Chiral thermoelectrics with quantum Hall edge states

Thermoelectric Rectification and Amplification in Interacting Quantum-Dot Circuit-Quantum-Electrodynamics Systems

Thermoelectric rectification and amplification were investigated in an interacting quantum-dot circuit-quantum-electrodynamics system. By applying the Keldysh nonequilibrium Green's function approach, we studied the elastic (energy-conserving) and inelastic (energy-nonconserving) transport through a cavity-coupled quantum dot under the voltage biases in a wide spectrum of electron-electron and electron-photon interactions. While significant charge and Peltier rectification effects were found for strong light-matter interactions, the dependence on electron-electron interaction could be nonmonotonic and dramatic. Electron-electron interaction-enhanced transport was found under certain resonance conditions. These nontrivial interaction effects were found in both linear and nonlinear transport regimes, which manifested in charge and thermal currents, rectification effects, and the linear thermal transistor effect.

Linear and nonlinear thermoelectric transport in a quantum spin Hall insulators coupled with a nanomagnet

Thermoelectric effects in quantum systems have been focused in recent years. Thermoelectric energy conversion study of systems with edge states, such as quantum Hall insulators and quantum spin Hall insulators, is one of the most important frontier topics in material science and condensed-matter physics. Based on the previous paper (Gresta in Phys Rev Lett 123:186801, 2019), we further investigated the linear and nonlinear thermoelectric transport properties of helical edge states of the quantum spin Hall insulators coupled with double nanomagnet, calculated the Seebeck coefficients [Formula: see text] and the thermoelectrical figure of merit ZT, discussed the influence of the length of the nanomagnet and the relative tilt angle of component of the magnetization perpendicular on the thermoelectric coefficients ([Formula: see text] and ZT), and summarized some meaningful conclusions in the linear response regime. In the nonlinear regime, we calculated the equivalent figure of merit [Formula: see text] and the power-generation efficiency [Formula: see text] in different length of the nanomagnet, obtain the temperature difference of achieving optimal thermoelectricity. The results of this paper further confirm that the setup can indeed be used as a device for achieving high performance thermoelectric.

Achieving Carnot efficiency in a finite-power Brownian Carnot cycle with arbitrary temperature difference

Achieving the Carnot efficiency at finite power is a challenging problem in heat engines due to the trade-off relation between efficiency and power that holds for general heat engines. It is pointed out that the Carnot efficiency at finite power may be achievable in the vanishing limit of the relaxation times of a system without breaking the trade-off relation. However, any explicit model of heat engines that realizes this scenario for arbitrary temperature difference has not been proposed. Here, we investigate an underdamped Brownian Carnot cycle where the finite-time adiabatic processes connecting the isothermal processes are tactically adopted. We show that in the vanishing limit of the relaxation times in the above cycle, the compatibility of the Carnot efficiency and finite power is achievable for arbitrary temperature difference. This is theoretically explained based on the trade-off relation derived for our cycle, which is also confirmed by numerical simulations.

Compatibility of Carnot efficiency with finite power in an underdamped Brownian Carnot cycle in small temperature-difference regime

We study the possibility of achieving the Carnot efficiency in a finite-power underdamped Brownian Carnot cycle. Recently, it was reported that the Carnot efficiency is achievable in a general class of finite-power Carnot cycles in the vanishing limit of the relaxation times. Thus, it may be interesting to clarify how the efficiency and power depend on the relaxation times by using a specific model. By evaluating the heat-leakage effect intrinsic in the underdamped dynamics with the instantaneous adiabatic processes, we demonstrate that the compatibility of the Carnot efficiency and finite power is achieved in the vanishing limit of the relaxation times in the small temperature-difference regime. Furthermore, we show that this result is consistent with a trade-off relation between power and efficiency by explicitly deriving the relation of our cycle in terms of the relaxation times.

Large positive magnetoresistance and Dzyaloshinskii-Moriya interaction in CrSi driven by Cr 3d localization

Spin chiral systems with Dzyaloshinskii–Moriya (DM) interaction due to broken inversion symmetry are extensively studied for their technological applications in spintronics and thermoelectrics. Here, we report an experimental study on the magnetization, magnetoresistance (MR) and electronic structure of a non-centrosymmetric compound CrSi with B20 crystal structure. Both magnetization and MR shows competing ferromagnetic (FM) and antiferromagnetic (AFM) correlations with the FM correlations being comparatively weaker indicating the presence of DM interaction in CrSi. A large positive MR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim \,25\%$$\end{document}∼25% obtained at 5 K and 5 T magnetic field arises due to the stronger AFM correlations. Resonant photoemission shows both localized and itinerant nature of Cr 3d electrons to be present in CrSi and this is supported by the temperature dependence of magnetic susceptibility. Drastic variation in the density of states along with valence band broadening at low temperature indicates the increase in hybridization between Cr 3d and Si 3s–3p states which enhances the localization effects. Spin polarized itinerant Cr 3d electrons give rise to AFM spin density wave in CrSi. Magnetic interaction between the localized and itinerant Cr 3d electrons are found to be crucial for realizing DM interaction in this system. Spectral density of states derived from high resolution valence band measurements provides evidence of electronic topological transition in CrSi. Large density of polarized itinerant electrons which varies with temperature and the large positive MR with AFM correlations suggests CrSi as a potential candidate for both the thermoelectric and spintronics applications.

Nonlocal Thermoelectricity in a Superconductor-Topological-Insulator-Superconductor Junction in Contact with a Normal-Metal Probe: Evidence for Helical Edge States

We consider a Josephson junction hosting a Kramers pair of helical edge states of a quantum spin Hall bar in contact with a normal-metal probe. In this hybrid system, the orbital phase, induced by a small magnetic field threading the junction known as a Doppler shift, combines with the conventional Josephson phase difference and originates an effect akin to a Zeeman field in the spectrum. As a consequence, when a temperature bias is applied to the superconducting terminals, a thermoelectric current is established in the normal probe. We argue that this purely nonlocal thermoelectric effect is a unique signature of the helical nature of the edge states coupled to superconducting leads and it can constitute a useful tool for probing the helical nature of the edge states in systems where the Hall bar configuration is difficult to achieve. We fully characterize thermoelectric response and performance of this hybrid junction in a wide range of parameters, demonstrating that the external magnetic flux inducing the Doppler shift can be used as a knob to control the thermoelectric response and the heat flow in a novel device based on topological junctions.

Nonequilibrium System as a Demon

Maxwell demons are creatures that are imagined to be able to reduce the entropy of a system without performing any work on it. Conventionally, such a Maxwell demon's intricate action consists of measuring individual particles and subsequently performing feedback. We show that much simpler setups can still act as demons: we demonstrate that it is sufficient to exploit a nonequilibrium distribution to seemingly break the second law of thermodynamics. We propose both an electronic and an optical implementation of this phenomenon, realizable with current technology.

Optimal Thermoelectricity with Quantum Spin Hall Edge States

We study the thermoelectric properties of a Kramers pair of helical edge states of the quantum spin Hall effect coupled to a nanomagnet with a component of the magnetization perpendicular to the direction of the spin-orbit interaction of the host. We show that the transmission function of this structure has the desired qualities for optimal thermoelectric performance in the quantum coherent regime. For a single magnetic domain, there is a power generation close to the optimal bound. In a configuration with two magnetic domains with different orientations, pronounced peaks in the transmission functions and resonances lead to a high figure of merit. We provide estimates for the fabrication of this device with HgTe quantum-well topological insulators.

Experimental Realization of a Quantum Dot Energy Harvester

We demonstrate experimentally an autonomous nanoscale energy harvester that utilizes the physics of resonant tunneling quantum dots. Gate-defined quantum dots on GaAs/AlGaAs high-electron-mobility transistors are placed on either side of a hot-electron reservoir. The discrete energy levels of the quantum dots are tuned to be aligned with low energy electrons on one side and high energy electrons on the other side of the hot reservoir. The quantum dots thus act as energy filters and allow for the conversion of heat from the cavity into electrical power. Our energy harvester, measured at an estimated base temperature of 75 mK in a He^{3}/He^{4} dilution refrigerator, can generate a thermal power of 0.13 fW for a temperature difference across each dot of about 67 mK.

Symmetry Properties of Mixed and Heat Photo-Assisted Noise in the Quantum Hall Regime

We investigate the photo-assisted charge-heat mixed noise and the heat noise generated by periodic drives in Quantum Hall states belonging to the Laughlin sequence. Fluctuations of the charge and heat currents are due to weak backscattering induced in a quantum point contact geometry and are evaluated at the lowest order in the tunneling amplitude. Focusing on the cases of a cosine and Lorentzian periodic drive, we show that the different symmetries of the photo-assisted tunneling amplitudes strongly affect the overall profile of these quantities as a function of the AC and DC voltage contributions, which can be tuned independently in experiments.

Unified Thermodynamic Uncertainty Relations in Linear Response

Thermodynamic uncertainty relations (TURs) are recently established relations between the relative uncertainty of time-integrated currents and entropy production in nonequilibrium systems. For small perturbations away from equilibrium, linear response (LR) theory provides the natural framework to study generic nonequilibrium processes. Here, we use LR to derive TURs in a straightforward and unified way. Our approach allows us to generalize TURs to systems without local time-reversal symmetry, including, e.g., ballistic transport and periodically driven classical and quantum systems. We find that, for broken time reversal, the bounds on the relative uncertainty are controlled both by dissipation and by a parameter encoding the asymmetry of the Onsager matrix. We illustrate our results with an example from mesoscopic physics. We also extend our approach beyond linear response: for Markovian dynamics, it reveals a connection between the TUR and current fluctuation theorems.

Helical thermoelectrics and refrigeration

The thermoelectric properties of a three-terminal quantum spin Hall (QSH) sample are examined. The inherent helicity of the QSH sample helps to generate a large charge power efficiently. Along with charge the system can be designed to work as a highly efficient spin heat engine too. The advantage of a helical over a chiral sample is that, while a multiterminal quantum Hall sample can only work as a quantum heat engine due to broken time reversal (TR) symmetry, a multiterminal QSH system can work effectively as both a charge or spin heat engine and as a charge or spin refrigerator as the TR symmetry is preserved.

Thermodynamic Bounds on Precision in Ballistic Multiterminal Transport

For classical ballistic transport in a multiterminal geometry, we derive a universal trade-off relation between total dissipation and the precision, at which particles are extracted from individual reservoirs. Remarkably, this bound becomes significantly weaker in the presence of a magnetic field breaking time-reversal symmetry. By working out an explicit model for chiral transport enforced by a strong magnetic field, we show that our bounds are tight. Beyond the classical regime, we find that, in quantum systems far from equilibrium, the correlated exchange of particles makes it possible to exponentially reduce the thermodynamic cost of precision.

Universal Coherence-Induced Power Losses of Quantum Heat Engines in Linear Response

We identify a universal indicator for the impact of coherence on periodically driven quantum devices by dividing their power output into a classical contribution and one stemming solely from superpositions. Specializing to Lindblad dynamics and small driving amplitudes, we derive general upper bounds on both the coherent and the total power of cyclic heat engines. These constraints imply that, for sufficiently slow driving, coherence inevitably leads to power losses in the linear-response regime. We illustrate our theory by working out the experimentally relevant example of a single-qubit engine.

Route towards the optimization at given power of thermoelectric heat engines with broken time-reversal symmetry

We investigate the performance at a given power of a thermoelectric heat engine with broken time-reversal symmetry, and derive analytically the efficiency at a given power of a thermoelectric generator within linear irreversible thermodynamics. A universal bound on the efficiency of the thermoelectric heat engine is achieved under a strong constraint on the Onsager coefficients, and some interesting features are further revealed. Our results demonstrate that there exists a trade-off between efficiency and power output, and the efficiency at a given power may surpass the Curzon-Ahlborn limit due to broken time-reversal symmetry. Moreover, optimal efficiency at a given power can be achieved, which indicates that broken time-reversal symmetry offers physically allowed ways to optimize the performance of heat engines. Our study may contribute to the interesting guidelines for optimizing actual engines.

Optimal Quantum Interference Thermoelectric Heat Engine with Edge States

We show theoretically that a thermoelectric heat engine, operating exclusively due to quantum-mechanical interference, can reach optimal linear-response performance. A chiral edge state implementation of a close-to-optimal heat engine is proposed in an electronic Mach-Zehnder interferometer with a mesoscopic capacitor coupled to one arm. We demonstrate that the maximum power and corresponding efficiency can reach 90% and 83%, respectively, of the theoretical maximum. The proposed heat engine can be realized with existing experimental techniques and has a performance robust against moderate dephasing.

Universal Trade-Off Relation between Power and Efficiency for Heat Engines

For a general thermodynamic system described as a Markov process, we prove a general lower bound for dissipation in terms of the square of the heat current, thus establishing that nonvanishing current inevitably implies dissipation. This leads to a universal trade-off relation between efficiency and power, with which we rigorously prove that a heat engine with nonvanishing power never attains the Carnot efficiency. Our theory applies to systems arbitrarily far from equilibrium, and does not assume any specific symmetry of the model.

Power-Efficiency-Dissipation Relations in Linear Thermodynamics

We derive general relations between the maximum power, maximum efficiency, and minimum dissipation regimes from linear irreversible thermodynamics. The relations simplify further in the presence of a particular symmetry of the Onsager matrix, which can be derived from detailed balance. The results are illustrated on a periodically driven system and a three-terminal device subject to an external magnetic field.

Thermodynamics of the mesoscopic thermoelectric heat engine beyond the linear-response regime

Mesoscopic thermoelectric heat engine is much anticipated as a device that allows us to utilize with high efficiency wasted heat inaccessible by conventional heat engines. However, the derivation of the heat current in this engine seems to be either not general or described too briefly, even inappropriately in some cases. In this paper, we give a clear-cut derivation of the heat current of the engine with suitable assumptions beyond the linear-response regime. It resolves the confusion in the definition of the heat current in the linear-response regime. After verifying that we can construct the same formalism as that of the cyclic engine, we find the following two interesting results within the Landauer-Büttiker formalism: the efficiency of the mesoscopic thermoelectric engine reaches the Carnot efficiency if and only if the transmission probability is finite at a specific energy and zero otherwise; the unitarity of the transmission probability guarantees the second law of thermodynamics, invalidating Benenti et al.'s argument in the linear-response regime that one could obtain a finite power with the Carnot efficiency under a broken time-reversal symmetry [Phys. Rev. Lett. 106, 230602 (2011)]. These results demonstrate how quantum mechanics constrains thermodynamics.

Onsager Coefficients in Periodically Driven Systems

We evaluate the Onsager matrix for a system under time-periodic driving by considering all its Fourier components. By application of the second law, we prove that all the fluxes converge to zero in the limit of zero dissipation. Reversible efficiency can never be reached at finite power. The implication for an Onsager matrix, describing reduced fluxes, is that its determinant has to vanish. In the particular case of only two fluxes, the corresponding Onsager matrix becomes symmetric.

Efficiency Statistics and Bounds for Systems with Broken Time-Reversal Symmetry

Universal properties of the statistics of stochastic efficiency for mesoscopic time-reversal symmetry broken energy transducers are revealed in the Gaussian approximation. We also discuss how the second law of thermodynamics restricts the statistics of stochastic efficiency. The tight-coupling limit becomes unfavorable, characterized by an infinitely broad distribution of efficiency at all times, when time-reversal symmetry breaking leads to an asymmetric Onsager response matrix. The underlying physics is demonstrated through the quantum Hall effect and further elaborated in a triple-quantum-dot three-terminal thermoelectric engine.