to demonstrate that transport of light through nanowire mats is strongly correlated and governed by mesoscopic interference contributions. Our results confirm the contribution of only a few open modes to the transmission.

Spin-flip Fano–Kondo resonant tunneling through a quantum dot interferometer responded by a rotating magnetic field

Abstract The Fano and Kondo cooperated resonant tunneling through a quantum dot interferometer under the perturbation of a rotating magnetic field is investigated theoretically. The spin-polarized current components have been derived generally by employing the Keldysh nonequilibrium Greenʼs function method, through which the charge and spin currents are determined directly. The numerical calculations on spin and charge currents are performed to show the compound features of mesoscopic transport associated with the Kondo, Fano, and Zeeman effects intimately. The induced spin current in the Kondo regime is much different from the one in the non-interacting regime. The spin current is tuned from resonant peak to valley by varying external parameters.

Large-scale Mesoscopic Transport in Nanostructured Graphene

Through exponential sample-size scaling of conductance, we demonstrate strong electron localization in three sets of nanostructured antidot graphene samples with localization lengths of 1.1, 2, and 3.4 μm. The large-scale mesoscopic transport is manifest as a parallel conduction channel to 2D variable range hopping, with a Coulomb quasigap around the Fermi level. The opening of the correlation quasigap, observable below 25 K through the temperature dependence of conductance, makes possible the exponential suppression of inelastic electron-electron scatterings and thereby leads to an observed dephasing length of 10 μm.

The DMPK equation for mesoscopic quantum transport revisited

A recent Drude model description of the metallic regime and of a channel-averaged elastic mean free path (mfp), ℓ0, in an N-channel tight-binding wire identifies the Thouless localization length, Nℓ0, as a proper lower bound of macroscopic length scales (“mean free path”) for the DMPK equation describing the localized regime of the wire. The mfp ℓ0 leads to a metallic regime which is consistent with Dorokhov's microscopic transmission analysis in terms of a nominal elastic mfp. On the other hand, the validity of Mello's derivation of universal conductance fluctuations in the metallic regime based on the DMPK equation is restored if the mfp ℓ′, of order Nℓ0, in that equation is replaced by the correct mean free path ℓ0.

Time-Dependent Impurity in Ultracold Fermions: Orthogonality Catastrophe and Beyond

Recent experimental realization of strongly imbalanced mixtures of ultracold atoms opens new possibilities for studying impurity dynamics in a controlled setting. We discuss how the techniques of atomic physics can be used to explore new regimes and manifestations of Anderson's orthogonality catastrophe (OC), which could not be accessed in solid state systems. We consider a system of impurity atoms localized by a strong optical lattice potential and immersed in a sea of itinerant Fermi atoms. Ramsey interference experiments with impurity atoms probe OC in the time domain, while radio-frequency (RF) spectroscopy probes OC in the frequency domain. The OC in such systems is universal for all times and is determined by the impurity scattering length and Fermi wave vector of itinerant fermions. We calculate the universal Ramsey response and RF absorption spectra. In addition to the standard power-law contribution, which corresponds to the excitation of multiple particle-hole pairs near the Fermi surface, we identify a novel contribution to OC that comes from exciting one extra particle from the bottom of the itinerant band. This gives rise to a non-analytic feature in the RF absorption spectra, which evolves into a true power-law singularity with universal exponent 1/4 at the unitarity. Furthermore, we discuss the manifestations of OC in spin-echo experiments, as well as in the energy counting statistic of the Fermi gas following a sudden quench of the impurity state. Finally, systems in which the itinerant fermions have two or more hyperfine states provide an even richer playground for studying non-equilibrium impurity physics, allowing one to explore non-equilibrium OC and to simulate quantum transport through nano-structures. This provides a useful connection between cold atomic systems and mesoscopic quantum transport.

Effect of Rough Walls on Transport in Mesoscopic 3He Films

The interplay of bulk and boundary scattering is explored in a regime where quantum size effects modify mesoscopic transport in a degenerate Fermi liquid film of $^3$He on a rough surface. We discuss mass transport and the momentum relaxation time of the film in a torsional oscillator geometry within the framework of a quasiclassical theory that includes the experimentally determined power spectrum of the rough surface. The theory explains the anomalous temperature dependence of the relaxation rate observed experimentally. We model further studies on $^3$He confined in nanofluidic sample chambers with lithographically defined surface roughness. The improved understanding of surface roughness scattering can be extended to the analogous system of electrons in metals and suggests routes to improve the conductivity of thin metallic films.

Controlled fabrication of artificial ferromagnetic (Fe,Mn)3O4 nanowall-wires by a three-dimensional nanotemplate pulsed laser deposition method

We have developed a new method to fabricate extremely small transition-metal oxide nanowires. Using a combination of nanoimprint template patterning and inclined substrate pulsed laser deposition, we successfully fabricated magnetic oxide Fe2.5Mn0.5O4 nanowall-wires, and controlled the width in a range from 120 nm down to about 20 nm by varying deposition parameters. Magnetoresistance measurements revealed ferromagnetic properties of the Fe2.5Mn0.5O4 nanowall-wire. This method enables the study of mesoscopic transport properties of transition-metal oxides towards the development of oxide-based nanodevices.

Dynamic scaling for anomalous transport in supercooled liquids

The anomalous mesoscopic transport in supercooled liquids was investigated using three-dimensional molecular dynamics simulation. We show that the dynamic correlation length, ξ, can be identified as a crossover length between the microscopic and macroscopic transports. We also find that in highly supercooled states, where a clear stress plateau is observed in the stress autocorrelation, cooperative transport, in both the (longitudinal) density diffusion and the (transverse) viscous relaxation, can be characterized by the single length scale, ξ. The present identification of the dynamic correlation length has an advantage over other characterization methods in that it directly interprets the anomalous hydrodynamic transport in terms of the growing length scale. In the context of the present study, we provide a simple explanation for the long-standing problem of the breakdown of the Stokes-Einstein relation.

Scattering matrix approach to interacting electron transport

We investigate the modification in mesoscopic electronic transport due to electron-electron interactions making use of scattering states. We demonstrate that for a specific (finite range) interaction kernel, the knowledge of the scattering matrix is sufficient to take interaction effects into account. We calculate perturbatively the corrections to the current and current-current correlator; in agreement with previous work, we find that, in linear response, interaction effects can be accounted for by an effective (renormalized) transmission probability. Beyond linear response, simple renormalization of scattering coefficients is not sufficient to describe the current-current correlator, as additional corrections arise due to irreducible two-particle processes. Furthermore, we find that the correlations between opposite-spin currents induced by interaction are enhanced for an asymmetric scatterer, generating a nonzero result already to lowest order in the interaction.

Fractional-time random walk subdiffusion and anomalous transport with finite mean residence times: Faster, not slower

Continuous time random walk (CTRW) subdiffusion along with the associated fractional Fokker-Planck equation (FFPE) is traditionally based on the premise of random clock with divergent mean period. This work considers an alternative CTRW and FFPE description which is featured by finite mean residence times (MRTs) in any spatial domain of finite size. Transient subdiffusive transport can occur on a very large time scale τ(c) which can greatly exceed mean residence time in any trap, τ(c) >>(τ), and even not being related to it. Asymptotically, on a macroscale transport becomes normal for t >> τ(c). However, mesoscopic transport is anomalous. Differently from viscoelastic subdiffusion no long-range anticorrelations among position increments are required. Moreover, our study makes it obvious that the transient subdiffusion and transport are faster than one expects from their normal asymptotic limit on a macroscale. This observation has profound implications for anomalous mesoscopic transport processes in biological cells because the macroscopic viscosity of cytoplasm is finite.

Conduction of Ultracold Fermions Through a Mesoscopic Channel

In a mesoscopic conductor, electric resistance is detected even if the device is defect-free. We engineered and studied a cold-atom analog of a mesoscopic conductor. It consists of a narrow channel connecting two macroscopic reservoirs of fermions that can be switched from ballistic to diffusive. We induced a current through the channel and found ohmic conduction, even when the channel is ballistic. We measured in situ the density variations resulting from the presence of a current and observed that density remains uniform and constant inside the ballistic channel. In contrast, for the diffusive case with disorder, we observed a density gradient extending through the channel. Our approach opens the way toward quantum simulation of mesoscopic devices with quantum gases.