Rectification of electronic heat current by a hybrid thermal diode

Thermal Rectification in Modularly Designed Bulk Metamaterials

Thermal rectification is a phenomenon of great practical importance where heat transfer is preferential in one direction. Programmable control of heat transfer in 3D space is key to enable thermal rectification at the macroscale but is rarely realized in natural materials or in current existing devices that are constructed at the nano and microscales with high system complexity. Here, modularly designed bulk metamaterials that can break the symmetry of heat transfer from one direction to the other are created, leading to thermal rectification in convergent or divergent states by tuning the metamaterial microstructural design. These thermal metamaterials are microstructured composites made using one material composition, however, they offer sufficient microstructural design freedom to allow tunable local thermal properties for unusual macroscopic heat transfer. The strategy and performance achieved are promising for next-generation thermal management.

Quantum heat valve and diode of strongly coupled defects in amorphous material

The mechanical strain can control the frequency of two-level atoms in amorphous material. In this work, we would like to employ two coupled two-level atoms to manipulate the magnitude and direction of heat transport by controlling mechanical strain to realize the function of a thermal switch and valve. It is found that a high-performance heat diode can be realized in the wide piezo voltage range at different temperatures. We also discuss the dependence of the rectification factor on temperatures and couplings of heat reservoirs. We find that the higher temperature differences correspond to the larger rectification effect. The asymmetry system-reservoir coupling strength can enhance the magnitude of heat transfer, and the impact of asymmetric and symmetric coupling strength on the performance of the heat diode is complementary. It may provide an efficient way to modulate and control heat transport's magnitude and flow preference. This work may give insight into designing and tuning quantum heat machines.

Approaching the perfect diode limit through a nonlinear interface

We consider a system formed by two different segments of particles, coupled to thermal baths, one at each end, modeled by Langevin thermostats. The particles in each segment interact harmonically and are subject to an on-site potential for which three different types are considered, namely, harmonic, ϕ^{4}, and Frenkel-Kontorova. The two segments are nonlinearly coupled, between interfacial particles, by means of a power-law potential with exponent μ, which we vary, scanning from subharmonic to superharmonic potentials, up to the infinite-square-well limit (μ→∞). Thermal rectification is investigated by integrating the equations of motion and computing the heat fluxes. As a measure of rectification, we use the difference of the currents, resulting from the interchange of the baths, divided by their average (all quantities taken in absolute value). We find that rectification can be optimized by a given value of μ that depends on the bath temperatures and details of the chains. But, regardless of the type of on-site potential considered, the interfacial potential that produces maximal rectification approaches the infinite square well (μ→∞) when reducing the average temperature of the baths. Our analysis of thermal rectification focuses on this regime, for which we complement numerical results with heuristic considerations.

Thermal rectification through the topological states of asymmetrical length armchair graphene nanoribbons heterostructures with vacancies

We present a theoretical investigation of electron heat current in asymmetrical length armchair graphene nanoribbon (AGNR) heterostructures with vacancies, focusing on the topological states (TSs). In particular, we examine the 9-7-9 AGNR heterostructures where the TSs are well-isolated from the conduction and valence subbands. This isolation effectively mitigates thermal noise of subbands arising from temperature fluctuations during charge transport. Moreover, when the TSs exhibit an orbital off-set, intriguing electron heat rectification phenomena are observed, primarily attributed to inter-TS electron Coulomb interactions. To enhance the heat rectification ratio (ηQ), we manipulate the coupling strengths between the heat sources and the TSs by introducing asymmetrical lengths in the 9-AGNRs. This approach offers control over the rectification properties, enabling significant enhancements. Additionally, we introduce vacancies strategically positioned between the heat sources and the TSs to suppress phonon heat current. This arrangement effectively reduces the overall phonon heat current, while leaving the TSs unaffected. Our findings provide valuable insights into the behavior of electron heat current in AGNR heterostructures, highlighting the role of topological states, inter-TS electron Coulomb interactions, and the impact of structural modifications such as asymmetrical lengths and vacancy positioning. These results pave the way for the design and optimization of graphene-based devices with improved thermal management and efficient control of electron heat transport.

Quantum thermal diode dominated by pure classical correlation via three triangular-coupled qubits

A quantum thermal diode is designed based on three pairwise coupled qubits, two connected to a common reservoir and the other to an independent reservoir. It is found that the internal couplings between qubits can enhance heat currents. If the two identical qubits uniformly couple with the common reservoir, the crossing dissipation will occur, leading to the initial-state-dependent steady state, which can be decomposed into the mixture of two particular steady states: the heat-conducting state generating maximum heat current and the heat-resisting state not transporting heat. However, the rectification factor doesn't depend on the initial state. In particular, we find that neither quantum entanglement nor quantum discord is present in the steady state, but the pure classical correlation shows a remarkably consistent behavior as the heat rectification factor, which reveals the vital role of classical correlation in the system.

Solid-state thermal rectification of bilayers by asymmetric elastic modulus

A highly efficient thermal rectification applicable to large panels still needs to be developed. Here, we experimentally achieve a high thermal rectification efficiency of 33% by carefully engineering elastic modulus asymmetry in a centimeter-scale bilayered silver-graphene oxide sponge. The thermal conduction primarily occurs in the out-of-plane direction, and the forward heat flow direction is from the hard silver to the soft graphene oxide. Surprisingly, the forward heat flow direction is reversed when a silver layer is formed on a harder polystyrene foam. The forward direction is always from the harder side to the softer side, and the asymmetry in elastic modulus is suggested as a possible mechanism based on the one-dimensional Frenkel-Kontorova (FK) model. The finite element analysis indicates that other mechanisms such as temperature-dependent thermal conductivity and radiation asymmetry cannot explain the high rectification efficiency. This scalable work over a wide temperature range may find immediate industrial applications.

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.

Energy dynamics, heat production and heat-work conversion with qubits: toward the development of quantum machines

We present an overview of recent advances in the study of energy dynamics and mechanisms for energy conversion in qubit systems with special focus on realizations in superconducting quantum circuits. We briefly introduce the relevant theoretical framework to analyze heat generation, energy transport and energy conversion in these systems with and without time-dependent driving considering the effect of equilibrium and non-equilibrium environments. We analyze specific problems and mechanisms under current investigation in the context of qubit systems. These include the problem of energy dissipation and possible routes for its control, energy pumping between driving sources and heat pumping between reservoirs, implementation of thermal machines and mechanisms for energy storage. We highlight the underlying fundamental phenomena related to geometrical and topological properties, as well as many-body correlations. We also present an overview of recent experimental activity in this field.

Highly-efficient radiative thermal rectifiers based on near-field gap variations

Near-field radiative thermal rectifiers (NFRTRs) enabling directional heat transport hold great promise for various applications, including thermal logic computing, thermal management, and energy conversion. Current NFRTR designs rely on dissimilar terminal materials with high contrasts in their temperature-dependent dielectric properties, which in turn hinders the spectral match for radiative heat transfer and thus limits the device's efficiency. Herein, this dilemma is solved by designing heterostructures where a pair of polaritonic layers are separately stacked on a thermally-expanding layer and a rigid substrate, spaced by a vacuum gap. In this scheme, the symmetric polaritonic layers can provide stable near-field radiative channels for heat transfer, while the thermally-expanding layer can modulate the gap size with flipped temperature bias to allow high contrasts in heat flux. In exemplified implementations, the hBN-based design has achieved a record-high thermal rectification factor (TRF, ∼10⁴) even under small thermal gradients (∼20 K), which can be further boosted by polaritonic hybridizations in the graphene/hBN-based design. This study paves the way to design novel NFRTRs with 2D materials, thus providing enriched polaritons to realize higher TRFs.

Magnus induced diode effect for skyrmions in channels with periodic potentials

Using a particle based model, we investigate the skyrmion dynamical behavior in a channel where the upper wall contains divots of one depth and the lower wall contains divots of a different depth. Under an applied driving force, skyrmions in the channels move with a finite skyrmion Hall angle that deflects them toward the upper wall for -xdirection driving and the lower wall for +xdirection driving. When the upper divots have zero height, the skyrmions are deflected against the flat upper wall for -xdirection driving and the skyrmion velocity depends linearly on the drive. For +xdirection driving, the skyrmions are pushed against the lower divots and become trapped, giving reduced velocities and a nonlinear velocity-force response. When there are shallow divots on the upper wall and deep divots on the lower wall, skyrmions get trapped for both driving directions; however, due to the divot depth difference, skyrmions move more easily under -xdirection driving, and become strongly trapped for +xdirection driving. The preferred -xdirection motion produces what we call a Magnus diode effect since it vanishes in the limit of zero Magnus force, unlike the diode effects observed for asymmetric sawtooth potentials. We show that the transport curves can exhibit a series of jumps or dips, negative differential conductivity, and reentrant pinning due to collective trapping events. We also discuss how our results relate to recent continuum modeling on a similar skyrmion diode system.

Heat transport and rectification via quantum statistical and coherence asymmetries

Recent experiments at the nanoscales confirm that thermal rectifiers, the thermal equivalent of electrical diodes, can operate in the quantum regime. We present a thorough investigation of the effect of different particle exchange statistics, coherence, and collective interactions on the quantum heat transport of rectifiers with two-terminal junctions. Using a collision model approach to describe the open system dynamics, we obtain a general expression of the nonlinear heat flow that fundamentally deviates from the Landauer formula whenever quantum statistical or coherence asymmetries are present in the bath particles. Building on this, we show that heat rectification is possible even with symmetric medium-bath couplings if the two baths differ in quantum statistics or coherence. Furthermore, the associated thermal conductance vanishes exponentially at low temperatures as in the Coulomb-blockade effect. However, at high temperatures it acquires a power-law behavior depending on the quantum statistics. Our results can be significant for heat management in hybrid open quantum systems or solid-state thermal circuits.

Simultaneous electrical and thermal rectification in a monolayer lateral heterojunction

Efficient waste heat dissipation has become increasingly challenging as transistor size has decreased to nanometers. As governed by universal Umklapp phonon scattering, the thermal conductivity of semiconductors decreases at higher temperatures and causes heat transfer deterioration under high-power conditions. In this study, we realized simultaneous electrical and thermal rectification (TR) in a monolayer MoSe₂-WSe₂ lateral heterostructure. The atomically thin MoSe₂-WSe₂ heterojunction forms an electrical diode with a high ON/OFF ratio up to 10⁴. Meanwhile, a preferred heat dissipation channel was formed from MoSe₂ to WSe₂ in the ON state of the heterojunction diode at high bias voltage with a TR factor as high as 96%. Higher thermal conductivity was achieved at higher temperatures owing to the TR effect caused by the local temperature gradient. Furthermore, the TR factor could be regulated from maximum to zero by rotating the angle of the monolayer heterojunction interface. This result opens a path for designing novel nanoelectronic devices with enhanced thermal dissipation.

Thermal Rectification and Thermal Logic Gates in Graded Alloy Semiconductors

Classical thermal rectification arises from the contact between two dissimilar bulk materials, each with a thermal conductivity (k) with a different temperature dependence. Here, we study thermal rectification in a Si(1−x)Gex alloy with a spatial dependence on the atomic composition. Rectification factors (R = kmax/kmin) of up to 3.41 were found. We also demonstrate the suitability of such an alloy for logic gates using a thermal AND gate as an example by controlling the thermal conductivity profile via the alloy composition. This system is readily extendable to other alloys, since it only depends on the effective thermal conductivity. These thermal devices are inherently advantageous alternatives to their electric counterparts, as they may be able to take advantage of otherwise undesired waste heat in the surroundings. Furthermore, the demonstration of logic operations is a step towards thermal computation.

Experimental evaluation of thermal rectification in a ballistic nanobeam with asymmetric mass gradient

Practical applications of heat transport control with artificial metamaterials will heavily depend on the realization of thermal diodes/rectifiers, in which thermal conductivity depends on the heat flux direction. Whereas various macroscale implementations have been made experimentally, nanoscales realizations remain challenging and efficient rectification still requires a better fundamental understanding of heat carriers’ transport and nonlinear mechanisms. Here, we propose an experimental realization of a thermal rectifier based on two leads with asymmetric mass gradients separated by a ballistic spacer, as proposed in a recent numerical investigation, and measure its thermal properties electrically with the microbridge technique. We use a Si\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{3}$$\end{document}3N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{4}$$\end{document}4 nanobeam on which an asymmetric mass gradient has been engineered and demonstrate that in its current form, this structure does not allow for thermal rectification. We explain this by a combination of too weak asymmetry and non-linearities. Our experimental observations provide important information towards fabricating rigorous thermal rectifiers in the ballistic phonon transport regime, which are expected to open new possibilities for applications in thermal management and quantum thermal devices.

Phosphorene grain boundary effect on phonon transport and phononic applications

Grain boundaries (GBs) widely exist in black phosphorene (BP), which plays a vital role in determining the properties of 2D materials. Significant GB effect on the thermal boundary resistance in BP structures is found by using molecular dynamics calculations and lattice dynamic analysis. A remarkably high interface thermal resistance is observed. By analyzing the strain distribution and phonon vibrational spectra, we reveal this high thermal resistance originates from phonon localization and strong phonon boundary scattering induced by the local stress at the GB area. Particularly, it is interesting to find that the partial phonon modes display weak localization when GBs present. The fraction of atoms participating in a particular phonon vibrational mode has been quantified through the calculation of phonon participation ratio. In addition, the thermal boundary resistance is found size-dependent, which further induces interesting thermal rectification effect in the BP structures. A high rectification ratio is obtained by adjusting the structural length and temperature bias. These findings provide a through insight into the GB effects on individual phonon mode transmission across the GBs, and highlight that the GB effect is an important factor and should be taken into account for the applications of BP-based phononic devices.

Photonic heat transport in three terminal superconducting circuit

We report an experimental realization of a three-terminal photonic heat transport device based on a superconducting quantum circuit. The central element of the device is a flux qubit made of a superconducting loop containing three Josephson junctions, which can be tuned by magnetic flux. It is connected to three resonators terminated by resistors. By heating one of the resistors and monitoring the temperatures of the other two, we determine photonic heat currents in the system and demonstrate their tunability by magnetic field at the level of 1 aW. We determine system parameters by performing microwave transmission measurements on a separate nominally identical sample and, in this way, demonstrate clear correlation between the level splitting of the qubit and the heat currents flowing through it. Our experiment is an important step towards realization of heat transistors, heat amplifiers, masers pumped by heat and other quantum heat transport devices.

Quantum heat transport devices are currently intensively studied. Here, the authors report the photonic heat transport modulated by superconducting qubit in a three-terminal device. Flux dependent heat power correlates with microwave measurements.

Negative rectification and anomalous diffusion in nonlinear substrate potentials: Dynamical relaxation and information entropy

We numerically investigate the rectification of the probability flux and dynamical relaxation of particles moving in a system with and without noise. The system, driven by two external forces, consists of two substrate potentials that have identical shapes and different potential barriers with different friction coefficients. The deterministic model exhibits the perfect rectification of the probability flux, ratchet effect, and the dependence of the unpredictability of the dynamics on basin of attraction. In contrast, the stochastic model displays that the rectification is sensitive to the temperature and an external bias. They can induce kinetic phase transitions between no transport and a finite net transport. These transitions lead to an unexpected phenomenon, called negative rectification. The results are analyzed through the corresponding time-dependent diffusion coefficient, information entropy (IE), etc. At a low temperature, anomalous diffusions occur in system. For the occurrence of the flux in certain parameter regimes, the larger the diffusion is, the smaller the corresponding IE is, and vice versa. We also present the selected parameter regimes for the emergence of the rectification and negative rectification. Additionally, we study the rectification of the interacting particles in the system and find that the flux may depend on the coupling strength and the number of the interacting particles, and that collective motions occur for the forward flux. Our work provides not only a way of the rectification for the transport of various particles (e.g., ions, electrons, photons, phonons, molecules, DNA chains, nanoswimmers, dust particles, etc.) in physics, chemistry, biology, and material science, but also a design of various circuits.

Heat rectification by two qubits coupled with Dzyaloshinskii-Moriya interaction

We investigate heat rectification in a two-qubit system coupled via the Dzyaloshinskii-Moriya (DM) interaction. We derive analytical expressions for heat currents and thermal rectification and provide possible physical mechanisms behind the observed results. We show that the anisotropy of DM interaction in itself is insufficient for heat rectification, and some other form of asymmetry is needed. We employ off-resonant qubits as the source of this asymmetry. We find the regime of parameters for higher rectification factors by examining the analytical expressions of rectification obtained from a global master equation solution. In addition, it is shown that the direction and quality of rectification can be controlled via various system parameters. Furthermore, we compare the influence of different orientations of the DM field anisotropy on the performance of heat rectification. Finally, we investigate the possible interplay between quantum correlations and the performance of the quantum thermal rectifier. We find that asymmetry in the coherences is a fundamental resource for the performance of the quantum thermal rectifier.

Giant rectification in segmented, strongly interacting spin chains despite the presence of perturbations

Balachandran et al. [Phys. Rev. Lett. 120, 200603 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.200603] presented a segmented XXZ spin chain with zero anisotropy in one half and a large anisotropy on the other half that gave rise to a spin current rectification which is perfect in the thermodynamic limit. Here we extend the previous study to segmented chains with interacting integrable as well as nonintegrable halves, considering even cases in which no ballistic transport can emerge in either half. We demonstrate that, also in this more general case, it is possible to obtain giant rectification when the two interacting half chains are sufficiently different. We also show that the mechanism causing this effect is the emergence of an energy gap in the excitation spectrum of the out-of-equilibrium insulating steady state in one of the two biases. Finally, we demonstrate that in the thermodynamic limit there is no perfect rectification when each of the two half chains is interacting.

Nanostructured jumping-droplet thermal rectifier

Analogous to an electrical rectifier, a thermal rectifier (TR) can ensure that heat flows in a preferential direction. In this paper, thermal transport nonlinearity is achieved through the development of a phase-change based TR comprising an enclosed vapor chamber having separated nanostructured copper oxide superhydrophobic and superhydrophilic functional surfaces. In the forward direction, heat transfer is facilitated through evaporation on the superhydrophilic surface and self-propelled jumping-droplet condensation on the superhydrophobic surface. In the reverse direction, heat transfer is minimized due to condensate film formation within the superhydrophilic condenser and inability to return the condensed liquid to the superhydrophobic evaporator. We examine the coupled effects of gap size, coolant mass, heat transfer rate, and applied electric field on the thermal performance of the TR. A maximum thermal diodicity, defined as the ratio of forward to reverse heat transfer, of 39 is achieved.

Quantum bath effects on nonequilibrium heat transport in model molecular junctions

Quantum-classical dynamics simulations enable the study of nonequilibrium heat transport in realistic models of molecules coupled to thermal baths. In these simulations, the initial conditions of the bath degrees of freedom are typically sampled from classical distributions. Herein, we investigate the effects of sampling the initial conditions of the thermal baths from quantum and classical distributions on the steady-state heat current in the nonequilibrium spin-boson model-a prototypical model of a single-molecule junction-in different parameter regimes. For a broad range of parameter regimes considered, we find that the steady-state heat currents are ∼1.3-4.5 times larger with the classical bath sampling than with the quantum bath sampling. Using both types of sampling, the steady-state heat currents exhibit turnovers as a function of the bath reorganization energy, with sharper turnovers in the classical case than in the quantum case and different temperature dependencies of the turnover maxima. As the temperature gap between the hot and cold baths increases, we observe an increasing difference in the steady-state heat currents obtained with the classical and quantum bath sampling. In general, as the bath temperatures are increased, the differences between the results of the classical and quantum bath sampling decrease but remain non-negligible at the high bath temperatures. The differences are attributed to the more pronounced temperature dependence of the classical distribution compared to the quantum one. Moreover, we find that the steady-state fluctuation theorem only holds for this model in the Markovian regime when quantum bath sampling is used. Altogether, our results highlight the importance of quantum bath sampling in quantum-classical dynamics simulations of quantum heat transport.

Thermoelectric properties of a double-dot system in serial configuration within the Coulomb blockade regime

In the present work, we theoretically study thermoelectric transport and heat transfer in a junction including a double quantum dot in a serial configuration coupled to nonferromagnetic electrodes. We focus on the electron transport within the Coulomb blockade regime in the limit of strong intradot interactions between electrons. It is shown that under these conditions, characteristics of thermoelectric transport in such systems strongly depend on electron occupation on the dots and on interdot Coulomb interactions. We demonstrate that these factors may lead to a heat current rectification and analyze potentialities of a double-dot in a serial configuration as a heat diod.

Shot Noise of a Temperature-Biased Tunnel Junction

We report the measurement of the current noise of a tunnel junction driven out of equilibrium by a temperature and/or voltage difference, i.e., the charge noise of heat and/or electrical current. This is achieved by a careful control of electron temperature below 1 K at the nanoscale, and a sensitive measurement of noise with wide bandwidth, from 0.1 to 1 GHz. An excellent agreement between experiment and theory with no fitting parameter is obtained. In particular, we find that the current noise of the junction of resistance R when one electrode is at temperature T and the other one at zero temperature is given by S=2 ln2k_{B}T/R.

Nonreciprocal thermal transport in a multiferroic helimagnet

Breaking of spatial inversion symmetry induces unique phenomena in condensed matter. In particular, by combining this symmetry with magnetic fields or another type of time-reversal symmetry breaking, noncentrosymmetric materials can be made to exhibit nonreciprocal responses, which are responses that differ for rightward and leftward stimuli. However, the effect of spatial inversion symmetry breaking on thermal transport in uniform media remains to be elucidated. Here, we show nonreciprocal thermal transport in the multiferroic helimagnet TbMnO₃ The longitudinal thermal conductivity depends on whether the thermal current is parallel or antiparallel to the vector product of the electric polarization and magnetization. This phenomenon is thermal rectification that is controllable with external fields in a uniform crystal. This discovery may pave the way to thermal diodes with controllability and scalability.

Quantifying the quantum heat contribution from a driven superconducting circuit

Heat flow management at the nanoscale is of great importance for emergent quantum technologies. For instance, a thermal sink that can be activated on-demand is a highly desirable tool that may accommodate the need to evacuate excess heat at chosen times, e.g., to maintain cryogenic temperatures or reset a quantum system to ground, and the possibility of controlled unitary evolution otherwise. Here we propose a design of such heat switch based on a single coherently driven qubit. We show that the heat flow provided by a hot source to the qubit can be switched on and off by varying external parameters, the frequency and the intensity of the driving. The complete suppression of the heat flow is a quantum effect occurring for specific driving parameters that we express and we analyze the role of the coherences in the free-qubit energy eigenbasis. We finally study the feasibility of this quantum heat switch in a circuit QED setup involving a charge qubit coupled to thermal resistances. We demonstrate robustness to experimental imperfections such as additional decoherence, paving the road towards experimental verification of this effect.

Method to characterize a thermal diode in saturated steam atmosphere

We present a novel measurement method for the characterization of thermal diodes in a saturated steam atmosphere. A measuring setup has been developed in which two pressure sensors are integrated. Using a developed analytical model, the heat flow, the volume flow, and the cracking pressure are determined from the measured absolute pressures and the pressure difference. The analytical model was verified using a flow through an orifice. We first calculated the volume flow through the orifice, with a diameter of 3 mm, using the Reader-Harris equation and then compared it to experimentally determined values. The experimentally determined values showed a discrepancy of 9%. With the measurement setup, we have characterized a check valve developed for magnetocaloric heat pumps, which has a thermally rectifying behavior. The developed check valve consists of three spring arms, which are radially attached to a valve disk. The heat flow through the check valve in the forward direction is 166 W for water, 239 W for ethanol, and 547 W for methanol at a temperature difference of 1 K. In the reverse direction, the heat flow is -0.03 W at a temperature difference of -1 K. For methanol, this corresponds to a rectification coefficient of more than 18 000.

Charge and heat current rectification by a double-dot system within the Coulomb blockade regime

Nanoscale rectifiers are known to have significant nanoelectronic and nanoheatronic applications. In the present work we theoretically analyze rectifying properties of a junction including a couple of quantum dots asymmetrically coupled to the electrodes. The charge and heat current rectification in the system is controlled by the dots occupation numbers and interdot Coulomb interactions. We examine the dependencies of the rectification ratio on the electron energy levels on the dots, on the intensity of electron-electron interactions, on the gate and bias voltages and on the thermal gradients applied across the system. It is shown that the considered double-dot system possesses significant potentialities as a common as well as a heat diode.

Heat-flow allocator based on a triple quantum dot

We theoretically propose a simple setup based on a three-terminal triple quantum dot in the Coulomb blockade regime as a heat-flow allocator to spatially separate heat flow along two different channels at arbitrary proportion. We show that a constant output heat-flow ratio can be obtained in a wide range of system parameters, and any ratio of the output heat flow, whether it is an integer ratio or a fractional ratio, can be obtained by directly adjusting the ratio of the energy-dependent tunneling rate.

Theoretical Paradigm for Thermal Rectification via Phonon Filtering and Spectral Confinement

Significant thermal rectification has the potential to revolutionize approaches to controlled heat flow and enable breakthrough technologies such as phononic computing. We demonstrate a framework based on phonon population confinement and filtering that has potential to reach rectifications that are an order of magnitude larger than previous literature. With the use of a straightforward modification of the phonon gas model, we illustrate theoretical thermal rectification in a thin film of diamond (1-10 nm) graded to dimensions >1  μm of between 25% and 250%. Utilizing this mechanism for thermal rectification sets the stage for significant development in thermal devices.

Nonequilibrium heat transport in a molecular junction: A mixed quantum-classical approach

In a recent study [J. Liu et al., J. Chem. Phys. 149, 224104 (2018)], we developed a general mixed quantum-classical framework for studying heat transport through molecular junctions, in which the junction molecule is treated quantum mechanically and the thermal reservoirs to which the molecule is coupled are treated classically. This framework yields expressions for the transferred heat and steady-state heat current, which could be calculated using a variety of mixed quantum-classical dynamics methods. In this work, we use the recently developed "Deterministic Evolution of Coordinates with Initial Decoupled Equations" (DECIDE) method for calculating the steady-state heat current in the nonequilibrium spin-boson model in a variety of parameter regimes. Our results are compared and contrasted with those obtained using the numerically exact multilayer multiconfiguration time-dependent Hartree approach, and using approximate methods, including mean field theory, Redfield theory, and adiabatic mixed quantum-classical dynamics. Despite some quantitative differences, the DECIDE method performs quite well, is capable of capturing the expected trends in the steady-state heat current, and, overall, outperforms the approximate methods. These results hold promise for DECIDE simulations of nonequilibrium heat transport in realistic models of nanoscale systems.

Thermal rectification and heat amplification in a nonequilibrium V-type three-level system

Thermal rectification and heat amplification are investigated in a nonequilibrium V-type three-level system with quantum interference. By applying the Redfield master equation combined with full counting statistics, we analyze the steady-state heat transport. The noise-induced interference is found to be able to rectify the heat current, which paves a new way to design quantum thermal rectifier. Within the three-reservoir setup, the heat amplification is clearly identified far from equilibrium, which is in absence of the negative differential thermal conductance.

Heat flowing from cold to hot without external intervention by using a "thermal inductor"

The cooling of boiling water all the way down to freezing, by thermally connecting it to a thermal bath held at ambient temperature without external intervention, would be quite unexpected. We describe the equivalent of a "thermal inductor," composed of a Peltier element and an electric inductance, which can drive the temperature difference between two bodies to change sign by imposing inertia on the heat flowing between them, and enable continuing heat transfer from the chilling body to its warmer counterpart without the need of an external driving force. We demonstrate its operation in an experiment and show that the process can pass through a series of quasi-equilibrium states while fully complying with the second law of thermodynamics. This thermal inductor extends the analogy between electrical and thermal circuits and could serve, with further progress in thermoelectric materials, to cool hot materials well below ambient temperature without external energy supplies or moving parts.

Heat current rectification in segmented XXZ chains

We study the rectification of heat current in an XXZ chain segmented in two parts. We model the effect of the environment with Lindblad heat baths. We show that in our system, rectification is large for strong interactions in half of the chain and if one bath is at a cold enough temperature. For the numerically accessible chain lengths, we observe that the rectification increases with the system size. We gain insight into the rectification mechanism by studying two-time correlations in the steady state. The presence of interactions also induces a strong nonlinear response to the temperature difference, resulting in superlinear and negative differential conductance regimes.

Transport and Energetic Properties of a Ring of Interacting Spins Coupled to Heat Baths

We study the heat and spin transport properties in a ring of interacting spins coupled to heat baths at different temperatures. We show that interactions, by inducing avoided crossings, can be a means to tune both the total heat current flowing between the ring and the baths, and the way it flows through the system. In particular, we recognize three regimes in which the heat current flows clockwise, counterclockwise, and in parallel. The temperature bias between the baths also induces a spin current within the ring, whose direction and magnitude can be tuned by the interaction. Lastly, we show how the ergotropy of the nonequilibrium steady state can increase significantly near the avoided crossings.

A Brief Review on the Recent Experimental Advances in Thermal Rectification at the Nanoscale

The concept of thermal rectification was put forward decades ago. It is a phenomenon in which the heat flux along one direction varies as the sign of temperature gradient changes. In bulk materials, thermal rectification has been realized at contact interfaces by manufacturing asymmetric effective contact areas, electron transport, temperature dependence of thermal conductivity and so on. The mechanism of thermal rectification has been studied intensively by using both experimental and theoretical methods. In recent years, with the rapid development of nanoscience and technology, the active control and management of heat transport at the nanoscale has become an important task and has attracted much attention. As the most fundamental component, the development and utilization of a nanothermal rectifier is the key technology. Although many research papers have been published in this field, due to the significant challenge in manufacturing asymmetric nanostructures, most of the publications are focused on molecular dynamics simulation and theoretical analysis. Great effort is urgently required in the experimental realization of thermal rectification at the nanoscale, laying a solid foundation for computation and theoretical modeling. The aim of this brief review is to introduce the most recent experimental advances in thermal rectification at the nanoscale and discuss the physical mechanisms. The new nanotechnology and method can be used to improve our ability to further design and produce efficient thermal devices with a high rectification ratio.

The effect of structural asymmetry on thermal rectification in nanostructures

Three SWCNT-graphene nanostructure-based models are designed to probe the thermal rectification caused by the structural asymmetry in the boundary thermal contacts, the device, and the whole system, respectively. We find that both the asymmetry of entire system and the asymmetry of the device are not necessary condition for the existence of thermal rectification, and the asymmetry in boundary thermal contacts is more important than the asymmetry in device toward determining both the magnitude and the direction of thermal rectification. Interestingly, notable thermal rectification can exist in the systems with overall structural symmetry when the boundary thermal contacts are structurally asymmetric. Moreover, nanostructures with a structurally symmetric device and structurally asymmetric boundary thermal contacts can still display significant thermal rectification. These findings could offer insight into the future design and performance improvement of nanostructured thermal rectifiers.

Phase-coherent solitonic Josephson heat oscillator

Since its recent foundation, phase-coherent caloritronics has sparkled continuous interest giving rise to numerous concrete applications. This research field deals with the coherent manipulation of heat currents in mesoscopic superconducting devices by mastering the Josephson phase difference. Here, we introduce a new generation of devices for fast caloritronics able to control local heat power and temperature through manipulation of Josephson vortices, i.e., solitons. Although most salient features concerning Josephson vortices in long Josephson junctions were comprehensively hitherto explored, little is known about soliton-sustained coherent thermal transport. We demonstrate that the soliton configuration determines the temperature profile in the junction, so that, in correspondence of each magnetically induced soliton, both the flowing thermal power and the temperature significantly enhance. Finally, we thoroughly discuss a fast solitonic Josephson heat oscillator, whose frequency is in tune with the oscillation frequency of the magnetic drive. Notably, the proposed heat oscillator can effectively find application as a tunable thermal source for nanoscale heat engines and coherent thermal machines.

Phase-Tunable Josephson Thermal Router

A fundamental aspect of electronics is the ability to distribute a charge current among different terminals. On the other hand, despite the great interest in dissipation, storage, and conversion of heat in solid state structures, the control of thermal currents at the nanoscale is still in its infancy. Here, we show the experimental realization of a phase-tunable thermal router able to control the spatial distribution of an incoming heat current, thus providing the possibility of tuning the electronic temperatures of two output terminals. This ability is obtained thanks to a direct current superconducting quantum interference device (dc SQUID), which can tune the coherent component of the electronic heat currents flowing through its Josephson junctions. By varying the external magnetic flux and the bath temperature, the SQUID allows us to regulate the size and the direction of the thermal gradient between two drain electrodes. Our results offer new opportunities for all microcircuits requiring an accurate energy management, including electronic coolers, quantum information architectures, and thermal logic components.

Efficient thermal diode with ballistic spacer

Thermal rectification is of importance not only for fundamental physics, but also for potential applications in thermal manipulations and thermal management. However, thermal rectification effect usually decays rapidly with system size. Here, we show that a mass-graded system, with two diffusive leads separated by a ballistic spacer, can exhibit large thermal rectification effect, with the rectification factor independent of system size. The underlying mechanism is explained in terms of the effective size-independent thermal gradient and the match or mismatch of the phonon bands. We also show the robustness of the thermal diode upon variation of the model's parameters. Our finding suggests a promising way for designing realistic efficient thermal diodes.

Phase-driven charge manipulation in Hybrid Single-Electron Transistor

Phase-tunable hybrid devices, built upon nanostructures combining normal metal and superconductors, have been the subject of intense studies due to their numerous combinations of different charge and heat transport configurations. They exhibit solid applications in quantum metrology and coherent caloritronics. Here we propose and realize a new kind of hybrid device with potential application in single charge manipulation and quantized current generation. We show that by tuning superconductivity on two proximized nanowires, coupled via a Coulombic normal-metal island, we are able to control its charge state configuration. This device supports a one-control-parameter cycle being actuated by the sole magnetic flux. In a voltage biased regime, the phase-tunable superconducting gaps can act as energy barriers for charge quanta leading to an additional degree of freedom in single electronics. The resulting configuration is fully electrostatic and the current across the device is governed by the quasiparticle populations in the source and drain leads. Notably, the proposed device can be realized using standard nanotechniques opening the possibility to a straightforward coupling with the nowadays well developed superconducting electronics.

Towards phase-coherent caloritronics in superconducting circuits

The emerging field of phase-coherent caloritronics (from the Latin word calor, heat) is based on the possibility of controlling heat currents by using the phase difference of the superconducting order parameter. The goal is to design and implement thermal devices that can control energy transfer with a degree of accuracy approaching that reached for charge transport by contemporary electronic components. This can be done by making use of the macroscopic quantum coherence intrinsic to superconducting condensates, which manifests itself through the Josephson effect and the proximity effect. Here, we review recent experimental results obtained in the realization of heat interferometers and thermal rectifiers, and discuss a few proposals for exotic nonlinear phase-coherent caloritronic devices, such as thermal transistors, solid-state memories, phase-coherent heat splitters, microwave refrigerators, thermal engines and heat valves. Besides being attractive from the fundamental physics point of view, these systems are expected to have a vast impact on many cryogenic microcircuits requiring energy management, and possibly lay the first stone for the foundation of electronic thermal logic.

Thermal rectification at the bimaterial nanocontact interface

Thermal rectification can help develop modern thermal manipulation devices but has been rarely engineered. Here, we validated the nanoscale bimaterial interface-induced thermal rectification experimentally for the first time and investigated its underlying mechanism via molecular dynamics simulations. The thermal diode consists of polyamide (PA) and silicon (Si) nanowires in contact with each other. The thermal rectification ratio measured by a high-precision nanoscale experiment reached 4% with an uncertainty of <1%. The temperature has little influence on the ratio, while the decrease in contact length or increase in temperature differences can increase the ratio. The molecular dynamics simulations further confirmed the thermal rectification in the PA/Si nanowires. We found that the localized modes generally gather on the edge, and the higher extent of phonon localization is responsible for the lower thermal conductance in the thermal rectification. Our findings not only have guiding significance, but can also promote the development of interface-based solid-state thermal diodes.

High Contrast Far-Field Radiative Thermal Diode

We propose a theoretical concept of a far-field radiative thermal rectification device that uses a phase change material to achieve a high degree of asymmetry in radiative heat transfer. The proposed device has a multilayer structure on one side and a blackbody on other side. The multilayer structure consists of transparent thin film of KBr sandwiched between a thin film of VO₂ and a reflecting layer of gold. When VO₂ is in its insulating phase, the structure is highly reflective due to the two transparent layers on highly reflective gold. When VO₂ is in the metallic phase, Fabry-Perot type of resonance occurs and the tri-layer structure acts like a wide-angle antireflection coating achieved by destructive interference of partially reflected waves making it highly absorptive for majority of spectral range of thermal radiation. The proposed structure forms the active part of configuration that acts like a far-field radiative thermal diode. Thermal rectification greater than 11 is obtained for a temperature bias of 20 K, which is the highest rectification ever predicted for far-field radiative diode configurations.

0-π phase-controllable thermal Josephson junction

Two superconductors coupled by a weak link support an equilibrium Josephson electrical current that depends on the phase difference ϕ between the superconducting condensates. Yet, when a temperature gradient is imposed across the junction, the Josephson effect manifests itself through a coherent component of the heat current that flows opposite to the thermal gradient for |ϕ| < π/2 (refs 2-4). The direction of both the Josephson charge and heat currents can be inverted by adding a π shift to ϕ. In the static electrical case, this effect has been obtained in a few systems, for example via a ferromagnetic coupling or a non-equilibrium distribution in the weak link. These structures opened new possibilities for superconducting quantum logic and ultralow-power superconducting computers. Here, we report the first experimental realization of a thermal Josephson junction whose phase bias can be controlled from 0 to π. This is obtained thanks to a superconducting quantum interferometer that allows full control of the direction of the coherent energy transfer through the junction. This possibility, in conjunction with the completely superconducting nature of our system, provides temperature modulations with an unprecedented amplitude of ∼100 mK and transfer coefficients exceeding 1 K per flux quantum at 25 mK. Then, this quantum structure represents a fundamental step towards the realization of caloritronic logic components such as thermal transistors, switches and memory devices. These elements, combined with heat interferometers and diodes, would complete the thermal conversion of the most important phase-coherent electronic devices and benefit cryogenic microcircuits requiring energy management, such as quantum computing architectures and radiation sensors.

High Temperature Near-Field NanoThermoMechanical Rectification

Limited performance and reliability of electronic devices at extreme temperatures, intensive electromagnetic fields, and radiation found in space exploration missions (i.e., Venus &Jupiter planetary exploration, and heliophysics missions) and earth-based applications requires the development of alternative computing technologies. In the pursuit of alternative technologies, research efforts have looked into developing thermal memory and logic devices that use heat instead of electricity to perform computations. However, most of the proposed technologies operate at room or cryogenic temperatures, due to their dependence on material's temperature-dependent properties. Here in this research, we show experimentally-for the first time-the use of near-field thermal radiation (NFTR) to achieve thermal rectification at high temperatures, which can be used to build high-temperature thermal diodes for performing logic operations in harsh environments. We achieved rectification through the coupling between NFTR and the size of a micro/nano gap separating two terminals, engineered to be a function of heat flow direction. We fabricated and tested a proof-of-concept NanoThermoMechanical device that has shown a maximum rectification of 10.9% at terminals' temperatures of 375 and 530 K. Experimentally, we operated the microdevice in temperatures as high as about 600 K, demonstrating this technology's suitability to operate at high temperatures.

Microscale solid-state thermal diodes enabling ambient temperature thermal circuits for energy applications

A micro-scale phase change thermal diode capable of ambient and solid-state operation is developed and incorporated into a thermal diode bridge circuit.

Temperature Trapping: Energy-Free Maintenance of Constant Temperatures as Ambient Temperature Gradients Change

It is crucial to maintain constant temperatures in an energy-efficient way. Here we establish a temperature-trapping theory for asymmetric phase-transition materials with thermally responsive thermal conductivities. Then we theoretically introduce and experimentally demonstrate a concept of an energy-free thermostat within ambient temperature gradients. The thermostat is capable of self-maintaining a desired constant temperature without the need of consuming energy even though the environmental temperature gradient varies in a large range. As a model application of the concept, we design and show a different type of thermal cloak that has a constant temperature inside its central region in spite of the changing ambient temperature gradient, which is in sharp contrast to all the existing thermal cloaks. This work has relevance to energy-saving heat preservation, and it provides guidance both for manipulating heat flow without energy consumption and for designing new metamaterials with temperature-responsive or field-responsive parameters in many disciplines such as thermotics, optics, electromagnetics, acoustics, mechanics, electrics, and magnetism.

Free-molecule heat transfer in a conservative force field between parallel surfaces

The heat flux between parallel surfaces is computed analytically assuming that heat is transferred by particles moving ballistically under the influence of a conservative force field. Particle reflection at the surfaces is governed by a Maxwell-type boundary condition. It is found that the force field can give rise to a substantial reduction, but also to an enhancement of the heat flux, depending on the ratio of the temperatures at the two surfaces. The influence of the accommodation coefficients is studied. An asymmetry introduced by the force field and/or the boundary conditions at the two surfaces causes a significant heat-flux rectification, characteristic for a thermal diode.

Nanoscale phase engineering of thermal transport with a Josephson heat modulator

Macroscopic quantum phase coherence has one of its pivotal expressions in the Josephson effect, which manifests itself both in charge and energy transport. The ability to master the amount of heat transferred through two tunnel-coupled superconductors by tuning their phase difference is the core of coherent caloritronics, and is expected to be a key tool in a number of nanoscience fields, including solid-state cooling, thermal isolation, radiation detection, quantum information and thermal logic. Here, we show the realization of the first balanced Josephson heat modulator designed to offer full control at the nanoscale over the phase-coherent component of thermal currents. Our device provides magnetic-flux-dependent temperature modulations up to 40 mK in amplitude with a maximum of the flux-to-temperature transfer coefficient reaching 200 mK per flux quantum at a bath temperature of 25 mK. Foremost, it demonstrates the exact correspondence in the phase engineering of charge and heat currents, breaking ground for advanced caloritronic nanodevices such as thermal splitters, heat pumps and time-dependent electronic engines.