Work Sum Rule for Open Quantum Systems

A key question in the thermodynamics of open quantum systems is how to partition thermodynamic quantities such as entropy, work, and internal energy between the system and its environment. We show that the only partition under which entropy is nonsingular is based on a partition of Hilbert space, which assigns half the system-environment coupling to the system and half to the environment. However, quantum work partitions nontrivially under Hilbert-space partition, and we derive a work sum rule that accounts for quantum work at a distance. All state functions of the system are shown to be path independent once this nonlocal quantum work is properly accounted for. Our results are illustrated with application to a driven resonant level strongly coupled to a reservoir.

The Metal-Insulator Transition in Vanadium Oxide Nanofilms Enables Microkelvin-Resolution Thermometry

High-resolution thermometry is critical for probing nanoscale energy transport. Here, we demonstrate how high-resolution thermometry can be accomplished using vanadium oxide (VOx), which features a sizable temperature-dependence of its resistance at room temperature and an even stronger dependence at its metal-insulator-transition (MIT) temperature. We microfabricate VOx nanofilm-based electrical resistance thermometers that undergo a metal-insulator-transition at ∼337 K and systematically quantify their temperature-dependent resistance, noise characteristics, and temperature resolution. We show that VOx sensors can achieve, in a bandwidth of ∼16 mHz, a temperature resolution of ∼5 μK at room temperature (∼300 K) and a temperature resolution of ∼1 μK at the MIT (∼337 K) when the amplitude of temperature perturbations is in the microkelvin range, which, in contrast to larger perturbations, is found to avoid hysteric resistance responses. These results demonstrate that VOx-based thermometers offer a ∼10-50-fold improvement in resolution over widely used Pt-based thermometers.

Long Propagating Polaritonic Heat Transfer: Shaping Radiation to Conduction

Surface phonon polaritons (SPhPs) originate from the coupling of mid-IR photons and optical phonons, generating evanescent waves along the polar dielectric surface. The emergence of SPhPs gives rise to a phase of quantum matter that facilitates long-range energy transfer (100s μm-scale). Albeit of the recent experimental progress to observe the enhanced thermal conductivity of polar dielectric nanostructures mediated by SPhPs, the potential mechanism to present the high thermal conductivity beyond the Landauer limit has not been addressed. Here, we revisit the comprehensive theoretical framework to unify the distinct pictures of two heat transfer mechanisms by conduction and radiation. We first designed our experimental platform to distinguish contributions of two distinct fundamental modes of SPhPs, resulting in far-field radiation and long propagating conduction, respectively, by tuning the configuration of a nanostructured heat channel integrated into the thermometer. We could effectively control the transmission of long-propagating SPhPs to influence the apparent thermal conductivity of the nanostructure. This study reveals the high thermal conductance of 1.63 nW/K by a fast SPhP mode comparable to that by classical phonons, with measurements showing apparent conductivity values of up to 2 W/m·K at 515 K. The origin of the enhanced thermal conductivity was exploited by observing the interference of dispersive evanescent waves by double heat channels. Furthermore, our experimental observations of length-dependent thermal conductance by SPhPs are in good agreement with the revisited Landauer formula to illustrate a polaritonic mode of heat conduction, considering the dispersive nature of radiation not limited to the physical boundaries of a solid object yet directionally guided along the surface.

Testing the Minimum System Entropy and the Quantum of Entropy

Experimental and theoretical results about entropy limits for macroscopic and single-particle systems are reviewed. All experiments confirm the minimum system entropy S⩾kln2. We clarify in which cases it is possible to speak about a minimum system entropykln2 and in which cases about a quantum of entropy. Conceptual tensions with the third law of thermodynamics, with the additivity of entropy, with statistical calculations, and with entropy production are resolved. Black hole entropy is surveyed. Claims for smaller system entropy values are shown to contradict the requirement of observability, which, as possibly argued for the first time here, also implies the minimum system entropy kln2. The uncertainty relations involving the Boltzmann constant and the possibility of deriving thermodynamics from the existence of minimum system entropy enable one to speak about a general principle that is valid across nature.

The phonon quantum of thermal conductance: Are simulations and measurements estimating the same quantity?

The thermal conductance quantum is a fundamental quantity in quantum transport theory. However, two decades after its first reported measurements and calculations for phonons in suspended nanostructures, reconciling experiments and theory remains elusive. Our massively parallel calculations of phonon transport in micrometer-sized three-dimensional structures suggest that part of the disagreement between theory and experiment stems from the inadequacy of macroscopic concepts to analyze the data. The computed local temperature distribution in the wave ballistic nonequilibrium regime shows that the spatial placement and dimensions of thermometers, heaters, and supporting microbeams in the suspended structures can noticeably affect the thermal conductance's measured values. In addition, diffusive transport assumptions made in the data analysis may result in measured values that considerably differ from the actual thermal conductance of the structure. These results urge for experimental validation of the suitability of diffusive transport assumptions in measuring devices operating at sub-kelvin temperatures.

Quantum bath augmented stochastic nonequilibrium atomistic simulations for molecular heat conduction

Classical molecular dynamics (MD) has been shown to be effective in simulating heat conduction in certain molecular junctions since it inherently takes into account some essential methodological components which are lacking in the quantum Landauer-type transport model, such as many-body full force-field interactions, anharmonicity effects and nonlinear responses for large temperature biases. However, the classical MD reaches its limit in the environments where the quantum effects are significant (e.g. with low-temperatures substrates, presence of extremely high frequency molecular modes). Here, we present an atomistic simulation methodology for molecular heat conduction that incorporates the quantum Bose-Einstein statistics into an "effective temperature" in the form of a modified Langevin equation. We show that the results from such a quasi-classical effective temperature MD method deviates drastically when the baths temperature approaches zero from classical MD simulations and the results converge to the classical ones when the bath approaches the high-temperature limit, which makes the method suitable for full temperature range. In addition, we show that our quasi-classical thermal transport method can be used to model the conducting substrate layout and molecular composition (e.g. anharmonicities, high-frequency modes). Anharmonic models are explicitly simulated via the Morse potential and compared to pure harmonic interactions to show the effects of anharmonicities under quantum colored bath setups. Finally, the chain length dependence of heat conduction is examined for one-dimensional polymer chains placed in between quantum augmented baths.

Resonant transport in a highly conducting single molecular junction via metal-metal covalent bond

Achieving highly transmitting molecular junctions through resonant transport at low bias is key to the next-generation low-power molecular devices. Although resonant transport in molecular junctions was observed by connecting a molecule between the metal electrodes via chemical anchors by applying a high source-drain bias (>1 V), the conductance was limited to <0.1G0, G0 being the quantum of conductance. Herein, we report electronic transport measurements by directly connecting a ferrocene molecule between Au electrodes under ambient conditions in a mechanically controllable break junction setup (MCBJ), revealing a conductance peak at ∼0.2G0 in the conductance histogram. A similar experiment was repeated for ferrocene terminated with amine (-NH2) and cyano (-CN) anchors, where conductance histograms exhibit an extended low conductance feature, including the sharp high conductance peak, similar to pristine ferrocene. The statistical analysis of the data and density functional theory-based transport calculation suggest a possible molecular conformation with a strong hybridization between the Au electrodes, and that the Fe atom of ferrocene is responsible for a near-perfect transmission in the vicinity of the Fermi energy, leading to the resonant transport at a small applied bias (<0.5 V). Moreover, calculations including van der Waals/dispersion corrections reveal a covalent-like organometallic bonding between Au and the central Fe atom of ferrocene, having bond energies of ∼660 meV. Overall, our study not only demonstrates the realization of an air-stable highly transmitting molecular junction, but also provides important insights about the nature of chemical bonding at the metal/organo-metallic interface.

Molecular Electronics: Creating and Bridging Molecular Junctions and Promoting Its Commercialization

Molecular electronics is driven by the dream of expanding Moore's law to the molecular level for next-generation electronics through incorporating individual or ensemble molecules into electronic circuits. For nearly 50 years, numerous efforts have been made to explore the intrinsic properties of molecules and develop diverse fascinating molecular electronic devices with the desired functionalities. The flourishing of molecular electronics is inseparable from the development of various elegant methodologies for creating nanogap electrodes and bridging the nanogap with molecules. This review first focuses on the techniques for making lateral and vertical nanogap electrodes by breaking, narrowing, and fixed modes, and highlights their capabilities, applications, merits, and shortcomings. After summarizing the approaches of growing single molecules or molecular layers on the electrodes, the methods of constructing a complete molecular circuit are comprehensively grouped into three categories: 1) directly bridging one-molecule-electrode component with another electrode, 2) physically bridging two-molecule-electrode components, and 3) chemically bridging two-molecule-electrode components. Finally, the current state of molecular circuit integration and commercialization is discussed and perspectives are provided, hoping to encourage the community to accelerate the realization of fully scalable molecular electronics for a new era of integrated microsystems and applications.

The Stiffest and Strongest Predicted Material: C2 N Atomic Chains Approach the Theoretical Limits

Though linear atomic chains exhibit extreme properties, it is presently unclear how these properties can be maximized by the choice of elemental composition. Considering that boron, carbon, and nitrogen can form high modulus and high strength atomic chains, here an algorithm is developed to construct 143 possible atomic chains of these elements with 6 or fewer atoms in the primitive cell and explore their stabilities and mechanical properties by first-principles calculations. It is found that the gravimetric modulus (1032 GPa g^-1 cm³ ) and strength (108 GPa g^-1 cm³ ) of the C₂ N chain significantly exceed those of any known material, including the previously stiffest predicted material (C chain, 945 GPa g^-1 cm³ ) and the previously strongest predicted material (BC chain, 92 GPa g^-1 cm³ ), and also approach the theoretical limits of gravimetric modulus (1036 GPa g^-1 cm³ ) and strength (130 GPa g^-1 cm³ ). Mechanistic analyses demonstrate that the higher gravimetric modulus and strength of the C₂ N chain, compared with the C and BC chains, originate from its short, stiff chemical bonding and the abnormal decrease in bond length alternation under tension. The likely ease of fabrication and potential synthesis routes for C₂ N chains are discussed.

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.

Magnetic control over the fundamental structure of atomic wires

When reducing the size of materials towards the nanoscale, magnetic properties can emerge due to structural variations. Here, we show the reverse effect, where the structure of nanomaterials is controlled by magnetic manipulations. Using the break-junction technique, we find that the interatomic distance in platinum atomic wires is shorter or longer by up to ∼20%, when a magnetic field is applied parallel or perpendicular to the wires during their formation, respectively. The magnetic field direction also affects the wire length, where longer (shorter) wires are formed under a parallel (perpendicular) field. Our experimental analysis, supported by calculations, indicates that the direction of the applied magnetic field promotes the formation of suspended atomic wires with a specific magnetization orientation associated with typical orbital characteristics, interatomic distance, and stability. A similar effect is found for various metal and metal-oxide atomic wires, demonstrating that magnetic fields can control the atomistic structure of different nanomaterials when applied during their formation stage.

Magnetic effects can emerge due to structural variations when the size of materials is reduced towards the nanoscale. Here, Chakrabarti et al demonstrates the opposite effect, showing that the interatomic distance in atomic wires changes by up to 20% depending on the orientation of an applied magnetic field.

Understanding the rheology of nanocontacts

Mechanical stiffness, as opposed to softness, is a fundamental property of solids. Its persistence or rheological evolution in vibrating solid-solid nanocontacts is important in physics, materials science and technology. A puzzling apparent liquefaction under oscillatory strain, totally unexpected at room temperature, was suggested by recent experiments on solid gold nano-junctions. Here we show theoretically that realistically simulated nanocontacts actually remain crystalline even under large oscillatory strains. Tensile and compressive slips, respectively of “necking” and “bellying” types, do take place, but recover reversibly even during fast oscillatory cycles. We also show that, counterintuitively, the residual stress remains tensile after both slips, driving the averaged stiffness from positive to negative, thus superficially mimicking a liquid’s. Unlike a liquid, however, rheological softening occurs by stick-slip, predicting largely frequency independent stiffness with violent noise in stress and conductance, properties compatible with experiments. The baffling large amplitude rheology of gold nanocontacts and its consequences should apply, with different parameters, to many other metals.

The rigidity of solid nanocontacts formed when metals touch is apparently lost liquidlike under large mechanical oscillations. As we show theoretically, there is no melting but oscillated nanocontacts undergo a remarkable reversible stick-slip rheology.

Pico-Watt Scanning Thermal Microscopy for Thermal Energy Transport Investigation in Atomic Materials

The thermophysical properties at the nanoscale are key characteristics that determine the operation of nanoscale devices. Additionally, it is important to measure and verify the thermal transfer characteristics with a few nanometer or atomic-scale resolutions, as the nanomaterial research field has expanded with respect to the development of molecular and atomic-scale devices. Scanning thermal microscopy (SThM) is a well-known method for measuring the thermal transfer phenomena with the highest spatial resolution. However, considering the rapid development of atomic materials, the development of an ultra-sensitive SThM for measuring pico-watt (pW) level heat transfer is essential. In this study, to measure molecular- and atomic-scale phenomena, a pico-watt scanning thermal microscopy (pW-SThM) equipped with a calorimeter capable of measuring heat at the pW level was developed. The heat resolution of the pW-SThM was verified through an evaluation experiment, and it was confirmed that the temperature of the metal line heater sample could be quantitatively measured by using the pW-SThM. Finally, we demonstrated that pW-SThM detects ultra-small differences of local heat transfer that may arise due to differences in van der Waals interactions between the graphene sheets in highly ordered pyrolytic graphite. The pW-SThM probe is expected to significantly contribute to the discovery of new heat and energy transfer phenomena in nanodevices and two-dimensional materials that have been inaccessible through experiments.

Nonequilibrium Green's function method for phonon heat transport in quantum system

Phonon heat transport property in quantum devices is of great interesting since it presents significant quantum behaviors. In the past few decades, great efforts have been devoted to establish the theoretical method for phonon heat transport simulation in nanostructures. However, modeling phonon heat transport from wavelike coherent regime to particlelike incoherent regime remains a challenging task. The widely adopted theoretical approach, such as molecular dynamics, semiclassical Boltzmann transport equation, captures quantum mechanical effects within different degrees of approximation. Among them, Non-equilibrium Green's function (NEGF) method has attracted wide attention, as its ability to perform full quantum simulation including many-body interactions. In this review, we summarized recent theoretical advances of phonon NEGF method and the applications on the numerical simulation for phonon heat transport in nanostructures. At last, the challenges of numerical simulation are discussed.

Structural Asymmetry of Metallic Single-Atom Contacts Detected by Current-Voltage Characteristics

The complex behavior of the simplest atomic-scale conductors indicates that the electrode structure itself is significant in the design of future nanoscale devices. In this study, the structural asymmetry of metallic atomic contacts formed between two macroscopic Au electrodes at room temperature was investigated. Characteristic signatures of the structural asymmetries were detected by fast current-voltage (I-V) measurements with a time resolution of approximately 100 μs. Statistical analysis of more than 300,000 I-V curves obtained from more than 1000 contact-stretching processes demonstrates that the current rectification properties are correlated with the conductance of the nanocontacts. A substantial suppression of the variation in current rectification was observed for the atomic contacts with integer multiples of the conductance quantum. Statistical analysis of the time-resolved I-V curves revealed that the current rectification variations increased significantly from 500 μs onward before the breakage of the atomic contacts. Ab initio atomistic simulations of the stretching processes and corresponding I-V characteristics confirmed the magnitude of the rectification and related it to the structural asymmetries in the breakdown process of the junctions. Overall, we provide a better understanding of the interplay between geometric and electronic structures at atomically defined metal-metal interfaces by probing charge transport properties in extremely sensitive nanocontacts.

Electronic thermal transport measurement in low-dimensional materials with graphene non-local noise thermometry

In low-dimensional systems, the combination of reduced dimensionality, strong interactions and topology has led to a growing number of many-body quantum phenomena. Thermal transport, which is sensitive to all energy-carrying degrees of freedom, provides a discriminating probe of emergent excitations in quantum materials and devices. However, thermal transport measurements in low dimensions are dominated by the phonon contribution of the lattice, requiring an experimental approach to isolate the electronic thermal conductance. Here we measured non-local voltage fluctuations in a multi-terminal device to reveal the electronic heat transported across a mesoscopic bridge made of low-dimensional materials. Using two-dimensional graphene as a noise thermometer, we measured the quantitative electronic thermal conductance of graphene and carbon nanotubes up to 70 K, achieving a precision of ~1% of the thermal conductance quantum at 5 K. Employing linear and nonlinear thermal transport, we observed signatures of energy transport mediated by long-range interactions in one-dimensional electron systems, in agreement with a theoretical model.

Thermoelectric Polarization Transport in Ferroelectric Ballistic Point Contacts

We formulate a scattering theory of polarization and heat transport through a ballistic ferroelectric point contact. We predict a polarization current under either an electric field or a temperature difference that depends strongly on the direction of the ferroelectric order and can be detected by its magnetic stray field and associated thermovoltage and Peltier effect.

Quantum Confinement Suppressing Electronic Heat Flow below the Wiedemann-Franz Law

The Wiedemann-Franz law states that the charge conductance and the electronic contribution to the heat conductance are proportional. This sets stringent constraints on efficiency bounds for thermoelectric applications, which seek a large charge conduction in response to a small heat flow. We present experiments based on a quantum dot formed inside a semiconducting InAs nanowire transistor, in which the heat conduction can be tuned significantly below the Wiedemann-Franz prediction. Comparison with scattering theory shows that this is caused by quantum confinement and the resulting energy-selective transport properties of the quantum dot. Our results open up perspectives for tailoring independently the heat and electrical conduction properties in semiconductor nanostructures.

Quantitative Mapping of Unmodulated Temperature Fields with Nanometer Resolution

Quantitative mapping of temperature fields with nanometric resolution is critical in various areas of scientific research and emerging technology, such as nanoelectronics, surface chemistry, plasmonic devices, and quantum systems. A key challenge in achieving quantitative thermal imaging with scanning thermal microscopy (SThM) is the lack of knowledge of the tip-sample thermal resistance (R_TS), which varies with local topography and is critical for quantifying the sample temperature. Recent advances in SThM have enabled simultaneous quantification of R_TS and topography in situations where the temperature field is modulated enabling quantitative thermometry even when topographical features cause significant variations in R_TS. However, such an approach is not applicable to situations where the temperature modulation of the device is not readily possible. Here we show, using custom-fabricated scanning thermal probes (STPs) with a sharp tip (radius ∼25 nm) and an integrated heater/thermometer, that one can quantitatively map unmodulated temperature fields, in a single scan, with ∼7 nm spatial resolution and ∼50 mK temperature resolution in a bandwidth of 1 Hz. This is accomplished by introducing a modulated heat input to the STP and measuring the AC and DC responses of the probe's temperature which allow for simultaneous mapping of the tip-sample thermal resistance and sample surface temperature. The approach presented here─contact resistance resolved scanning thermal microscopy (CR-SThM)─can greatly facilitate temperature mapping of a variety of microdevices under practical operating conditions.

Visualization of Thermal Transport Properties of Self-Assembled Monolayers on Au(111) by Contact and Noncontact Scanning Thermal Microscopy

Thermal transport properties of patterned binary self-assembled monolayers (SAMs) on Au(111) were examined using scanning thermal microscopy (SThM) with both contact and noncontact methods. We fabricated two-dimensional (2D) patterns with two separate domains of n-hexadecanethiol/benzenethiol, benzenethiol/n-butanethiol, or n-hexadecanethiol/n-butanethiol. In the experimental setup, the efficiency of thermal transport from a SThM tip to the SAM surface can be evaluated in terms of the temperature change at the SThM tip. In the contact regime, where a SThM tip physically contacts the SAM surface, direct thermal transport through the SAM and radiation-based thermal transport through the space where SAMs exist may contribute to a drop in temperature at the tip. In the noncontact regime, thermal transport relies on radiation-based heat dissipation from the heated tip to the SAMs. 2D mapping of the spatial temperature distribution on SAMs reflects the difference in thermal transport properties of the two SAM domains. We found that the contact method is effective for visualizing the temperature contrast, which reflects the thermal transport properties of the constituent molecules when the domains of the SAMs have a similar height, while the noncontact method allows visualization of the temperature distribution, which is related to the height of each domain of the SAMs, rather than the chemical structures of the constituent molecules. Combination of contact and noncontact SThM enables 2D imaging of thermal transport properties and topographic imaging simultaneously and represents a new technique for investigating the thermal properties of materials surfaces, which is essential for nanoscale thermal management.

High purity separation of n-pentane from neopentane using a nano-crystal of zeolite Y

A method for the separation of a mixture of n-pentane and neopentane using a nano-crystallite of zeolite Y is reported. This method judiciously combines two well-known, counter-intuitive phenomena, the levitation and the blowtorch effects. The result is that the two components are separated by being driven to the opposite ends of the zeolite column. The calculations are based on the non-equilibrium Monte Carlo method with moves from a region at one temperature to a region at another temperature. The necessary acceptance probability for such moves has been derived here on the basis of stationary solution of an inhomogeneous Fokker-Planck equation. Simulations have been carried out with a realistic and experimentally relevant Gaussian hot zone and also a square hot zone, both of which lead to very good separation. Simulations without the hot zones do not show any separation. The results are reported at a loading of 1 molecule per cage. The temperature of the hot zone is just ∼30 K higher than the ambient temperature. The separation factors of the order of 10¹⁷ are achieved using single crystals of zeolite, which are less than 1 μm long. The conditions for including the hot zone may be experimentally realizable in the future considering the rapid advances in nanoscale thermometry. The separation process is likely to be energetically more efficient by several orders of magnitude as compared to the existing methods of separation, making the method very green.

Observation of superdiffusive phonon transport in aligned atomic chains

Fascinating phenomena can occur as charge and/or energy carriers are confined in one dimension^1-4. One such example is the divergent thermal conductivity (κ) of one-dimensional lattices, even in the presence of anharmonic interatomic interactions-a direct consequence of the Fermi-Pasta-Ulam-Tsingou paradox proposed in 1955⁵. This length dependence of κ, also known as superdiffusive phonon transport, presents a classical anomaly of continued interest^6-9. So far the concept has remained purely theoretical, because isolated single atomic chains of sufficient length have been experimentally unattainable. Here we report on the observation of a length-dependent κ extending over 42.5 µm at room temperature for ultrathin van der Waals crystal NbSe₃ nanowires. We found that κ follows a 1/3 power law with wire length, which provides experimental evidence pointing towards superdiffusive phonon transport. Contrary to the classical size effect due to phonon-boundary scattering, the observed κ shows a 25-fold enhancement as the characteristic size of the nanowires decreases from 26 to 6.8 nm while displaying a normal-superdiffusive transition. Our analysis indicates that these intriguing observations stem from the transport of one-dimensional phonons excited as a result of elastic stiffening with a fivefold enhancement of Young's modulus. The persistent divergent trend of the observed thermal conductivity with sample length reveals a real possibility of creating novel van der Waals crystal-based thermal superconductors with κ values higher than those of any known materials.

Anomalous Hydrodynamics in a One-Dimensional Electronic Fluid

We construct multimode viscous hydrodynamics for one-dimensional spinless electrons. Depending on the scale, the fluid has six (shortest lengths), four (intermediate, exponentially broad regime), or three (asymptotically long scales) hydrodynamic modes. Interaction between hydrodynamic modes leads to anomalous scaling of physical observables and waves propagating in the fluid. In the four-mode regime, all modes are ballistic and acquire Kardar-Parisi-Zhang (KPZ)-like broadening with asymmetric power-law tails. "Heads" and "tails" of the waves contribute equally to thermal conductivity, leading to ω^{-1/3} scaling of its real part. In the three-mode regime, the system is in the universality class of a classical viscous fluid [O. Narayan and S. Ramaswamy, Anomalous Heat Conduction in One-Dimensional Momentum-Conserving Systems, Phys. Rev. Lett. 89, 200601 (2002).PRLTAO0031-900710.1103/PhysRevLett.89.200601, H. Spohn, Nonlinear fluctuating hydrodynamics for anharmonic chains, J. Stat. Phys. 154, 1191 (2014).JSTPBS0022-471510.1007/s10955-014-0933-y]. Self-interaction of the sound modes results in a KPZ-like shape, while the interaction with the heat mode results in asymmetric tails. The heat mode is governed by Levy flight distribution, whose power-law tails give rise to ω^{-1/3} scaling of heat conductivity.

Anomalous thermopower oscillations in graphene-nanowire vertical heterostructures

Thermoelectric measurements have the potential to uncover the density of states (DOSs) of low-dimensional materials. Here, we present the anomalous thermoelectric behavior of monolayer graphene-nanowire (NW) heterostructures, showing large oscillations as a function of the doping concentration. Our devices consist of InAs NW and graphene vertical heterostructures, which are electrically isolated by thin (∼10 nm) hexagonal boron nitride (hBN) layers. In contrast to conventional thermoelectric measurements, where a heater is placed on one side of a sample, we use the InAs NW (diameter ∼50 nm) as a local heater placed in the middle of the graphene channel. We measure the thermoelectric voltage induced in graphene due to Joule heating in the NW as a function of temperature (1.5-50 K) and carrier concentration. The thermoelectric voltage in bilayer graphene (BLG)-NW heterostructures shows sign change around the Dirac point, as predicted by Mott's formula. In contrast, the thermoelectric voltage measured across monolayer graphene (MLG)-NW heterostructures shows anomalous large-amplitude oscillations around the Dirac point, not seen in the Mott response derived from the electrical conductivity measured on the same device. The anomalous oscillations are a signature of the modified DOSs in MLG by the electrostatic potential of the NW, which is much weaker in the NW-BLG devices. Thermal calculations of the heterostructure stack show that the temperature gradient is dominant in the graphene region underneath the NW, and thus sensitive to the modified DOSs resulting in anomalous oscillations in the thermoelectric voltage. Furthermore, with the application of a magnetic field, we detect modifications in the DOSs due to the formation of Landau levels in both MLG and BLG.

Peculiar Atomic Bond Nature in Platinum Monatomic Chains

Metal atomic chains have been reported to change their electronic or magnetic properties by slight mechanical stimulus. However, the mechanical response has been veiled because of lack of information on the bond nature. Here, we clarify the bond nature in platinum (Pt) monatomic chains by our in situ transmission electron microscope method. The stiffness is measured with sub-N/m precision by quartz length-extension resonator. The bond stiffnesses at the middle of the chain and at the connection to the base are estimated to be 25 and 23 N/m, respectively, which are higher than the bulk counterpart. Interestingly, the bond length of 0.25 nm is found to be elastically stretched to 0.31 nm, corresponding to a 24% strain. Such peculiar bond nature could be explained by a novel concept of "string tension". This study is a milestone that will significantly change the way we think about atomic bonds in one-dimension.

Side-group-mediated thermoelectric properties of anthracene single-molecule junction with anchoring groups

Charge transfer characteristics of single-molecule junctions at the nanoscale, and consequently, their thermoelectric properties can be dramatically tuned by chemical or conformational modification of side groups or anchoring groups. In this study, we used density functional theory (DFT) combined with the non-equilibrium Green's function (NEGF) formalism in the linear response regime to examine the thermoelectric properties of a side-group-mediated anthracene molecule coupled to gold (Au) electrodes via anchoring groups. In order to provide a comparative inspection three different side groups, i.e. amine, nitro and methyl, in two different positions were considered for the functionalization of the molecule terminated with thiol or isocyanide anchoring groups. We showed that when the anchored molecule is perturbed with side group, the peaks of the transmission spectrum were shifted relative to the Fermi energy in comparison to the unperturbed molecule (i.e. without side group) leading to modified thermoelectric properties of the system. Particularly, in the thiol-terminated molecule the amine side group showed the greatest figure of merit in both positions which was suppressed by the change of side group position. However, in the isocyanide-terminated molecule the methyl side group attained the greatest thermoelectric efficiency where its magnitude was relatively robust to the change of side group position. In this way, different combinations of side groups and anchoring groups can improve or suppress thermopower and the figure of merit of the molecular junction depending on the interplay between charge donating/accepting nature of the functionals or their position.

Electron tunneling between vibrating atoms in a copper nano-filament

Nanowires, atomic point contacts, and chains of atoms are one-dimensional nanostructures, which display size-dependent quantum effects in electrical and thermal conductivity. In this work a Cu nanofilament of a defined resistance and formed between a Cu and Pt electrode is heated remotely in a controlled way. Depending on the robustness of the conductive filament and the amount of heat transferred several resistance-changing effects are observed. In case of sufficiently fragile nanofilament exhibiting electrical quantum conductance effects and moderate heating applied to it, a dramatic increase of resistance is observed just after the completion of the heating cycle. However, when the filament is allowed to cool off, a spontaneous restoration of the originally set resistance of the filament is observed within less than couple tens of seconds. When the filament is sufficiently fragile or the heating too excessive, the filament is permanently ruptured, resulting in a high resistance of the cell. In contrast, for robust, low resistance filaments, the remote heating does not affect the resistance. The spontaneous restoration of the initial resistance value is explained by electron tunneling between neighboring vibrating Cu atoms. As the vibrations of the Cu atoms subside during the cooling off period, the electron tunneling between the Cu atoms becomes more likely. At elevated temperatures, the average tunneling distance increases, leading to a sharp decrease of the tunneling probability and, consequently, to a sharp increase in transient resistance.

Strategies for Manipulating Phonon Transport in Solids

In this review, we summarize the recent efforts on manipulating phonon transport in solids by using specific techniques that modify their phonon thermal conductivity (i.e., specific heat, phonon group velocity, and mean free path) and phonon thermal conductance (i.e., transmission probability and density of states). The strategies discussed for tuning thermal conductivity are as follows: large unit cell approach and liquid-like conduction for maneuvering specific heat; rattler, mini-bandgap, and phonon confinement for manipulating phonon group velocity; nanoparticles, nanosized grains, coated grains, alloy (isotope) scattering, selection rules in phonon dispersion, Grüneisen parameter, lone-pair electronics, dynamic disorder, and local static distortion for restricting mean free path. We have also included the discussion on tuning phonon thermal conductance, as thermal conduction can be viewed as a transmission process. Additionally, phonon filtering, ballistic transport, and waveguiding are discussed to alter density of states and transmission probability. We hope this review can bring meaningful insights to the researchers in the field of phonon transport in solids.

Probing energy dissipation in molecular-scale junctions via surface enhanced Raman spectroscopy: vibrational pumping and hot carrier enhanced light emission

Experimentally resolving the microscopic energy dissipation and redistribution pathways in a molecular-scale junction, the smallest possible nanoelectronic device, is of great current interest. Here we report measurements of the vibrational pumping and light emission processes in current-carrying molecular junctions using surface enhanced Raman spectroscopy. We show that the heating of vibrational modes exhibits distinct features when the molecular junctions are driven by electrical bias or optical power. We further discuss the hot carrier origin of the broadband continuum emission observed in the Raman scattering spectrum.

Thermoelectricity of near-resonant tunnel junctions and their relation to Carnot efficiency

We present a conceptual study motivated by electrical and thermoelectrical measurements on various near-resonant tunnel junctions. The squeezable nano junction technique allows the quasi-synchronous measurement of conductance G, I(V) characteristics and Seebeck coefficient S. Correlations between G and S are uncovered, in particular boundaries for S(G). We find the simplest and consistent description of the observed phenomena in the framework of the single level resonant tunneling model within which measuring I(V) and S suffice for determining all model parameters. We can further employ the model for assigning thermoelectric efficiencies \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}η without measuring the heat flow. Within the ensemble of thermoelectric data, junctions with assigned \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}η close to the Carnot limit can be identified. These insights allow providing design rules for optimized thermoelectric efficiency in nanoscale junctions.

Thermal and electrical transport at nanosized metallic contacts: In the diffusive-ballistic region at room temperature

The Wiedemann-Franz law has been proved at the quantized metallic contacts but has never been verified at the nanosized contacts when the electrons travel in the diffusive-ballistic region. Herein, by developing a home-made inelastic tunneling spectroscope, the electrical and thermal resistances of the nanosized metallic contacts are investigated. The contact is established by pressing two wires crosswise against each other under the Lorentz force in the magnetic field. The nonmetallic surface layer is in situ removed by the resistive heating under high vacuum. The temperature dependence of the electrical contact resistance is used to separate the contributions from the diffusive and the ballistic transports. The thermal contact resistance is found to increase linearly with the electrical counterpart, indicating the validity of the Wiedemann-Franz law at the clean metallic contacts.

Effective Lorenz Number of the Point Contact between Silver Nanowires

Electrical and thermal transport through metal point contacts, a key issue in the design and operation of various engineering devices, is of great recent interest. The effective Lorenz number (L), which relates the thermal to electrical conductance of point contacts, could provide valuable information on the relative contribution of electrons and phonons to thermal transport. Through measuring electrical and thermal transport across point contacts between silver nanowires, we report that L significantly deviates from the Sommerfeld value by up to 5.2 times and exhibits nonmonotonic variation with temperature. Analyses show that these observations are due to the more important phonon contribution to the thermal conductance of the point contact as Sharvin resistance greatly hinders electron transport, which is further confirmed by the size dependence of L with a higher value for a smaller contact size. These results provide critical insights into engineering designs involving point contacts between metal nanostructures.

Stochastic simulation of nonequilibrium heat conduction in extended molecular junctions

Understanding phononic heat transport processes in molecular junctions is a central issue in the developing field of nanoscale heat conduction. Here, we present a Langevin dynamics simulation framework to investigate heat transport processes in molecular junctions at and beyond the linear response regime and apply it to saturated and unsaturated linear hydrocarbon chains connecting two gold substrates. Thermal boundary conditions represented by Markovian noise and damping are filtered through several (up to four) gold layers to provide a realistic and controllable bath spectral density. Classical simulations using the full universal force field are compared with quantum calculations that use only the harmonic part of this field. The close agreement found at about room temperature between these very different calculations suggests that heat transport at such temperatures is dominated by lower frequency vibrations whose dynamics is described well by classical mechanics. The results obtained for alkanedithiol molecules connecting gold substrates agree with previous quantum calculations based on the Landauer formula and match recent experimental measurements [e.g., thermal conductance around 20 pW/K for alkanedithiols in single-molecule junctions (SMJs)]. Heat conductance simulations on polyynes of different lengths illuminate the effects of molecular conjugation on thermal transport. The difference between alkanes and polyynes is not large but correlates with the larger rigidity and stronger mode localization that characterize the polyyne structure. This computational approach has been recently used [R. Chen, I. Sharony, and A. Nitzan, J. Phys. Chem. Lett. 11, 4261-4268 (2020)] to unveil local atomic heat currents and phononic interference effect in aromatic-ring based SMJs.

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.

Electric field control of radiative heat transfer in a superconducting circuit

Heat is detrimental for the operation of quantum systems, yet it fundamentally behaves according to quantum mechanics, being phase coherent and universally quantum-limited regardless of its carriers. Due to their robustness, superconducting circuits integrating dissipative elements are ideal candidates to emulate many-body phenomena in quantum heat transport, hitherto scarcely explored experimentally. However, their ability to tackle the underlying full physical richness is severely hindered by the exclusive use of a magnetic flux as a control parameter and requires complementary approaches. Here, we introduce a dual, magnetic field-free circuit where charge quantization in a superconducting island enables thorough electric field control. We thus tune the thermal conductance, close to its quantum limit, of a single photonic channel between two mesoscopic reservoirs. We observe heat flow oscillations originating from the competition between Cooper-pair tunnelling and Coulomb repulsion in the island, well captured by a simple model. Our results highlight the consequences of charge-phase conjugation on heat transport, with promising applications in thermal management of quantum devices and design of microbolometers.

Exploring the thermoelectric properties of oligo(phenylene-ethynylene) derivatives

Seebeck coefficient measurements provide unique insights into the electronic structure of single-molecule junctions, which underpins their charge and heat transport properties. Since the Seebeck coefficient depends on the slope of the transmission function at the Fermi energy (EF), the sign of the thermoelectric voltage will be determined by the location of the molecular orbital levels relative to EF. Here we investigate thermoelectricity in molecular junctions formed from a series of oligophenylene-ethynylene (OPE) derivatives with biphenylene, naphthalene and anthracene cores and pyridyl or methylthio end-groups. Single-molecule conductance and thermoelectric voltage data were obtained using a home-built scanning tunneling microscope break junction technique. The results show that all the OPE derivatives studied here are dominated by the lowest unoccupied molecular orbital level. The Seebeck coefficients for these molecules follow the same trend as the energy derivatives of their corresponding transmission spectra around the Fermi level. The molecule terminated with pyridyl units has the largest Seebeck coefficient corresponding to the highest slope of the transmission function at EF. Density-functional-theory-based quantum transport calculations support the experimental results.

Determining plasmonic hot-carrier energy distributions via single-molecule transport measurements

Hot carriers in plasmonic nanostructures, generated via plasmon decay, play key roles in applications such as photocatalysis and in photodetectors that circumvent bandgap limitations. However, direct experimental quantification of steady-state energy distributions of hot carriers in nanostructures has so far been lacking. We present transport measurements from single-molecule junctions, created by trapping suitably chosen single molecules between an ultrathin gold film supporting surface plasmon polaritons and a scanning probe tip, that can provide quantification of plasmonic hot-carrier distributions. Our results show that Landau damping is the dominant physical mechanism of hot-carrier generation in nanoscale systems with strong confinement. The technique developed in this work will enable quantification of plasmonic hot-carrier distributions in nanophotonic and plasmonic devices.

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.

Wiedemann-Franz Law for Molecular Hopping Transport

The Wiedemann-Franz (WF) law is a fundamental result in solid-state physics that relates the thermal and electrical conductivity of a metal. It is derived from the predominant transport mechanism in metals: the motion of quasi-free charge-carrying particles. Here, an equivalent WF relationship is developed for molecular systems in which charge carriers are moving not as free particles but instead hop between redox sites. We derive a concise analytical relationship between the electrical and thermal conductivity generated by electron hopping in molecular systems and find that the linear temperature dependence of their ratio as expressed in the standard WF law is replaced by a linear dependence on the nuclear reorganization energy associated with the electron hopping process. The robustness of the molecular WF relation is confirmed by examining the conductance properties of a paradigmatic molecular junction. This result opens a new way to analyze conductivity in molecular systems, with possible applications advancing the design of molecular technologies that derive their function from electrical and/or thermal conductance.

Structure and Electron Transport at Metal Atomic Junctions Doped with Dichloroethylene

We have investigated the structure and electron transport at dichloroethylene-doped metal atomic junctions at low temperatures (20 K) in ultra-high vacuum, using Fe, Ni, Pd, Cu, Ag, and Au. The metal atomic junctions were fabricated using the mechanically controllable break junction technique. After introducing the dichloroethylene (DCE), the conductance behavior of Fe, Ni, and Pd junctions was considerably changed, whereas little change was observed for Cu, Ag, and Au. For the Pd and Cu junctions, a clear peak was observed in their conductance histograms, showing that the single-molecule junction was selectively formed. To investigate the structure of the metal atomic junctions further, their plateau lengths were analyzed. The length analysis revealed that the Au atomic wire was elongated, and the metal atomic wires were formed for the other transition metals: those that do not normally form metal atomic wires without DCE doping, as DCE adsorption stabilized the metal atomic states. There is a strong interaction between DCE and the metals, where DCE supports the formation of the metal atomic wire for Fe, Ni, and Pd.

Heat dissipation in quasi-ballistic single-atom contacts at room temperature

We report on evaluations of local heating in Au single-atom chains at room temperature. We performed onsite thermometry of atomic-scale Au junctions under applied sinusoidal voltage of variable amplitudes. The AC approach enabled to preclude electromigration effects for characterizing the influence of energy dissipations on the lifetime. We elucidated nonlinear increase in the effective temperature of the current-carrying single-atom chains with the voltage amplitudes, which was attributed to subtle interplay between electron-phonon scattering and electron-mediated thermal transport in the quasi-ballistic conductor. We also found that only 0.2% of the electric power contributed to local heating while the majority was consumed at the diffusive bank. The present findings can be used for thermal management of future integrated nanoelectronics.

Electronic heat flow and thermal shot noise in quantum circuits

When assembling individual quantum components into a mesoscopic circuit, the interplay between Coulomb interaction and charge granularity breaks down the classical laws of electrical impedance composition. Here we explore experimentally the thermal consequences, and observe an additional quantum mechanism of electronic heat transport. The investigated, broadly tunable test-bed circuit is composed of a micron-scale metallic node connected to one electronic channel and a resistance. Heating up the node with Joule dissipation, we separately determine, from complementary noise measurements, both its temperature and the thermal shot noise induced by the temperature difference across the channel. The thermal shot noise predictions are thereby directly validated, and the electronic heat flow is revealed. The latter exhibits a contribution from the channel involving the electrons' partitioning together with the Coulomb interaction. Expanding heat current predictions to include the thermal shot noise, we find a quantitative agreement with experiments.

Thermal transports of one-dimensional ultrathin carbon structures

Carbon atomic chain, linear benzene polymers, and carbon nanothreads are all one-dimensional (1D) ultrathin carbon structures. They possess excellent electronic and mechanical properties; however, their thermal transport properties have been rarely explored. Here, we systematically study their thermal conductance by combining the nonequilibrium Green's function and force field methods. The thermal conductance varies from 0.24 to 1.00 nW K^-1 at 300 K, and phonon transport in the linear benzene polymers and carbon nanothreads is strongly dependent on the connectivity styles between the benzene rings. We propose a simple 1D model, namely force-constant model, that explains the complicated transport processes in these structures. Our study not only reveals intrinsic mechanisms of phonon transport in these carbon structures, but also provides an effective method to analyze thermal properties of other 1D ultrathin structures made of only several atomic chains.

Thermal Transport through Single-Molecule Junctions

Molecular junctions exhibit a rich and tunable set of thermal transport phenomena. However, the predicted high thermoelectric efficiencies, phonon quantum interference effects, rectification, and nonlinear heat transport properties of organic molecules are yet to be verified because suitable experimental techniques have been missing. Here, by combining the break junction technique with suspended heat-flux sensors with picowatt per Kelvin sensitivity, we measured the thermal and electrical conductance of single organic molecules at room temperature simultaneously. We used this method to study the thermal transport properties of two model systems, namely, dithiol-oligo(phenylene ethynylene) and octane dithiol junctions with gold electrodes. In agreement with our density functional theory and phase-coherent transport calculations, we show that heat transport across these systems is governed by the phonon mismatch between the molecules and the metallic electrodes. This work represents the first measurement of thermal transport through single molecules and opens new opportunities for studying heat management at the nanoscale level.

Exciton Gas Transport through Nanoconstrictions

An indirect exciton is a bound state of an electron and a hole in spatially separated layers. Two-dimensional indirect excitons can be created optically in heterostructures containing double quantum wells or atomically thin semiconductors. We study theoretically the transmission of such bosonic quasiparticles through nanoconstrictions. We show that the quantum transport phenomena, for example, conductance quantization, single-slit diffraction, two-slit interference, and the Talbot effect, are experimentally realizable in systems of indirect excitons. We discuss similarities and differences between these phenomena and their counterparts in electronic devices.

Quantum Phonon Transport in Nanomaterials: Combining Atomistic with Non-Equilibrium Green's Function Techniques

A crucial goal for increasing thermal energy harvesting will be to progress towards atomistic design strategies for smart nanodevices and nanomaterials. This requires the combination of computationally efficient atomistic methodologies with quantum transport based approaches. Here, we review our recent work on this problem, by presenting selected applications of the PHONON tool to the description of phonon transport in nanostructured materials. The PHONON tool is a module developed as part of the Density-Functional Tight-Binding (DFTB) software platform. We discuss the anisotropic phonon band structure of selected puckered two-dimensional materials, helical and horizontal doping effects in the phonon thermal conductivity of boron nitride-carbon heteronanotubes, phonon filtering in molecular junctions, and a novel computational methodology to investigate time-dependent phonon transport at the atomistic level. These examples illustrate the versatility of our implementation of phonon transport in combination with density functional-based methods to address specific nanoscale functionalities, thus potentially allowing for designing novel thermal devices.

Thermal Transport in One-Dimensional Electronic Fluids

We study thermal conductivity for one-dimensional electronic fluids. The many-body Hilbert space is partitioned into bosonic and fermionic sectors that carry the thermal current in parallel. For times shorter than the bosonic umklapp time, the momenta of Bose and Fermi components are separately conserved, giving rise to the ballistic heat propagation and imaginary heat conductivity proportional to T/iω. The real part of thermal conductivity is controlled by decay processes of fermionic and bosonic excitations, leading to several regimes in frequency dependence. At lowest frequencies or longest length scales, the thermal transport is dominated by Lévy flights of low-momentum bosons that lead to a fractional scaling, ω^{-1/3} and L^{1/3}, of heat conductivity with the frequency ω and system size L, respectively.