We investigate a scattering of electron which is injected individually into an empty ballistic channel containing a cavity that is Coulomb coupled to a quantum ring charged with a single-electron.
We solve the time-dependent Schrödinger equation for the electron pair with an exact account for the electron-electron correlation. Absorption of energy and angular momentum by the quantum ring is not an even function of the external magnetic field. As a consequence we find that the electron backscattering probability is asymmetric in the magnetic field and thus violates Onsager symmetry.
We present a Monte Carlo analysis of shot-noise suppression due to long-range Coulomb interaction in semiconductor samples under a crossover between diffusive and ballistic transport regimes. By varying the mean time between collisions we find that the strong suppression observed under the ballistic regime persists under quasi-ballistic conditions, before being washed out when a complete diffusive regime is reached.
We work out a theory of the Coulomb drag current created under the ballistic transport regime in a one-dimensional nanowire by a ballistic non-Ohmic current in a nearby parallel nanowire. As in the Ohmic case, we predict sharp oscillation of the drag current as a function of gate voltage or the chemical potential of electrons. We study also dependence of the drag current on the voltage V across the driving wire. For relatively large values of V the drag current is proportional to V^2.
A linear theory of electron transport is developed for a system of two ideal quantum wires, of length L, coupled by tunneling and Coulomb interaction. The interaction of electrons with acoustical phonons is included and the results are valid in both the ballistic and diffusive regime. In the {\it ballistic} regime, both tunneling and Coulomb drag lead to a {\it negative} transresistance R_{TR}, while in the {\it diffusive} regime the tunneling opposes the drag and leads to a {\it positive} R_{TR}. If L is smaller than the phase-breaking length, the tunneling leads to interference oscillations …
We present a microscopic analysis of shot-noise suppression due to long-range Coulomb interaction in semiconductor devices under ballistic transport conditions. An ensemble Monte Carlo simulator self-consistently coupled with a Poisson solver is used for the calculations. A wide range of injection-rate densities leading to different degrees of suppression is investigated. A sharp tendency of noise suppression at increasing injection densities is found to scale with a dimensionless Debye length related to the importance of space-charge effects in the structure.
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 2kT/epsilon_F, where T is the temperature and epsilon_F the Fermi energy of the injected electrons. The Coulomb noise suppression factor may attain much lower values epsilon_F/2qU, because of its dependence on the applied bias U >> kT/q. The asymptotic behaviour of th…
The role of energy exchange between a quantum system and its environment is investigated from the perspective of the Onsager conductance matrix. We consider the thermoelectric linear transport of an interacting quantum dot coupled to two terminals under the influence of an electrical potential and a thermal bias. We implement in our model the effect of coupling to electromagnetic environmental modes created by nearby electrons within the P(E)-theory of dynamical Coulomb blockade. Our findings relate the lack of some symmetries among the Onsager matrix coefficients with an enhancement of the ef…
Within a Monte Carlo simulation we investigate the statistical properties of an electron flow injected with a Poissonian distribution and transmitted under ballistic regime in the presence of long-range Coulomb interaction. Electrons are shown to exhibit a motional squeezing which tends to space them more regularly rather than strictly at random, and evidence a sub-Poissonian statistics with a substantially reduced Fano factor $F_n\ll 1$. The temporal (anti)correlation among carriers is demonstrated to be a collective effect which persists over the transit of several successive electrons and r…
The Coulomb drag between parallel, {\it ballistic} quantum wires is studied theoretically in the presence of a perpendicular magnetic field B. The transresistance R_D shows peaks as a function of the Fermi level and splitting energy between the 1D subbands of the wires. The sharpest peaks appear when the Fermi level crosses the subband extrema so that the Fermi momenta are small. Two other kinds of peaks appear when either {\it intra}- or {\it inter}-subband transitions of electrons have maximum probability; the {\it intra}-subband transitions correspond to a small splitting energy. R_D depend…
We demonstrate that the injection of the ballistic electrons into the two-dimensional electron plasma in lateral n$^+$-i-n-n$^+$ graphene field-effect transistors (G-FET) might lead to a substantial Coulomb drag of the quasi-equilibrium electrons due the violation of the Galilean and Lorentz invariance in the systems with a linear electron dispersion. This effect can result in the S-shaped current-voltage characteristics (IVs). The resulting negative differential conductivity enables the hysteresis effects and current filamentation that can be used for the implementation of voltage switching d…
We investigate the shot noise of nonequilibrium carriers injected into a ballistic conductor and interacting via long-range Coulomb forces. Coulomb interactions are shown to act as an energy analyzer of the profile of injected electrons by means of the fluctuations of the potential barrier at the emitter contact. We show that the details in the energy profile can be extracted from shot-noise measurements in the Coulomb interaction regime, but cannot be obtained from time-averaged quantities or shot-noise measurements in the absence of interactions.
We predict the self-excitation of terahertz (THz) oscillations due to the plasma instability in the lateral n+-i-n-n+$ graphene field-effect transistors (G-FET). The instability is associated with the Coulomb drag of the quasi-equilibrium electrons in the gated channel by the injected ballistic electrons resulting in a positive feedback between the amplified dragged electrons current and the injected current. The plasma excitations arise when the drag effect is sufficiently strong. The drag efficiency and the plasma frequency are determined by the quasi-equilibrium electrons Fermi energy (i.e.…
We investigate the current injection into a ballistic conductor under the space-charge limited regime, when the distribution function of injected carriers is an arbitrary function of energy F_c(epsilon). The analysis of the coupled kinetic and Poisson equations shows that the injected current fluctuations may be essentially suppressed by Coulomb correlations, and the suppression level is determined by the shape of F_c(epsilon). This is in contrast to the time-averaged quantities: the mean current and the spatial profiles are shown to be insensitive to F_c(epsilon) in the leading-order terms at…
We discuss a consequence of time reversal symmetry on thermoelectric effect in nonequilibrium coherent quantum transport. Starting with a quantum version of the fluctuation theorem, we show that there exist universal relations between the Peltier coefficient and the Seebeck coefficient of general mesoscopic systems with Coulomb interaction in a nonlinear regime. This extended Kelvin-Onsager relation may be used to obtain useful information on heat current, e.g. the nonlinear Peltier coefficient, which is difficult to be measured in a usual setup of experiments, only from electric current measu…
We have investigated within the theory of Fermi liquid dependence of Coulomb drag current in a passive quantum wire on the applied voltage $V$ across an active wire and on the temperature $T$ for any values of $eV/k_BT$. We assume that the bottoms of the 1D minibands in both wires almost coincide with the Fermi level. We come to conclusions that 1) within a certain temperature interval the drag current can be a descending function of the temperature $T$; 2) the experimentally observed temperature dependence $T^{-0.77}$ of the drag current can be interpreted within the framework of Fermi liquid…
Dynamics of ballistic photocurrents driven by Coulomb scattering
Molecular Foundry, Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室分子发现中心）；Quantum Simulations Group, Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室量子模拟组）
We study a model of two concentric onedimensional rings with incommensurate areas $A_1$ and $A_2$, in a constant magnetic field. The two rings are coupled by a nonhomogeneous inter-ring tunneling amplitude, which makes the one-particle spectrum chaotic. For noninteracting particles the energy of the many-body ground state and the first excited state exhibit random fluctuations characterized by the Wigner-Dyson statistics. In contrast, we show that the electron-electron interaction orders the magnetic field dependence of these quantities, forcing them to become periodic functions, with period $…
Precise control over interactions between ballistic electrons will enable us to exploit Coulomb interactions in novel ways, to develop high-speed sensing, to reach a non-linear regime in electron quantum optics and to realise schemes for fundamental two-qubit operations on flying electrons. Time-resolved collisions between electrons have been used to probe the indistinguishability, Wigner function and decoherence of single electron wavepackets. Due to the effects of screening, none of these experiments were performed in a regime where Coulomb interactions were particularly strong. Here we expl…
We work out a theory of shot noise in a special case. This is a noise of the Coulomb drag current excited under the ballistic transport regime in a one-dimensional nanowire by a ballistic non-Ohmic current in a nearby parallel nanowire. We predict sharp oscillation of the noise power as a function of gate voltage or the chemical potential of electrons. We also study dependence of the noise on the voltage V across the driving wire. For relatively large values of V the noise power is proportional to V^2.
A self-consistent theory of shot noise in ballistic two-terminal conductors under the action of long-range Coulomb correlations is presented. Analytical formulas for the electron distribution function and its fluctuation along the conductor, which account for the Coulomb correlations, have been derived. Based upon these formulas, the current-noise reduction factor has been obtained for biases ranging from thermal to shot-noise limits as dependent on two parameters: the ratio between the length of the sample and the Debye screening length λ=d/L_D and the applied voltage qU/k_BT. The difference …
We work out a semiclassical theory of shot noise in ballistic n+-i-n+ semiconductor structures aiming at studying two fundamental physical correlations coming from Pauli exclusion principle and long range Coulomb interaction. The theory provides a unifying scheme which, in addition to the current-voltage characteristics, describes the suppression of shot noise due to Pauli and Coulomb correlations in the whole range of system parameters and applied bias. The whole scenario is summarized by a phase diagram in the plane of two dimensionless variables related to the sample length and contact chem…
Quasiballistic 1D quantum wires are known to have a conductance of the order of 2e^2/h, with small sample-to-sample fluctuations. We present a study of the transconductance G_12 of two Coulomb-coupled quasiballistic wires, i.e., we consider the Coulomb drag geometry. We show that the fluctuations in G_12 differ dramatically from those of the diagonal conductance G_ii: the fluctuations are large, and can even exceed the mean value, thus implying a possible reversal of the induced drag current. We report extensive numerical simulations elucidating the fluctuations, both for correlated and uncorr…
The influence of a longitudinal magnetic field on the Coulomb drag current created in the ballistic transport regime in a quantum well by a ballistic current in a nearby parallel quantum well is investigated. We consider the case where the magnetic field is so strong that the Larmour radius is smaller than the width of the well. Both in Ohmic and non-Ohmic case, sharp oscillations of the drag current as a function of the gate voltage or chemical potential are predicted. We also study dependence of the drag current on the voltage $V$ across the driving wire, as well as on the magnetic field $B$…
We develop a kinetic equation description of Coulomb drag between ballistic one-dimensional electron systems, which enables us to demonstrate that equilibration processes between right- and left-moving electrons are crucially important for establishing dc drag. In one-dimensional geometry, this type of equilibration requires either backscattering near the Fermi level or scattering with small momentum transfer near the bottom of the electron spectrum. Importantly, pairwise forward scattering in the vicinity of the Fermi surface alone is not sufficient to produce a nonzero dc drag resistivity $ρ…
We demonstrate that forward electron-electron scattering due to Coulomb interation in a two-dimensional ballistic electron gas leads to the (T\ln {T})^{-1} temperature dependence of the thermal conductivity, which is logarithmically suppressed compared to the usual Fermi liquid behaviour.
We consider clean cylindrical nanostructures with an applied longitudinal static magnetic field. Without Coulomb interaction, the field induces, for particular values, points of degeneracy where a change of ground state takes place due to Aharonov-Bohm effect. The Coulomb potential introduces interaction between the electronic configurations. As a consequence, when there is degeneracy, the ground state of the system becomes a many body state - unable to be described by a mean-field theory - and a gap is opened. To study this problem, we propose a variational multireference wave function which …
We provide a framework for analyzing the problem of interacting electrons in a ballistic quantum dot with chaotic boundary conditions within an energy $E_T$ (the Thouless energy) of the Fermi energy. Within this window we show that the interactions can be characterized by Landau Fermi liquid parameters. When $g$, the dimensionless conductance of the dot, is large, we find that the disordered interacting problem can be solved in a saddle-point approximation which becomes exact as $g\to\infty$ (as in a large-N theory). The infinite $g$ theory shows a transition to a strong-coupling phase charact…
Although interesting per se, decoherence and relaxation of single-electron excitations induced by strong effective screened Coulomb interactions in Quantum Hall edge channels are an important challenge for the applications of electron quantum optics in quantum information and quantum sensing. In this paper, we study intrinsic single-electron decoherence within an ideal single-electron channel with long-range effective Coulomb interactions to determine the influence of the material and sample properties. We find that weak-coupling materials characterized by a high velocity of hot-electron excit…
The presence of pronounced electronic correlations in one-dimensional systems strongly enhances Coulomb coupling and is expected to result in distinctive features in the Coulomb drag between them that are absent in the drag between two-dimensional systems. We review recent Fermi and Luttinger liquid theories of Coulomb drag between ballistic one-dimensional electron systems, and give a brief summary of the experimental work reported so far on one-dimensional drag. Both the Fermi liquid (FL) and the Luttinger liquid (LL) theory predict a maximum of the drag resistance R_D when the one-dimension…
We analyze the operation of the graphene n+-i-n-n+ field-effect transistors (GFETs) and lateral diodes (GLDs) with the injection of ballistic electrons into the n-region. The momentum transfer of the injected ballistic electrons could lead to an effective Coulomb drag of the quasi-equilibrium electrons in the n-region and the plasma instability in the GFETs and GLDs. The instability enables the generation of terahertz radiation. The obtained results can be used for the optimization of the structures under consideration for different devices, in particular, terahertz emitters.
We study nonlinear transport through a classical ballistic system accounting for the Coulomb interaction between electrons. The joint effect of the applied bias $V$ and magnetic field $H$ on the electron trajectories results in a component of the non-linear current $I(V,H)$ which lacks the $H\to -H$ symmetry: $δI=α_{cl} V^2 H$. At zero temperature the magnitude of $α_{cl}$ is of the same order as that arising from the quantum interference mechanism. At higher temperatures the classical mechanism is expected to dominate due to its relatively weak temperature dependence.
We report Coulomb drag measurements on GaAs-AlGaAs electron-hole bilayers. The two layers are separated by a 10 or 25nm barrier. Below T$\approx$1K we find two features that a Fermi-liquid picture cannot explain. First, the drag on the hole layer shows an upturn, which may be followed by a downturn. Second, the effect is either absent or much weaker in the electron layer, even though the measurements are within the linear response regime. Correlated phases have been anticipated in these, but surprisingly, the experimental results appear to contradict Onsager's reciprocity theorem.
Recent experiments on Coulomb drag in the quantum Hall regime have yielded a number of surprises. The most striking observations are that the Coulomb drag can become negative in high Landau levels and that its temperature dependence is non-monotonous. We develop a systematic diagrammatic theory of Coulomb drag in strong magnetic fields explaining these puzzling experiments. The theory is applicable both in the diffusive and the ballistic regimes; we focus on the experimentally relevant ballistic regime (interlayer distance $a$ smaller than the cyclotron radius $R_c$). It is shown that the drag…
We have measured a nanoribbon of MoS2 at low temperature, and observed the evolution of the system from a regime of multiple small quantum dots in series to one where the entire nanoribbon acts as a single quantum dot. At higher Fermi energies, resonant transmission through disorder-induced potential wells is evident. Our findings shed light on the length scale of quasi-ballistic transport in the material.
Quantum mechanics and Coulomb interaction dictate the behavior of small circuits. The thermal implications cover fundamental topics from quantum control of heat to quantum thermodynamics, with prospects of novel thermal machines and an ineluctably growing influence on nanocircuit engineering. Experimentally, the rare observations thus far include the universal thermal conductance quantum and heat interferometry. However, evidences for many-body thermal effects paving the way to markedly different heat and electrical behaviors in quantum circuits remain wanting. Here we report on the observatio…
We study the ballistic conductivity of graphene bilayer in the presence of next-nearest neighbor hoppings between the layers. An undoped and unbiased system was found in Ref. [1] to show a nonuniversal (length-dependent) conductivity $σ(L)$, approaching the value of $σ_\star=3/π\simeq{}0.95$ for large $L$. Here we demonstrate one-parameter scaling and determine the scaling function $β(σ)=d\ln{}\!σ/d\ln{}\!L$. The scaling flow has an attractive fixed point [$\,β(σ_\star)=0$, $β'(σ_\star)<0\,$] reproducing the scenario predicted for random impurity scattering of Dirac fermions with Coulomb repul…
We present a theory for Coulomb drag between two mesoscopic systems which expresses the drag in terms of scattering matrices and wave functions. The formalism can be applied to both ballistic and disordered systems and the consequences can be studied either by numerical simulations or analytic means such as perturbation theory or random matrix theory. The physics of Coulomb drag in the mesoscopic regime is very different from Coulomb drag between extended electron systems. In the mesoscopic regime we in general find fluctuations of the drag comparable to the mean value. Examples are the vanish…
We investigate the Coulomb blockade resonances and the phase of the transmission amplitude of a deformed ballistic quantum dot weakly coupled to leads. We show that preferred single--particle levels exist which stay close to the Fermi energy for a wide range of values of the gate voltage. These states give rise to sequences of Coulomb blockade resonances with correlated peak heights and transmission phases. The correlation of the peak heights becomes stronger with increasing temperature. The phase of the transmission amplitude shows lapses by $π$ between the resonances. Implications for recent…
Electron transport in a self-consistent potential along a ballistic two-terminal conductor has been investigated. We have derived general formulas which describe the nonlinear current-voltage characteristics, differential conductance, and low-frequency current and voltage noise assuming an arbitrary distribution function and correlation properties of injected electrons. The analytical results have been obtained for a wide range of biases: from equilibrium to high values beyond the linear-response regime. The particular case of a three-dimensional Fermi-Dirac injection has been analyzed. We sho…
A general formula for current noise in a two-terminal ballistic nondegenerate conductor under the action of long-range Coulomb correlations has been derived. The noise reduction factor (in respect to the uncorrelated value) is obtained for biases ranging from thermal to shot noise limits, and it is related to spatial variations in transport characteristics. The contributions of different energy groups of carriers to the noise are found, that leads us to suggest an electron energy spectroscopy experiment to probe the Coulomb correlations in ballistic conductors.
Amplitude of the Coulomb blockade oscillations is calculated for a single-mode Josephson junction with arbitrary electron transparency $D$. It is shown that the Coulomb blockade is suppressed in ballistic junctions with $D\to 1$. The suppression is described quantitatively as the Landau-Zener transition in imaginary time.
Recently, the electron transport through a quasi-one dimensional (quasi-1D) electron gas was investigated experimentally as a function of the confining potential. We present a physical model for quantum ballistic transport of electrons through a short conduction channel, and investigate the role played by the Coulomb interaction in modifying the energy levels of two-electron states at low temperatures as the width of the channel is increased. In this regime, the effect of the Coulomb interaction on the two-electron states has been shown to lead to four split energy levels, including two anti-c…
We analyze the heat current flowing across interacting quantum dots within the Coulomb blockade regime. Power can be generated by either voltage or temperature biases. In the former case, we find nonlinear contributions to the Peltier effect that are dominated by conventional Joule heating for sufficiently high voltages. In the latter case, the differential thermal conductance shows maxima or minima depending on the energy level position. Furthermore, we discuss departures from the Kelvin-Onsager reciprocity relation beyond linear response.
We study matrix element fluctuations of the two-body screened Coulomb interaction and of the one-body surface charge potential in ballistic quantum dots, comparing behavior in actual chaotic billiards with analytic results previously obtained in a normalized random wave model. We find that the matrix element variances in actual chaotic billiards typically exceed by a factor of 3 or 4 the predictions of the random wave model, for dot sizes commonly used in experiments. We discuss dynamical effects that are responsible for this enhancement. These dynamical effects have an even more striking effe…
The edge channels of the quantum Hall effect provide one dimensional chiral and ballistic wires along which electrons can be guided in optics like setup. Electronic propagation can then be analyzed using concepts and tools derived from optics. After a brief review of electron optics experiments performed using stationary current sources which continuously emit electrons in the conductor, this paper focuses on triggered sources, which can generate on-demand a single particle state. It first outlines the electron optics formalism and its analogies and differences with photon optics and then turn…
We investigate the low temperature transport in 8 nm diameter Si junctionless nanowire field effect transistors fabricated by top down techniques with a wrap-around gate and two different activated doping densities. First we extract the intrinsic gate capacitance of the device geometry from a device that shows Coulomb blockade at 13 mK with over 500 Coulomb peaks across a gate voltage range of 6 V indicating the formation of a single island in the entire nanowire channel. In two other devices, doped Si:P $4\times10^{19}\,\text{cm}^{-3}$ and $2\times10^{20}\,\text{cm}^{-3}$, we observe quantum …
We have measured the collective excitation spectrum of interacting electrons in one-dimension. The experiment consists of controlling the energy and momentum of electrons tunneling between two clean and closely situated, parallel quantum wires in a GaAs/AlGaAs heterostructure while measuring the resulting conductance. We measure excitation spectra that clearly deviate from the non-interacting spectrum, attesting to the importance of Coulomb interactions. Notable is an observed 30% enhancement of the velocity of the main excitation branch relative to non-interacting electrons with the same dens…
We have measured the low-temperature transport properties of an open quantum dot formed in a clean one-dimensional channel. For the first time, at zero magnetic field, continuous and periodic oscillations superimposed upon ballistic conductance steps are observed when the conductance through the dot $G$ exceeds $2e^2/h$. We ascribe the observed conductance oscillations to evidence for Coulomb charging effects in an open dot. This is supported by the evolution of the oscillating features for $G>2e^2/h$ as a function of both temperature and barrier transparency. Our results strongly suggest that…
Low-temperature transport properties of a lateral quantum dot formed by overlaying finger gates in a clean one-dimensional channel are investigated. Continuous and periodic oscillations superimposed upon ballistic conductance steps are observed, when the conductance G of the dot changes within a wide range 0<G<6e^2/h. Calculations of the electrostatics confirm that the measured periodic conductance oscillations correspond to successive change of the total charge of the dot by $e$. By modelling the transport it is shown that the progression of the Coulomb oscillations into the region G>2e^2/h m…
We propose an experiment to test Bell's inequality violation in condensed-matter physics. We show how to generate, manipulate and detect entangled states using ballistic electrons in Coulomb-coupled semiconductor quantum wires. Due to its simplicity (only five gates are required to prepare entangled states and to test Bell's inequality), the proposed semiconductor-based scheme can be implemented with currently available technology. Moreover, its basic ingredients may play a role towards large-scale quantum-information processing in solid-state devices.
Traditional spintronics relies on spin transport by charge carriers, such as electrons in semiconductor crystals. This brings several complications: the Pauli principle prevents the carriers from moving with the same speed; Coulomb repulsion leads to rapid dephasing of electron flows. Spin-optronics is a valuable alternative to traditional spintronics. In spin-optronic devices the spin currents are carried by electrically neutral bosonic quasi-particles: excitons or exciton-polaritons. They can form highly coherent quantum liquids and carry spins over macroscopic distances. The price to pay is…
We evaluate the influence of the Coulomb drag of the electrons and holes in the gated n- and p-regions by the ballistic electrons and holes generated in the depleted i-region due to the interband tunneling on the current-voltage characteristics and impedance of the p+-p-i-n-n+ graphene tunneling transistor structures (GTTSs). The drag leads to a current amplification in the gated n- and p-regions and a positive feedback between the amplified dragged current and the injected tunneling current. A sufficiently strong drag can result in the negative real part of the GTTS impedance enabling the pla…
We study matrix element fluctuations of the two-body screened Coulomb interaction and of the one-body surface charge potential in ballistic quantum dots. For chaotic dots, we use a normalized random wave model to obtain analytic expansions for matrix element variances and covariances in the limit of large kL (where k is the Fermi wave number and L the linear size of the dot). These leading-order analytical results are compared with exact numerical results. Both two-body and one-body matrix elements are shown to follow strongly non-Gaussian distributions, despite the Gaussian random nature of t…
