Nonequilibrium Current Fluctuations Research Articles

Fermi Liquid Theory for Nonlinear Transport through a Multilevel Anderson Impurity

We present a microscopic Fermi liquid view on the low-energy transport through an Anderson impurity with N discrete levels, at arbitrary electron filling N_{d}. It is applied to nonequilibrium current fluctuations, for which the two-quasiparticle collision integral and the three-body correlations that determine the quasiparticle energy shift play important roles. Using the numerical renormalization group up to N=6, we find that for strong interactions the three-body fluctuations are determined by a single parameter other than the Kondo energy scale in a wide filling range 1≲N_{d}≲N-1. It significantly affects the current noise for N>2 and the behavior of noise in magnetic fields.

Uncertainty relations for time-delayed Langevin systems.

The thermodynamic uncertainty relation, which establishes a universal trade-off between nonequilibrium current fluctuations and dissipation, has been found for various Markovian systems. However, this relation has not been revealed for non-Markovian systems; therefore, we investigate the thermodynamic uncertainty relation for time-delayed Langevin systems. We prove that the fluctuation of arbitrary dynamical observables is constrained by the Kullback-Leibler divergence between the distributions of the forward path and its reversed counterpart. Specifically, for observables that are antisymmetric under time reversal, the fluctuation is bounded from below by a function of a quantity that can be identified as a generalization of the total entropy production in Markovian systems. We also provide a lower bound for arbitrary observables that are odd under position reversal. The term in this bound reflects the extent to which the position symmetry has been broken in the system and can be positive even in equilibrium. Our results hold for finite observation times and a large class of time-delayed systems because detailed underlying dynamics are not required for the derivation. We numerically verify the derived uncertainty relations using two single time-delay systems and one distributed time-delay system.

Microreversibility, nonequilibrium current fluctuations, and response theory

Microreversibility rules the fluctuations of the currents flowing across open systems in nonequilibrium (or equilibrium) steady states. As a consequence, the statistical cumulants of the currents and their response coefficients at arbitrary orders in the deviations from equilibrium obey time-reversal symmetry relations, as established in quantum statistical mechanics. It is shown that some of these relations satisfy recurrences that can be simplified by means of the coefficients of Euler polynomials. This result allows us to systematically reduce the amount of independent quantities that need to be measured experimentally or computed theoretically in order to fully characterize the linear and nonlinear transport properties of general open systems. This reduction is shown to approach one half for quantities of arbitrarily high orders.

Enhanced current fluctuation in Coulomb blockade regime of multilevel quantum dot

Nonequilibrium current fluctuation is theoretically studied through a multilevel quantum dot in the Coulomb blockade regime, where the higher-order tunneling processes, “cotunneling,” are dominant in the transport. The current fluctuation shows a Poisson (super-Poisson) noise in the elastic (inelastic) cotunneling regime when the bias voltage eV between the leads is smaller (larger) than the excitation energy Δ from the ground level in the quantum dot. The super-Poisson noise is remarkably enhanced by the degeneracy of the excited states around the beginning of inelastic cotunneling at eV ≈ Δ, qualitatively in good agreement with a recent experimental result. An analytical expression is given for the current fluctuation as a function of degeneracy.

Dissipation Bounds All Steady-State Current Fluctuations.

Near equilibrium, small current fluctuations are described by a Gaussian distribution with a linear-response variance regulated by the dissipation. Here, we demonstrate that dissipation still plays a dominant role in structuring large fluctuations arbitrarily far from equilibrium. In particular, we prove a linear-response-like bound on the large deviation function for currents in Markov jump processes. We find that nonequilibrium current fluctuations are always more likely than what is expected from a linear-response analysis. As a small-fluctuations corollary, we derive a recently conjectured uncertainty bound on the variance of current fluctuations.

Photon-Assisted Shot Noise in Normal Metal-Insulator-Superconductor Heterostructures

Photon-assisted electron transport in mesoscopic heterostructures is studied via a scattering approach. The nonequilibrium current fluctuations of normal metal-insulator-superconductor systems under illumination with monochromatic microwaves have been calculated. Using a time-periodic potential applied across the tunnel junction we model the emission and absorption of photons. We have concluded that the photon-assisted shot noise decreases when the insulating barrier becomes more transparent. The voltage dependence of the shot-noise power as a function of microwave frequency has been investigated as well.

Nonequilibrium noise and current fluctuations at the superconducting phase transition

We study non-Gaussian out-of-equilibrium current fluctuations in a mesoscopic NSN circuit at the point of a superconducting phase transition. The setup consists of a voltage-biased thin film nanobridge superconductor (S) connected to two normal-metal (N) leads by tunnel junctions. We find that above a critical temperature fluctuations of the superconducting order parameter associated with the preformed Cooper pairs mediate inelastic electron scattering that promotes strong current fluctuations. Though the conductance is suppressed due to the depletion of the quasiparticle density of states, higher cumulants of current fluctuations are parametrically enhanced. We identify experimentally relevant transport regime where excess current noise may reach or even exceed the level of the thermal noise.

Anomalous nonequilibrium current fluctuations in the Heisenberg model

We study fluctuation properties of a one-dimensional anisotropic Heisenberg model out of equilibrium, focusing in particular on the gapped regime. Within the open-system setting we study large-deviation properties of the spin current. Numerically evaluating the first four current cumulants in a nonequilibrium stationary state at high energies, we find that the first two cumulants scale with the system size in a diffusive way, while the third and the fourth cumulants do not. This means that the model is not an ordinary diffusive spin conductor.

Cumulant generating function formula of heat transfer in ballistic systems with lead-lead coupling

Based on two-time observation protocol, we consider heat transfer in a given time interval $t_{M}$ in lead-junction-lead system taking coupling between the leads into account. In view of the two-time observation, consistency conditions are carefully verified in our specific family of quantum histories. Furthermore, its implication is briefly explored. Then using nonequilibrium Green's function (NEGF) method, we obtain an exact formula for the cumulant generating function for heat transfer between the two leads valid in both transient and steady-state regimes. Also, a compact formula for the cumulant generating function in the long-time limit is derived, for which the Gallavotti-Cohen (GC) fluctuation symmetry is explicitly verified. In addition, a brief discussion of Di Ventra's trick regarding whether the effect of the repartitioning procedure of the total Hamiltonian on nonequilibium steady-state current fluctuation exists is given. All kinds of properties of nonequilibrium current fluctuations such as the fluctuation theorem in different time regimes could be readily given according to these exact formulas.

Full Counting Statistics for Orbital-Degenerate Impurity Anderson Model with Hund’s Rule Exchange Coupling

We study nonequilibrium current fluctuations through a quantum dot, which includes a ferromagnetic Hund's rule coupling J, in the low-energy Fermi liquid regime using the renormalized perturbation theory. The resulting cumulant for the current distribution in the particle-hole symmetric case shows that spin-triplet and spin-singlet pairs of quasiparticles are formed in the current due to the Hund's rule coupling, and these pairs enhance the current fluctuations. In the fully screened higher-spin Kondo limit, the Fano factor takes a value F(b)=(9M+6)/(5M+4) determined by the orbital degeneracy M. We also investigate the crossover between the small and large J limits in the two-orbital case M=2, using the numerical renormalization group approach.

Strong quantum memory at resonant Fermi edges revealed by shot noise.

Studies of non-equilibrium current fluctuations enable assessing correlations involved in quantum transport through nanoscale conductors. They provide additional information to the mean current on charge statistics and the presence of coherence, dissipation, disorder, or entanglement. Shot noise, being a temporal integral of the current autocorrelation function, reveals dynamical information. In particular, it detects presence of non-Markovian dynamics, i.e., memory, within open systems, which has been subject of many current theoretical studies. We report on low-temperature shot noise measurements of electronic transport through InAs quantum dots in the Fermi-edge singularity regime and show that it exhibits strong memory effects caused by quantum correlations between the dot and fermionic reservoirs. Our work, apart from addressing noise in archetypical strongly correlated system of prime interest, discloses generic quantum dynamical mechanism occurring at interacting resonant Fermi edges.

Shot noise induced by electron-nuclear spin-flip scattering in a nonequilibrium quantum wire

We study the shot noise (nonequilibrium current fluctuation) associated with dynamic nuclear polarization in a nonequilibrium quantum wire (QW) fabricated in a two-dimensional electron gas. We observe that the spin-polarized conductance quantization of the QW in the integer quantum Hall regime collapses when the QW is voltage biased to be driven to nonequilibrium. By measuring the shot noise, we prove that the spin polarization of electrons in the QW is reduced to $\sim 0.7$ instead of unity as a result of electron-nuclear spin-flip scattering. The result is supported by Knight shift measurements of the QW using resistively detected NMR.

Generating function formula of heat transfer in harmonic networks

We consider heat transfer across an arbitrary classical harmonic network connected to two heat baths at different temperatures. The network has N positional degrees of freedom, of which N(L) are connected to a bath at temperature T(L) and N(R) are connected to a bath at temperature T(R). We derive an exact formula for the cumulant generating function for heat transfer between the two baths. The formula is valid even for N(L)≠N(R) and satisfies the Gallavotti-Cohen fluctuation symmetry. Since harmonic crystals in three dimensions are known to exhibit different regimes of transport such as ballistic, anomalous, and diffusive, our result implies validity of the fluctuation theorem in all regimes. Our exact formula provides a powerful tool to study other properties of nonequilibrium current fluctuations.

Studying Voltage Dependent Noise in Polymer and Solid State Nanopores

Studying the noise properties of ion currents in nanopores can improve detection limits for nanopore sensors as well as give insight into behavior of transport at the nanoscale. We focused on the so-called 1/f noise that is observed in the low frequency regime of the ion current power spectra. We found that 1/f noise in single conically shaped nanopores in polymer films exhibits voltage-dependent noise properties, which are not observed for cylindrical pores. The current passing through the nanopore in the low conductance state shows equilibrium 1/f noise, similar to the noise observed in solid state nanopores. Equilibrium fluctuations are defined as the voltage independent power spectrum magnitude normalized by the current squared. The high conductance state causes the 1/f noise to increase exponentially with increased applied voltage, showing a non-equilibrium 1/f noise. Therefore we can switch between the equilibrium and non equilibrium behavior simply by adjusting the voltage. The current in the high conductance state is about 5 times higher then the current in the low conductance state but the noise at 1 Hz is over 100 times higher. Cylindrically shaped nanopores in polymer and solid-state films do not show current rectification and show equilibrium 1/f noise. We discuss these results and give a comparison of the nanopore noise in these various systems. We hypothesize that the non-equilibrium current fluctuations originate from structural fluctuations of flexible polymer pores. The hypothesis is tested by comparison of noise properties between polymer and silicon nitride pores studied at different electrolyte concentrations.

Resonant Pair Tunneling in Double Quantum Dots

We present exact results on the nonequilibrium current fluctuations for 2 quantum dots in series throughout a crossover from non-Fermi liquid to Fermi liquid behavior described by the 2 impurity Kondo model. The result corresponds to resonant tunneling of carriers of charge 2e for a critical interimpurity coupling. At low energy scales, the result can be understood from a Fermi liquid approach that we develop and use to also study nonequilibrium transport in an alternative double dot realization of the 2 impurity Kondo model under current experimental study.

Fluctuation theorem in a quantum-dot Aharonov-Bohm interferometer

In the present study, we investigate the full counting statistics in a two-terminal Aharonov-Bohm interferometer embedded with an interacting quantum dot. We introduce a nonequilibrium saddle-point solution for a cumulant-generating function, which satisfies the fluctuation theorem and accounts for the interaction in the mean-field level approximation. The approximation properly leads to the following two consequences. (i) The nonlinear conductance can be an uneven function of the magnetic field for a noncentrosymmetric mesoscopic system. (ii) The nonequilibrium current fluctuations couple with the charge fluctuations via the Coulomb interaction. As a result, nontrivial corrections appear in the nonequilibrium current noise. Nonlinear transport coefficients satisfy universal relations imposed by microscopic reversibility, though the scattering matrix itself is not reversible. When the magnetic field is applied, the skewness in equilibrium can be finite owing to the interaction. The equilibrium skewness is an odd function of the magnetic field and is proportional to the asymmetric component of the nonlinear conductance. The universal relations predicted can be confirmed experimentally.

Nonequilibrium current fluctuation in an AB ring with a quantum dot

Nonequilibrium steady states (NESS) and current fluctuations are investigated for a noninteracting system consisting of a single-level quantum dot (QD) embedded in an Aharonov–Bohm (AB) ring. With the aid of asymptotic incoming fields, NESS are explicitly constructed. In terms of current fluctuations, the interplay between particle-like and wave-like behaviors of electrons is investigated. The current–current correlation function is found to be related to the differential conductance (an extension of the Kubo formula) and a relative entropy production is shown to be nonnegative at NESS.

Magnetic field generation from nonequilibrium phase transitions

We study the generation of magnetic fields during the stage of particle production resulting from spinodal instabilities during phase transitions out of equilibrium. The main premise is that long-wavelength instabilities that drive the phase transition lead to strong nonequilibrium charge and current fluctuations which generate electromagnetic fields. We present a formulation based on the nonequilibrium Schwinger-Dyson equations that leads to an exact expression for the spectrum of electromagnetic fields valid for general theories and cosmological backgrounds and whose main ingredient is the transverse photon polarization out of equilibrium. This formulation includes the dissipative effects of the conductivity in the medium. As a prelude to cosmology, we study magnetogenesis in Minkowski spacetime in a theory of N charged scalar fields to lowest order in the gauge coupling and to leading order in the large N within two scenarios of cosmological relevance. The long-wavelength power spectrum for electric and magnetic fields at the end of the phase transition is obtained explicitly. It follows that equipartition between electric and magnetic fields does not hold out of equilibrium. In the case of a transition from a high-temperature phase, the conductivity of the medium severely hinders the generation of magnetic fields; however, the magnetic fields generated are correlated on scales of the order of the domain size, which is much larger than the magnetic diffusion length. The implications of the results to cosmological phase transitions driven by spinodal instabilities are discussed.

Shot-noise suppression by Fermi and Coulomb correlations in ballistic conductors

We investigate the injection of degenerate Fermi-Dirac electrons into a multimode ballistic conductor under the space-charge-limited regime. The nonequilibrium current fluctuations were found to be suppressed by both Coulomb and Fermi correlations. We show that the Fermi shot-noise-suppression factor is limited below by the value ${2k}_{B}T/{\ensuremath{\varepsilon}}_{F},$ where T is the temperature and ${\ensuremath{\varepsilon}}_{F}$ the Fermi energy of the injected electrons. The Coulomb noise suppression factor may attain much lower values ${\ensuremath{\varepsilon}}_{F}/2qU,$ because of its dependence on the applied bias $U\ensuremath{\gg}{k}_{B}T/q.$ The asymptotic behavior of the overall shot-noise suppression factor in a high degenerate limit was found to be ${k}_{B}T/qU,$ independent of the material parameters.

Double quantum dots as detectors of high-frequency quantum noise in mesoscopic conductors

We propose a measurement setup for detecting quantum noise over a wide frequency range using inelastic transitions in a tunable two-level system as a detector. The frequency-resolving detector consists of a double quantum dot which is capacitively coupled to the leads of a nearby mesoscopic conductor. The inelastic current through the double quantum dot is calculated in response to equilibrium and nonequilibrium current fluctuations in the nearby conductor, including zero-point fluctuations at very low temperatures. As a specific example, the fluctuations across a quantum point contact are discussed.