Mesoscopic conductance fluctuations in graphene samples at energies not very close to the Dirac point are studied analytically. We demonstrate that the conductance variance $<[δG]^2>$ is very sensitive to the elastic scattering breaking the valley symmetry. In the absence of such scattering (disorder potential smooth at atomic scales, trigonal warping negligible), the variance $<[δG]^2 > = 4 < [δG]^2 >_\text{metal}$ is four times greater than that in conventional metals, which is due to the two-fold valley degeneracy. In the absence of intervalley scattering, but for strong intravalley scattering and/or strong warping $<[δG]^2 > =2 < [δG]^2 >_\text{metal}$. Only in the limit of strong intervalley scattering $<[δG]^2 > = < [δG]^2 >_\text{metal}$. Our theory explains recent numerical results and can be used for comparison with existing experiments.
We show theoretically and experimentally that the conductance of small disordered samples exhibits random oscillations as a function of temperature. The amplitude of the oscillations decays as a power law of temperature, and their characteristic period is of the order of the temperature itself.
Quantum corrections to the electrical conduction of magnetic semiconductors are comparatively unexplored. We report measurements of time-dependent universal conductance fluctuations (TDUCF) and magnetic field dependent universal conductance fluctuations (MFUCF) in micron-scale structures fabricated from two different In$_{1-x}$Mn$_{x}$As thin films. TDUCF and MFUCF increasing in magnitude with decreasing temperature are observed. At 4 K and below, TDUCF are suppressed at finite magnetic fields independent of field orientation.
In cold, mesoscopic conductors, two-level fluctuators lead to time-dependent universal conductance fluctuations (TDUCF) manifested as $1/f$ noise. In Au nanowires, we measure the magnetic field dependence of TDUCF, weak localization (WL), and magnetic field-driven (MF) UCF before and after treatments that alter magnetic scattering and passivate surface fluctuators. Inconsistencies between $L_ϕ^{\rm WL}$ and $L_ϕ^{\rm TDUCF}$ strongly suggest either that the theory of these mesoscopic phenomena in weakly disordered, highly pure Au is incomplete, or that the assumption that the TDUCF frequency d…
We present a theory of conductance and noise in generic mesoscopic conductors connected in parallel, and we demonstrate that the additivity of conductance and of shot noise arises as a sole property of the junctions connecting the two (or more) conductors in parallel. Consequences on the functionality of devices based on the Aharonov-Bohm effect are also drawn.
We study by computer simulation distribution functions (DF) of mesoscopic hopping conductance. The DFs obtained for one-dimensional systems were found to be quite close to the predictions of the theory by Raikh and Ruzin. For D=2, the DFs both for narrow system and thin film look similar (and close to the 1D case).The distribution function for the conductance of the square sample is nearly Gaussian.
We investigate spin-dependent transport in three--terminal mesoscopic cavities with spin--orbit coupling. Focusing on the inverse spin Hall effect, we show how injecting a pure spin current or a polarized current from one terminal generates additional charge current and/or voltage across the two output terminals. This allows to extract the spin conductance of the cavity from two purely electrical measurements on the output. We use random matrix theory to show that the spin conductance of chaotic ballistic cavities fluctuates universally about zero mesoscopic average and describe experimental i…
The influence of contacts on linear transport through a molecular wire attached to mesoscopic tubule leads is studied. It is shown that low dimensional leads, such as carbon nanotubes, in contrast to bulky electrodes, strongly affect transport properties. By focusing on the specificity of the lead-wire contact, we show, in a fully analytical treatment, that the geometry of this hybrid system supports a mechanism of channel selection and a sum rule, which is a distinctive hallmark of the mesoscopic nature of the electrodes.
The conductance distribution of metallic mesoscopic systems is considered. The variance of this distribution describes the universal conductance fluctuations, yielding a Gaussian distribution of the conductance. We calculate diagrammatically the third cumulant of this distribution, the leading deviation from the Gaussian. We confirm random matrix theory calculations that the leading contribution in quasi-one dimension vanishes. However, in quasi two dimensions the third cumulant is negative, whereas in three dimensions it is positive.
We evaluate a typical value of higher order cumulants (irreducible moments) of conductance fluctuations that could be extracted from magneto-conductance measurements in a single sample when an external magnetic field is swept over an interval $B_0$. We find that the n-th cumulant has a sample-dependent random part $\pm \gN 2^{n/2}\sqrt{a_{n}B_{c}/B_{0}}$, where $\gN 2$ is the variance of conductance fluctuations, $B_{c}$ is a correlation field, and $a_{n}\sim n!$. This means that an apparent deviation of the conductance distribution from a Gaussian shape, manifested by non-vanishing higher cum…
The calculation of the conductance of ballistic rings requires a theory that goes well beyond the Kubo-Drude formula. Assuming "mesoscopic" circumstance of very weak environmental relaxation, the conductance is much smaller compared with the naive expectation. Namely, the electro-motive-force induces an energy absorption with a rate that depends crucially on the possibility to make connected sequences of transitions. Thus the calculation of the mesoscopic conductance is similar to solving a percolation problem. The "percolation" is in energy space rather than in real space. Non-universal struc…
The nonlinear dc conductance of a two-terminal chaotic cavity is investigated. The fluctuations of the conductance (anti)symmetric with respect to magnetic flux inversion through multichannel cavities are found analytically for arbitrary temperature, magnetic field, and interaction strength. For few-channel dots the effect of dephasing is investigated numerically. A comparison with recent experimental data is provided.
We use the high sensitivity to magnetic flux of mesoscopic conductance fluctuations in large quantum dots to investigate changes in the two-dimensional electron dispersion caused by an in-plane magnetic field. In particular, changes in effective mass and the breaking of momentum reversal symmetry in the electron dispersion are extracted quantitatively from correlations of conductance fluctuations. New theory is presented, and good agreement between theory and experiment is found.
We demonstrate that in the atomic-scale limit the thermal conductance $\mathcal K$ of the FPU model and its variants strongly deviates from the mesoscopic behavior due to the relevance of contact resistance. As a result, atomic chains follow $\log \mathcal K = ν\log T$, where the power law coefficient $ν$ is exactly two times larger than the mesoscopic value. We smoothly interconnect the atomic and mesoscopic limits, and demonstrate that this turnover behavior takes place in other nonlinear FPU-like models. Our results are significant for nanoscale applications, manifesting an atomic thermal c…
We report on intrinsic time-dependent conductance fluctuations observed in mesoscopic AuFe spin glass wires. These dynamical fluctuations have a 1/f-like spectrum and appear below the measured spin glass freezing temperature of our samples. The dependence of the fluctuation amplitude on temperature, magnetic field, voltage and Fe concentration allows a consistent interpretation in terms of quantum interference effects which are sensitive to the slowly fluctuating spin configuration.
The frequency dependence of the equilibrium ac conductance (or the noise power spectrum) through a mesoscopic structure is shown to exhibit steps and dips. The steps, at energies related to the resonances of the structure, are closely related to the partial Friedel phases of these resonances, thus allowing a direct measurement of these phases (without interferometry). The dips in the spectrum are related to a destructive interference in the absorption of energy by transitions between these resonances, in some similarity with the Fano effect.
In both research and textbook literature one often finds two ``different'' Kubo formulas for the zero-temperature conductance of a non-interacting Fermi system. They contain a trace of the product of velocity operators and single-particle (retarded and advanced) Green operators: $\text{Tr} (\hat{v}_x \hat{G}^r \hat{v}_x \hat{G}^a)$ or $\text{Tr} (\hat{v}_x \text{Im} \hat{G} \hat{v}_x \text{Im} \hat{G})$. The study investigates the relationship between these expressions, as well as the requirements of current conservation, through exact evaluation of such quantum-mechanical traces for a nanosca…
In graphene, the valleys represent spin-like quantities and can act as a physical resource in valley-based electronics to novel quantum computation schemes. Here we demonstrate a direct route to tune and read the valley quantum states of disordered graphene by measuring the mesoscopic conductance fluctuations. We show that the conductance fluctuations in graphene at low temperatures are reduced by a factor of four when valley triplet states are gapped in the presence of short range potential scatterers at high carrier densities. We also show that this implies a gate tunable universal symmetry …
We study the transport properties of an Aharonov-Bohm ring containing two quantum dots. One of the dots has well-separated resonant levels, while the other is chaotic and is treated by random matrix theory. We find that the conductance through the ring is significantly affected by mesoscopic fluctuations. The Breit-Wigner resonant peak is changed to an antiresonance by increasing the ratio of the level broadening to the mean level spacing of the random dot. The asymmetric Fano form turns into a symmetric one and the resonant peak can be controlled by magnetic flux. The conductance distribution…
We study the system-size dependence of the averaged critical conductance $g(L)$ at the Anderson transition. We have: (i) related the correction $δg(L)=g(\infty)-g(L)\propto L^{-y}$ to the spectral correlations; (ii) expressed $δg(L)$ in terms of the quantum return probability; (iii) argued that $y=η$ -- the critical exponent of eigenfunction correlations. Experimental implications are discussed.
We report a theoretical investigation of quantized spin-Hall conductance fluctuation of graphene devices in the diffusive regime. Two graphene models that exhibit quantized spin-Hall effect (QSHE) are analyzed. Model-I is with unitary symmetry under an external magnetic field $B\ne 0$ but with zero spin-orbit interaction, $t_{SO}=0$. Model-II is with symplectic symmetry where B=0 but $t_{SO} \ne 0$. Extensive numerical calculations indicate that the two models have exactly the same universal QSHE conductance fluctuation value $0.285 e/4π$ regardless of the symmetry. Qualitatively different fro…
We measured the conductance fluctuation of bi- and trilayer graphene devices prepared on mechanical exfoliated graphene by an all-dry, lithography-free process using an ultrathin quartz filament as a shadow mask. Reproducible fluctuations in conductance as a function of applied gate voltage or magnetic field were found. As the gate voltage was tuned so that the graphene device was pushed to the charge neutral point, the amplitude of the conductance fluctuation was found to be suppressed quickly from a value consistent with universal conductance fluctuation when the devices were still well with…
Elastic backscattering of electrons moving along the helical edge is prohibited by time-reversal symmetry (TRS). We demonstrate, however, that an ensemble of magnetic impurities may cause TRS-preserving quasi-elastic backscattering, resulting in interference effects in the conductance. The characteristic energy transferred in a backscattering event is suppressed due to the RKKY interaction of localized spins (the suppression is exponential in the total number of magnetic impurities). We predict the statistics of conductance fluctuations to differ from those in the conventional case of a one-di…
We have investigated the weakly non-linear quantum transport properties of a two-dimensional quantum conductor. We have developed a numerical scheme which is very general for this purpose. The nonlinear conductance is computed by explicitly evaluating the various partial density of states, the sensitivity and the characteristic potential. Interesting spatial structure of these quantities are revealed. We present detailed results concerning the crossover behavior of the second order nonlinear conductance when the conductor changes from geometrically symmetrical to asymmetrical. Other issues of …
We investigate the combined effects of magnetic impurities and applied magnetic field on the interference contribution to the conductance of disordered metals. We show that in a metal with weak spin-orbit interaction, the polarization of impurity spins reduces the rate of electron phase relaxation, thus enhancing the weak localization correction to conductivity. Magnetic field also suppresses thermal fluctuations of magnetic impurities, leading to a recovery of the conductance fluctuations. This recovery occurs regardless the strength of the spin-orbit interaction. We calculate the magnitudes …
We study the heat conductance of hybrid superconducting junctions. Our analysis involves single-channel junctions with arbitrary transmission as well as diffusive connectors and shows the influence of the superconducting gaps and phases of the contacts on the heat conductance. If the junction is diffusive, these effects are completely quenched on average, however, we find that their influence persists in weak-localization corrections and conductance fluctuations. While these statistical properties strongly deviate from the well-known analogues for the charge conductance, we demonstrate that th…
We present the results of million atom electronic quantum transport calculations for graphene nanoconstrictions with edges that are smooth apart from atomic scale steps. We find conductances quantized in integer multiples of 2e2/h and a plateau at ~0.5*2e2/h as in recent experiments [Tombros et al., Nature Physics 7, 697 (2011)]. We demonstrate that, surprisingly, conductances quantized in integer multiples of 2e2/h occur even for strongly non-adiabatic electron backscattering at the stepped edges that lowers the conductance by one or more conductance quanta below the adiabatic value. We also …
We present a simple phenomenological model which offers a unifying interpretation of the experimental observations on the 0.7 conductance anomaly of quantum point contacts. The model utilizes the Landauer-Buttiker formalism and involves enhanced spin correlations and thermal depopulation of spin subbands. In particular our model can account for the plateau value 0.7 and the unusual temperature and magnetic field dependence. Furthermore it predicts an anomalous suppression of shot noise at the 0.7 plateau.
We study the conductance of disordered graphene superlattices with short-range structural correlations. The system consists of electron- and hole-doped graphenes of various thicknesses, which fluctuate randomly around their mean value. The effect of the randomness on the probability of transmission through the system of various sizes is studied. We show that in a disordered superlattice the quasiparticle that approaches the barrier interface almost perpendicularly transmits through the system. The conductivity of the finite-size system is computed and shown that the conductance vanishes when t…
Ballistic transport through an impurity-free section of the Corbino disk in graphene is investigated by means of the Landauer-Büttiker formalism in the mesoscopic limit. In the linear-responce regime the conductance is quantized in steps close to integer multiples of $4e^{2}/h$, yet Fabry-Perot oscillations are strongly suppressed. The quantization arises for small opening angles $θ\lesssimπ/3$ and large radii ratios $R_2/R_1\gtrsim{}10$. We find that the condition for emergence of the $n$-th conductance step can be written as $\sqrt{n}θ/π\ll{}1$. A brief comparison with the conductance spectr…
The phase of Aharonov-Bohm oscillations in mesoscopic metal rings in the presence of a magnetic field can be modulated by application of a DC-bias current I_DC. We address the question of how a variation of I_DC and hence of the microscopic phases of the electronic wave functions results in the macroscopic phase of the conductance oscillations. Whereas the first one can be varied continuously the latter has to be quantized for a ring in two-wire configuration by virtue of the Onsager symmetry relations. We observe a correlation between a phase flip by +/- pi and the amplitude of the oscillatio…
Tunneling conductance spectroscopy in normal metal-superconductor junctions is an important tool for probing Andreev bound states in mesoscopic superconducting devices, such as Majorana nanowires. In an ideal superconducting device, the subgap conductance obeys specific symmetry relations, due to particle-hole symmetry and unitarity of the scattering matrix. However, experimental data often exhibits deviations from these symmetries or even their explicit breakdown. In this work, we identify a mechanism that leads to conductance asymmetries without quasiparticle poisoning. In particular, we inv…
Using a scattering matrix approach and quasiclassical Green's function technique, we calculate the conductance of the S/N system (see Fig.1). We establish that the difference between the superconducting and normal state conductance $(δG = G_s - G_n)$ is negative for large S/N interface resistances $(R_{S/N})$ and changes sign with decreasing $R_{S/N}$. The comparision of the result obtained with experimental data is carried out.
We study the tunneling current through a mesoscopic two-terminal ring with spin-orbit coupling, which is threaded by a magnetic flux. The electron-electron interaction in the ring is described in terms of a Tomonaga-Luttinger model which also allows us to account for a capacitive coupling between the ring and the gate electrode. In the regime of weak tunneling, we describe how, at temperatures lower than the mean level spacing, the peak positions of the conductance depend on magnetic flux, spin-orbit coupling strength, gate voltage, charging energy, and interaction parameters (charge and spin …
We model the 2-probe conductance of a quantum point contact (QPC), in linear response. If the QPC is highly non-adiabatic or near to scatterers in the open reservoir regions, then the usual distinction between leads and reservoirs breaks down and a technique based on scattering theory in the full two-dimensional half-plane is more appropriate. Therefore we relate conductance to the transmission cross section for incident plane waves. This is equivalent to the usual Landauer formula using a radial partial-wave basis. We derive the result that an arbitrarily small (tunneling) QPC can reach a p-w…
We show a dramatic deviation from ergodicity for the conductance fluctuations in graphene. In marked contrast to the ergodicity of dirty metals, fluctuations generated by varying magnetic field are shown to be much smaller than those obtained when sweeping Fermi energy. They also exhibit a strongly anisotropic response to the symmetry-breaking effects of a magnetic field, when applied perpendicular or parallel to the graphene plane. These results reveal a complex picture of quantum interference in graphene, whose description appears more challenging than for conventional mesoscopic systems.
The conductance of metallic graphene nanoribbons (GNRs) with single defects and weak disorder at their edges is investigated in a tight-binding model. We find that a single edge defect will induce quasi-localized states and consequently cause zero-conductance dips. The center energies and breadths of such dips are strongly dependent on the geometry of GNRs. Armchair GNRs are much more sensitive to a vacancy than zigzag GNRs, but are less sensitive to a weak scatter. More importantly, we find that with a weak disorder, zigzag GNRs will change from metallic to semiconducting due to Anderson loca…
We investigate the competition between superconductivity and ferromagnetism in chaotic ultra-small metallic grains in a regime where both phases can coexist. We use an effective Hamiltonian that combines a BCS-like pairing term and a ferromagnetic Stoner-like spin exchange term. We study the transport properties of the grain in the Coulomb blockade regime and identify signatures of the coexistence between pairing and exchange correlations in the mesoscopic fluctuations of the conductance peak spacings and peak heights.
We investigate the electronic transport properties of unbiased and biased bilayer graphene nanoribbon in n-p and n-n junctions subject to a perpendicular magnetic field. Using the non-equilibrium Green's function method and the Landauer-Büttiker formalism, the conductance is studied for the cases of clean, on-site, and edge disordered bilayer graphene. We show that the lowest Hall plateau remains unchanged in the presence of disorder, whereas asymmetry destroys both the plateaus and conductance quantization. In addition, we show that disorder induces an enhancement of the conductance in the n-…
Using a generalized Landauer approach we study the non-linear transport in mesoscopic graphene with zig-zag and armchair edges. We find that for clean systems, the low-bias low-temperature conductance, G, of an armchair edge system in quantized as G/t=4 n e^2/h, whereas for a zig-zag edge the quantization changes to G/t t=4(n+1/2)e^2/h, where t is the transmission probability and n is an integer. We also study the effects of a non-zero bias, temperature, and magnetic field on the conductance. The magnetic field dependence of the quantization plateaus in these systems is somewhat different from…
The statistics of eigenfunction amplitudes are studied in mesoscopic disordered electron systems of finite size. The exact eigenspectrum and eigenstates are obtained by solving numerically Anderson Hamiltonian on a three-dimensional lattice for different strengths of disorder introduced either in the potential on-site energy (``diagonal'') or in the hopping integral (``off-diagonal''). The samples are characterized by the exact zero-temperature conductance computed using real-space Green function technique and related Landauer-type formula. The comparison of eigenstate statistics in two models…
This brief review discusses electronic properties of mesoscopic graphene-based structures. These allow controlling the confinement and transport of charge and spin; thus, they are of interest not only for fundamental research, but also for applications. The graphene-related topics covered here are: edges, nanoribbons, quantum dots, $pn$-junctions, $pnp$-structures, and quantum barriers and waveguides. This review is partly intended as a short introduction to graphene mesoscopics.
In this letter we study the coherent electronic transport through a metallic nanowire with magnetic impurities. The spins of these impurities are considered as frozen to mimic a low temperature spin glass phase. The transport properties of the wire are derived from a numerical Landauer technique which provides the conductance of the wire as a function of the disorder configuration. We show that the correlation of conductance between two spin configurations provides a measure of the correlation between these spin configurations. This correlation corresponds to the mean field overlap in the abse…
We examine contributions to the dc-current of mesoscopic samples which are non-linear in applied voltage. In the presence of a magnetic field, the current can be decomposed into components which are odd (antisymmetric) and even (symmetric) under flux reversal. For a two-terminal chaotic cavity, these components turn out to be very sensitive to the strength of the Coulomb interaction and the asymmetry of the contact conductances. For both two- and multi-terminal quantum dots we discuss correlations of current non-linearity in voltage measured at different magnetic fields and temperatures.
We study the sub-gap conductance of a ferromagnetic mesoscopic region attached to a ferromagnetic and a superconducting electrode by means of tunnel junctions. In the absence of the exchange field, the ratio $r= γ/ ε_T$ of the two tunnel junction resistances determines the behaviour of the sub-gap conductance which possesses a zero-bias peak for $r\gg 1$ and for $r\ll 1$ a peak at finite voltage. We show that the inclusion of the exchange field leads to a peak splitting for $r\ll 1$, while it shifts the zero-bias anomaly to finite voltages for $r\gg 1$.
We present a new formulation to calculate the electric conductance of mesoscopic conductors by utilizing the singular value decomposition, which is a mathematical technique to manipulate matrices. Our formulation is useful in treating conductors with rather complicated atomic structures, for which naive recursion formula is cumbersome. It also has an advantage in scaling up the calculation by using parallel computation, which potentially allows us the real-scale calculations at the atomic level. On the other hands, the effects of electron-electron interactions are hard to be treated within thi…
We study conductance cumulants $<< g^n >>$ and current cumulants $C_j$ related to heat and electrical transport in coherent mesoscopic quantum wires near the diffusive regime. We consider the asymptotic behavior in the limit where the number of channels and the length of the wire in the units of the mean free path are large but the bare conductance is fixed. A recursion equation unifying the descriptions of the standard and Bogoliubov--de Gennes (BdG) symmetry classes is presented. We give values and come up with a novel scaling form for the higher-order conductance cumulants. In the BdG wires…
Magneto-fluctuations of the normal resistance R_N have been reproducibly observed in high critical temp erature superconductor (HTS) grain boundary junctions, at low temperatures. We attribute them to mesoscopic transport in narrow channels across the grain boundary line. The Thouless energy appears to be the relevant energy scale. Our findings have significant implications on quasiparticle relaxation and coherent transport in HTS grain boundaries.
We report a systematic experimental study of mesoscopic conductance fluctuations in superconductor/normal/superconductor (SNS) devices Nb/InAs-nanowire/Nb. These fluctuations far exceed their value in the normal state and strongly depend on temperature even in the low-temperature regime. This dependence is attributed to high sensitivity of perfectly conducting channels to dephasing and the SNS fluctuations thus provide a sensitive probe of dephasing in a regime where normal transport fails to detect it. Further, the conductance fluctuations are strongly non-linear in bias voltage and reveal su…
Recently, Hecker et al. [Phys. Rev. Lett. 79, 1547 (1997)] experimentally studied magnetoconductance fluctuations in a mesoscopic Au wire connected to a superconducting Nb contact. They claimed to have observed an enhancement of the rms magnitude of these conductance fluctuations in the superconducting state (rms(Gns)) relative to that in the normal state (rms(Gn)) by a factor of 2.8. In this comment, we argue that the measured rms(Gns) is NOT significantly enhanced compared to rms(Gn) when we correct for the presence of an incoherent series resistance from the contacts, which is different whe…
We consider the conductance distributions in chaotic mesoscopic cavities for all three invariant classes of random matrices for the arbitrary number of channels N1, N2 in the connecting leads. We show that the Laplace transforms of the distributions can be expressed in terms of determinants in the unitary case and Pfaffians in the orthogonal and symplectic cases. The inverse Laplace transforms then give the exact distributions. This formalism is particularly useful for small values of N = min (N1, N2), and thus is of direct experimental relevance. We also obtain the conductance distributions f…
The calculation of the conductance of disordered rings requires a theory that goes beyond the Kubo-Drude formulation. Assuming "mesoscopic" circumstances the analysis of the electro-driven transitions show similarities with a percolation problem in energy space. We argue that the texture and the sparsity of the perturbation matrix dictate the value of the conductance, and study its dependence on the disorder strength, ranging from the ballistic to the Anderson localization regime. An improved sparse random matrix model is introduced to captures the essential ingredients of the problem, and lea…
We present a formulation of the nanoscale radiative heat transfer (RHT) using concepts of mesoscopic physics. We introduce the analog of the Sharvin conductance using the quantum of thermal conductance. The formalism provides a convenient framework to analyse the physics of RHT at the nanoscale. Finally, we propose a RHT experiment in the regime of quantized conductance.
Excess conductance fluctuations with peculiar temperature-dependence from 1.4 to 250 K were observed in curved nano-graphite sheets with an electrode gap length of 300 and 450 nm, whereas the conductance fluctuation is greatly suppressed above 4.2 K when the electrode gap length increases to 800 and 1000 nm. The former is discussed in the context of the presence of a small energy bandgap in the nano-graphite sheets, while the latter is attributed to the crossover from coherent transport to diffusive transport regime.
We study fluctuations of conductance of two connected in series dots in the Coulomb blockade regime. The pattern of the fluctuations turns out to be extremely sensitive to a magnetic field. These conductance fluctuations also provide information about the mesoscopic fluctuations of charge of a partially-opened single quantum dot, which are hard to measure directly.
We investigate the amplitude of mesoscopic fluctuations of the differential conductance of a metallic wire at arbitrary bias voltage V. For non-interacting electrons, the variance <delta g^2> increases with V. The asymptotic large-V behavior is <delta g^2> \sim V/V_c (where eV_c=D/L^2 is the Thouless energy), in agreement with the earlier prediction by Larkin and Khmelnitskii. We find, however, that this asymptotics has a very small numerical prefactor and sets in at very large V/V_c only, which strongly complicates its experimental observation. This high-voltage behavior is preceded by a cros…
We study the magnetoconductance fluctuations of mesoscopic normal-metal/superconductor (NS) samples consisting of a gold-wire in contact with a niobium film. The magnetic field strength is varied over a wide range, including values that are larger than the upper critical field B_c2 of niobium. In agreement with recent theoretical predictions we find that in the NS sample the rms of the conductance fluctuations (CF) is by a factor of 2.8 +/- 0.4 larger than in the high field regime where the entire system is driven normal conducting. Further characteristics of the CF are discussed.
We investigate the 1/f noise properties of epitaxial graphene devices at low temperatures as a function of temperature, current and magnetic flux density. At low currents, an exponential decay of the 1/f noise power spectral density with increasing temperature is observed that indicates mesoscopic conductance fluctuations as the origin of 1/f noise at temperatures below 50 K. At higher currents, deviations from the typical quadratic current dependence and the exponential temperature dependence occur as a result of nonequilibrium conditions due to current heating. By applying the theory of Kuba…
We study linear electron transport through a molecular wire sandwiched between nanotube leads. We show that the presence of such electrodes strongly influences the calculated conductance. We find that depending on the quality and geometry of the contacts between the molecule and the tubular reservoirs, linear transport can be tuned between an effective Newns spectral behavior and a more structured one. The latter strongly depends on the topology of the leads. We also provide analytical evidence for an anomalous behavior of the conductance as a function of the contact strength.
A theory of non-equilibrium (``shot'') noise and high frequency conductance in diffusive mesoscopic conductors with screening is presented. Detailed results are obtained for two simple geometries, for both large and short electron-electron scattering length $l_{ee}$, at frequencies of the order of the inverse Thouless time $1/τ_T$. The conductance and the noise are found to exhibit significant frequency dependence. For $L \ll l_{ee}$, the high-frequency ($ωτ_T \gg 1$) shot noise spectral density $S_I(ω)$ approaches a finite value between $2eI/3$ and $2eI$, depending on the screening properties…
We study fluctuations of the conductance of micron-sized graphene devices as a function of the Fermi energy and magnetic field. The fluctuations are studied in combination with analysis of weak localization which is determined by the same scattering mechanisms. It is shown that the variance of conductance fluctuations depends not only on inelastic scattering that controls dephasing but also on elastic scattering. In particular, contrary to its effect on weak localization, strong intervalley scattering suppresses conductance fluctuations in graphene. The correlation energy, however, is independ…
