Mesoscopic Coulomb drag, broken detailed balance, and fluctuation relations

Non-reciprocal Coulomb drag between Chern insulators

Coulomb interaction between two closely spaced but electrically isolated conductors can induce a voltage in one of them upon feeding a current into the other. This effect has been widely studied in nonmagnetic strongly interacting systems and historically interpreted in terms of momentum and energy exchanges, which thus complies with Onsager's reciprocity. Here we report the non-reciprocal Coulomb drag observed between two ferromagnetic Chern insulators that host quantum anomalous Hall effects. By measurements with current and circuit reversals, we discovered strong drag signals in both the longitudinal and transverse directions which violate Onsager's reciprocity. These drag signals only emerge when the Chern insulator is in a multidomain state. Combined with the nonlinear I - V characteristics and power-law temperature dependence, this drag is attributed to the rectifications of mesoscopic fluctuations and quantum shot noise as well as the current cumulant. The drag signals are accompanied by strong magnetic fluctuations, highlighting the role played by magnetic dynamics. The present study expands the Coulomb drag to the realm of magnetic topological systems.

Estimator of entropy production for partially accessible Markov networks based on the observation of blurred transitions

A central task in stochastic thermodynamics is the estimation of entropy production for partially accessible Markov networks. We establish an effective transition-based description for such networks with transitions that are not distinguishable and therefore blurred for an external observer. We demonstrate that, in contrast to a description based on fully resolved transitions, this effective description is typically non-Markovian at any point in time. Starting from an information-theoretic bound, we derive an operationally accessible entropy estimator for this observation scenario. We illustrate the operational relevance and the quality of this entropy estimator with a numerical analysis of various representative examples.

Parametric study for optimal performance of Coulomb-coupled quantum dots

We study the optimal output power and efficiency of the three-terminal quantum heat engine with Coulomb-coupled quantum-dots (CCQD). It has been well known that in the weak coupling regime, two kinds of dominant transport mechanisms are sequential tunneling and cotunneling processes in CCQD. What process becomes dominant, which can be controlled by several parameters such as temperature difference, bias voltage, Coulomb interaction and tunneling parameters, is one of the key problems to determine the performance of the heat engine. We show the parametric dependence of the output power and coefficient and find the optimal performance of this CCQD heat engine through genetic algorithm.

Full counting statistics of the particle currents through a Kitaev chain and the exchange fluctuation theorem

Exchange fluctuation theorems (XFTs) describe a fundamental symmetry relation for particle and energy exchange between several systems. Here we study the XFTs of a Kitaev chain connected to two reservoirs at the same temperature but different bias. By varying the parameters in the Kitaev chain model, we calculate analytically the full counting statistics of the transport current and formulate the corresponding XFTs for multiple current components. We also demonstrate the XFTs with numerical results. We find that due to the presence of the U(1) symmetry breaking terms in the Hamiltonian of the Kitaev chain, various forms of the XFTs emerge, and they can be interpreted in terms of various well-known transport processes.

Andreev-Coulomb Drag in Coupled Quantum Dots

The Coulomb drag effect has been observed as a tiny current induced by both electron-hole asymmetry and interactions in normal coupled quantum dot devices. In the present work we show that the effect can be boosted by replacing one of the normal electrodes by a superconducting one. Moreover, we show that at low temperatures and for sufficiently strong coupling to the superconducting lead, the Coulomb drag is dominated by Andreev processes, is robust against details of the system parameters, and can be controlled with a single gate voltage. This mechanism can be distinguished from single-particle contributions by a sign inversion of the drag current.

Effective Equilibrium in Out-of-Equilibrium Interacting Coupled Nanoconductors

In the present work, we study a mesoscopic system consisting of a double quantum dot in which both quantum dots or artificial atoms are electrostatically coupled. Each dot is additionally tunnel coupled to two electronic reservoirs and driven far from equilibrium by external voltage differences. Our objective is to find configurations of these biases such that the current through one of the dots vanishes. In this situation, the validity of the fluctuation–dissipation theorem and Onsager’s reciprocity relations has been established. In our analysis, we employ a master equation formalism for a minimum model of four charge states, and limit ourselves to the sequential tunneling regime. We numerically study those configurations far from equilibrium for which we obtain a stalling current. In this scenario, we explicitly verify the fluctuation–dissipation theorem, as well as Onsager’s reciprocity relations, which are originally formulated for systems in which quantum transport takes place in the linear regime.

Generalized Master Equation Approach to Time-Dependent Many-Body Transport

We recall theoretical studies on transient transport through interacting mesoscopic systems. It is shown that a generalized master equation (GME) written and solved in terms of many-body states provides the suitable formal framework to capture both the effects of the Coulomb interaction and electron-photon coupling due to a surrounding single-mode cavity. We outline the derivation of this equation within the Nakajima-Zwanzig formalism and point out technical problems related to its numerical implementation for more realistic systems which can neither be described by non-interacting two-level models nor by a steady-state Markov-Lindblad equation. We first solve the GME for a lattice model and discuss the dynamics of many-body states in a two-dimensional nanowire, the dynamical onset of the current-current correlations in electrostatically coupled parallel quantum dots and transient thermoelectric properties. Secondly, we rely on a continuous model to get the Rabi oscillations of the photocurrent through a double-dot etched in a nanowire and embedded in a quantum cavity. A many-body Markovian version of the GME for cavity-coupled systems is also presented.

On the competition between the Kondo effect and the exchange interaction in a parallel double quantum dot system

We study the competition between the Kondo effect and the exchange interaction in the parallel double quantum dot (DQD) system within an effective action field theory. The strong on-site Coulomb interactions in DQDs are treated by using the Hubbard-Stratonovich transformation and the introduction of scalar potential fields. We show that a self-consistent perturbation approach, which takes into account the statistical properties of the potential fields acting on electrons in DQDs, describes well the crossover from the Kondo regime to the spin-singlet state in this system. The linear conductance and the intradot/interdot spin excitation spectra of this system are obtained.

Stochastic thermodynamics for a periodically driven single-particle pump

We present the stochastic thermodynamic analysis of a time-periodic single-particle pump, including explicit results for flux, thermodynamic force, entropy production, work, heat, and efficiency. These results are valid far from equilibrium. The deviations from the linear (Onsager) regime are discussed.

Cotunneling Drag Effect in Coulomb-Coupled Quantum Dots

In Coulomb drag, a current flowing in one conductor can induce a voltage across an adjacent conductor via the Coulomb interaction. The mechanisms yielding drag effects are not always understood, even though drag effects are sufficiently general to be seen in many low-dimensional systems. In this Letter, we observe Coulomb drag in a Coulomb-coupled double quantum dot and, through both experimental and theoretical arguments, identify cotunneling as essential to obtaining a correct qualitative understanding of the drag behavior.

Correlated Coulomb Drag in Capacitively Coupled Quantum-Dot Structures

We study theoretically Coulomb drag in capacitively coupled quantum dots (CQDs)-a bias-driven dot coupled to an unbiased dot where transport is due to Coulomb mediated energy transfer drag. To this end, we introduce a master-equation approach that accounts for higher-order tunneling (cotunneling) processes as well as energy-dependent lead couplings, and identify a mesoscopic Coulomb drag mechanism driven by nonlocal multielectron cotunneling processes. Our theory establishes the conditions for a nonzero drag as well as the direction of the drag current in terms of microscopic system parameters. Interestingly, the direction of the drag current is not determined by the drive current, but by an interplay between the energy-dependent lead couplings. Studying the drag mechanism in a graphene-based CQD heterostructure, we show that the predictions of our theory are consistent with recent experiments on Coulomb drag in CQD systems.

Measurement Back-Action in Stacked Graphene Quantum Dots

We present an electronic transport experiment in graphene where both classical and quantum mechanical charge detector back-action on a quantum dot are investigated. The device consists of two stacked graphene quantum dots separated by a thin layer of boron nitride. This device is fabricated by van der Waals stacking and is equipped with separate source and drain contacts to both dots. By applying a finite bias to one quantum dot, a current is induced in the other unbiased dot. We present an explanation of the observed measurement-induced current based on strong capacitive coupling and energy dependent tunneling barriers, breaking the spatial symmetry in the unbiased system. This is a special feature of graphene-based quantum devices. The experimental observation of transport in classically forbidden regimes is understood by considering higher-order quantum mechanical back-action mechanisms.

Voltage fluctuation to current converter with Coulomb-coupled quantum dots

We study the rectification of voltage fluctuations in a system consisting of two Coulomb-coupled quantum dots. The first quantum dot is connected to a reservoir where voltage fluctuations are supplied and the second one is attached to two separate leads via asymmetric and energy-dependent transport barriers. We observe a rectified output current through the second quantum dot depending quadratically on the noise amplitude supplied to the other Coulomb-coupled quantum dot. The current magnitude and direction can be switched by external gates, and maximum output currents are found in the nA region. The rectification delivers output powers in the pW region. Future devices derived from our sample may be applied for energy harvesting on the nanoscale beneficial for autonomous and energy-efficient electronic applications.

Thermoelectric energy harvesting with quantum dots

We review recent theoretical work on thermoelectric energy harvesting in multi-terminal quantum-dot setups. We first discuss several examples of nanoscale heat engines based on Coulomb-coupled conductors. In particular, we focus on quantum dots in the Coulomb-blockade regime, chaotic cavities and resonant tunneling through quantum dots and wells. We then turn toward quantum-dot heat engines that are driven by bosonic degrees of freedom such as phonons, magnons and microwave photons. These systems provide interesting connections to spin caloritronics and circuit quantum electrodynamics.

Minimal self-contained quantum refrigeration machine based on four quantum dots

We present a theoretical study of an electronic quantum refrigerator based on four quantum dots arranged in a square configuration, in contact with as many thermal reservoirs. We show that the system implements the minimal mechanism for acting as a self-contained quantum refrigerator, by demonstrating heat extraction from the coldest reservoir and the cooling of the nearby quantum dot.

Noise and fluctuation relations of a spin diode

: We consider fluctuation relations between the transport coefficients of a spintronic system where magnetic interactions play a crucial role. We investigate a prototypical spintronic device - a spin-diode - which consists of an interacting resonant level coupled to two ferromagnetic electrodes. We thereby obtain the cumulant generating function for the spin transport in the sequential tunnelling regime. We demonstrate the fulfilment of the nonlinear fluctuation relations when up and down spin currents are correlated in the presence of both spin-flip processes and external magnetic fields.

Thermodynamics of a physical model implementing a Maxwell demon

We present a physical implementation of a Maxwell demon which consists of a conventional single electron transistor (SET) capacitively coupled to another quantum dot detecting its state. Altogether, the system is described by stochastic thermodynamics. We identify the regime where the energetics of the SET is not affected by the detection, but where its coarse-grained entropy production is shown to contain a new contribution compared to the isolated SET. This additional contribution can be identified as the information flow generated by the "Maxwell demon" feedback in an idealized limit.

Stochastic thermodynamics, fluctuation theorems and molecular machines

Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.

Fluctuation relations for spintronics

Fluctuation relations are derived in systems where the spin degree of freedom and magnetic interactions play a crucial role. The form of the nonequilibrium fluctuation theorems relies on the assumption of a local balance condition. We demonstrate that in some cases the presence of magnetic interactions violates this condition. Nevertheless, fluctuation relations can be obtained from the microreversibility principle sustained only at equilibrium as a symmetry of the cumulant generating function for spin currents. We illustrate the spintronic fluctuation relations for a quantum dot coupled to partially polarized helical edge states.

Stochastic thermodynamics under coarse graining

A general formulation of stochastic thermodynamics is presented for open systems exchanging energy and particles with multiple reservoirs. By introducing a partition in terms of "mesostates" (e.g., sets of "microstates"), the consequence on the thermodynamic description of the system is studied in detail. When microstates within mesostates rapidly thermalize, the entire structure of the microscopic theory is recovered at the mesostate level. This is not the case when these microstates remain out of equilibrium, leading to additional contributions to the entropy balance. Some of our results are illustrated for a model of two coupled quantum dots.

Measurement of finite-frequency current statistics in a single-electron transistor

Electron transport in nanoscale structures is strongly influenced by the Coulomb interaction that gives rise to correlations in the stream of charges and leaves clear fingerprints in the fluctuations of the electrical current. A complete understanding of the underlying physical processes requires measurements of the electrical fluctuations on all time and frequency scales, but experiments have so far been restricted to fixed frequency ranges, as broadband detection of current fluctuations is an inherently difficult experimental procedure. Here we demonstrate that the electrical fluctuations in a single-electron transistor can be accurately measured on all relevant frequencies using a nearby quantum point contact for on-chip real-time detection of the current pulses in the single-electron device. We have directly measured the frequency-dependent current statistics and, hereby, fully characterized the fundamental tunnelling processes in the single-electron transistor. Our experiment paves the way for future investigations of interaction and coherence-induced correlation effects in quantum transport.

Positive and negative Coulomb drag in vertically integrated one-dimensional quantum wires

Electron interactions in and between wires become increasingly complex and important as circuits are scaled to nanometre sizes, or use reduced-dimensional conductors such as carbon nanotubes, nanowires and gated high-mobility two-dimensional electron systems. This is because the screening of the long-range Coulomb potential of individual carriers is weakened in these systems, which can lead to phenomena such as Coulomb drag, where a current in one wire induces a voltage in a second wire through Coulomb interactions alone. Previous experiments have demonstrated Coulomb electron drag in wires separated by a soft electrostatic barrier of width ≳80 nm (ref. 12), which was interpreted as resulting entirely from momentum transfer. Here, we measure both positive and negative drag between adjacent vertical quantum wires that are separated by ∼15 nm and have independent contacts, which allows their electron densities to be tuned independently. We map out the drag signal versus the number of electron sub-bands occupied in each wire, and interpret the results both in terms of momentum-transfer and charge-fluctuation induced transport models. For wires of significantly different sub-band occupancies, the positive drag effect can be as large as 25%.