Vacuum phonon tunneling

Optimally Suppressed Phonon Tunneling in van der Waals Graphene-WS2 Heterostructure with Ultralow Thermal Conductivity

Van der Waals heterostructures have great potential for realizing ultimately low thermal conductivity because defectless interfaces can be constructed at a length scale smaller than the phonon wavelength, allowing modulation of coherent phonon transport. In this Letter, we demonstrate the mechanism for thermal conductivity reduction at a mode-resolved level. The graphene-WS2 heterostructure with the lowest cross-plane thermal conductivity of 0.048 W/(m·K) is identified from 16,384 candidates by combining Bayesian optimization and molecular dynamics simulations. Then, the angle-resolved phonon transmission is calculated using the mode-resolved atomistic Green's function. The results reveal that the optimal heterostructure nearly completely terminates phonon transport with finite incident angles, owing to the reduced critical incident angle and suppression of phonon tunneling.

Moiré Pattern Controlled Phonon Polarizer Based on Twisted Graphene

Twisted van der Waals materials featuring Moiré patterns present new design possibilities and demonstrate unconventional behaviors in electrical, optical, spintronic, and superconducting properties. However, experimental exploration of thermal transport across Moiré patterns has not been as extensive, despite its critical role in nanoelectronics, thermal management, and energy technologies. Here, the first experimental study is conducted on thermal transport across twisted graphene, demonstrating a phonon polarizer concept from the rotational misalignment between stacked layers. The direct thermal and acoustic measurements, structural characterizations, and atomistic modeling, reveal a modulation up to 631% in thermal conductance with various Moiré angles, while maintaining a high acoustic transmission. By comparing experiments with density functional theory and molecular dynamics simulations, mode-dependent phonon transmissions are quantified based on the angle alignment of graphene band structures and attributed to the coupling among flexural phonon modes. The agreement confirms the dominant tuning mechanisms in adjusting phonon transmission from high-frequency thermal modes while having negligible effects on low-frequency acoustic modes near Brillouin zone center. This study offers crucial insights into the fundamental thermal transport in Moiré structures, opening avenues for the invention of quantum thermal devices and new design methodologies based on manipulations of vibrational band structures and phonon spectra.

Enhancement of Graphene Phonon Excitation by a Chemically Engineered Molecular Resonance

The abstraction of pyrrolic hydrogen from a single phthalocyanine on graphene turns the molecule into a sensitive probe for graphene phonons. The inelastic electron transport measured with a scanning tunneling microscope across the molecular adsorbate and graphene becomes strongly enhanced for a graphene out-of-plane acoustic phonon mode. Supporting density functional and transport calculations elucidate the underlying physical mechanism. A molecular orbital resonance close to the Fermi energy controls the inelastic current while specific phonon modes of graphene are magnified due to their coupling to symmetry-equivalent vibrational quanta of the molecule.

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.

Phononic properties of a periodic nanostructure including vacuum gap in the presence of effective interatomic interactions

Using the harmonic approximation and Green's function technique, we investigate the contribution of phonons to heat transport across a narrow vacuum gap by an extended mass-spring chain model. We base the investigation on the van Beest-Kramer-van Santen potential that applies to two cases of simple and alternating mass systems at a finite temperature. Employing this model, we show that in specific values of interaction strengths, incoming phonon frequency, and gap distance, the phonon transmission across the vacuum gap can be improved. Finally, the thermal conductance of the system is computed as a function of interaction strength, gap distance, and temperature. These calculations reveal a suitable fitting function that can provide valuable insight into determining the internal interaction strengths from this quantity or controlling it by variation of the gap distance.

Contribution of the acoustic waves to near-field heat transfer

Calculations of the radiative and phonon heat transfer between metals in an extreme near field in presence of electrostatic potential difference are given. Potential difference leads to a coupling between the radiation field and acoustic waves in solid, as a result of which the heat flux between two gold plates associated with p -polarized electromagnetic waves increases by many orders of magnitude as the potential difference varies from 0 to 10 V. The radiative heat transfer is compared with the phonon heat transfer associated with the electrostatic and van der Waals interactions between the surface displacements. For large potential difference and small distances the radiative heat transfer is reduced to the electrostatic phonon heat transfer. A particular case of surface acoustic waves-Rayleigh waves is studied in details. Conditions are obtained for the existence of surface phonon polaritons associated with the interaction of Rayleigh waves with an electromagnetic field. The surface Rayleigh and bulk acoustic waves can give contributions of the same order. The obtained results can be used to control heat fluxes at the nanoscale using the potential difference and to create coherent radiation sources based on the properties of the Rayleigh waves.

Phonon heat transfer across a vacuum through quantum fluctuations

Heat transfer in solids is typically conducted through either electrons or atomic vibrations known as phonons. In a vacuum, heat has long been thought to be transferred by radiation but not by phonons because of the lack of a medium¹. Recent theory, however, has predicted that quantum fluctuations of electromagnetic fields could induce phonon coupling across a vacuum and thereby facilitate heat transfer^2-4. Revealing this unique quantum effect experimentally would bring fundamental insights to quantum thermodynamics⁵ and practical implications to thermal management in nanometre-scale technologies⁶. Here we experimentally demonstrate heat transfer induced by quantum fluctuations between two objects separated by a vacuum gap. We use nanomechanical systems to realize strong phonon coupling through vacuum fluctuations, and observe the exchange of thermal energy between individual phonon modes. The experimental observation agrees well with our theoretical calculations and is unambiguously distinguished from other effects such as near-field radiation and electrostatic interaction. Our discovery of phonon transport through quantum fluctuations represents a previously unknown mechanism of heat transfer in addition to the conventional conduction, convection and radiation. It paves the way for the exploitation of quantum vacuum in energy transport at the nanoscale.

Scanning Tunneling Microscopy Observation of Phonon Condensate

Using quantum tunneling of electrons into vibrating surface atoms, phonon oscillations can be observed on the atomic scale. Phonon interference patterns with unusually large signal amplitudes have been revealed by scanning tunneling microscopy in intercalated van der Waals heterostructures. Our results show that the effective radius of these phonon quasi-bound states, the real-space distribution of phonon standing wave amplitudes, the scattering phase shifts, and the nonlinear intermode coupling strongly depend on the presence of defect-induced scattering resonance. The observed coherence of these quasi-bound states most likely arises from phase- and frequency-synchronized dynamics of all phonon modes, and indicates the formation of many-body condensate of optical phonons around resonant defects. We found that increasing the strength of the scattering resonance causes the increase of the condensate droplet radius without affecting the condensate fraction inside it. The condensate can be observed at room temperature.

Giant heat transfer in the crossover regime between conduction and radiation

Heat is transferred by radiation between two well-separated bodies at temperatures of finite difference in vacuum. At large distances the heat transfer can be described by black body radiation, at shorter distances evanescent modes start to contribute, and at separations comparable to inter-atomic spacing the transition to heat conduction should take place. We report on quantitative measurements of the near-field mediated heat flux between a gold coated near-field scanning thermal microscope tip and a planar gold sample at nanometre distances of 0.2-7 nm. We find an extraordinary large heat flux which is more than five orders of magnitude larger than black body radiation and four orders of magnitude larger than the values predicted by conventional theory of fluctuational electrodynamics. Different theories of phonon tunnelling are not able to describe the observations in a satisfactory way. The findings demand modified or even new models of heat transfer across vacuum gaps at nanometre distances.

Surface-state enhancement of tunneling thermopower on the Ag(111) surface

Thermoelectric effects in tunnel junctions are currently being revisited for their prospects in cooling and energy harvesting applications, and as sensitive probes of electron transport. Quantitative interpretation of these effects calls for advances in both theory and experiment, particularly with respect to the electron transmission probability across a tunnel barrier which encodes the energy dependence and the magnitude of tunneling thermopower. Using noble metal surfaces as clean model systems, we demonstrate a comparatively simple and quantitative approach where the transmission probability is directly measured experimentally. Importantly, we estimate not only thermovoltage, but also its energy and temperature dependencies. We have thus resolved surface-state enhancement of thermovoltage, which manifests as 10-fold enhancement of thermopower on terraces of the Ag(111) surface compared to single-atom step sites and surface-supported nanoparticles. To corroborate experimental analysis, the methodology was applied to the transmission probability obtained from first-principles calculations for the (111) surfaces of the three noble metals, finding good agreement between overall trends. Surface-state effects themselves point to a possibility of achieving competitive performance of all-metal tunnel junctions when compared to molecular junctions. At the same time, the approach presented here opens up possibilities to investigate the properties of nominally doped or gated thermoelectric tunnel junctions as well as temperature gradient in nanometer gaps.

Classical to quantum transition of heat transfer between two silica clusters

Heat transfer between two silica clusters is investigated by using the nonequilibrium Green's function method. In the gap range between 4 Å and 3 times the cluster size, the thermal conductance decreases as predicted by the surface charge-charge interaction. Above 5 times the cluster size, the volume dipole-dipole interaction predominates. Finally, when the distance becomes smaller than 4 Å, a quantum interaction where the electrons of both clusters are shared takes place. This quantum interaction leads to the dramatic increase of the thermal coupling between neighbor clusters due to strong interactions. This study finally provides a description of the transition between radiation and heat conduction in gaps smaller than a few nanometers.

Thermal balance and quantum heat transport in nanostructures thermalized by local Langevin heat baths

Modeling of thermal transport in practical nanostructures requires making tradeoffs between the size of the system and the completeness of the model. We study quantum heat transfer in a self-consistent thermal bath setup consisting of two lead regions connected by a center region. Atoms both in the leads and in the center region are coupled to quantum Langevin heat baths that mimic the damping and dephasing of phonon waves by anharmonic scattering. This approach treats the leads and the center region on the same footing and thereby allows for a simple and physically transparent thermalization of the system, enabling also perfect acoustic matching between the leads and the center region. Increasing the strength of the coupling reduces the mean-free path of phonons and gradually shifts phonon transport from ballistic regime to diffusive regime. In the center region, the bath temperatures are determined self-consistently from the requirement of zero net energy exchange between the local heat bath and each atom. By solving the stochastic equations of motion in frequency space and averaging over noise using the general fluctuation-dissipation relation derived by Dhar and Roy [J. Stat. Phys. 125, 801 (2006)], we derive the formula for thermal current, which contains the Caroli formula for phonon transmission function and reduces to the Landauer-Büttiker formula in the limit of vanishing coupling to local heat baths. We prove that the bath temperatures measure local kinetic energy and can, therefore, be interpreted as true atomic temperatures. In a setup where phonon reflections are eliminated, the Boltzmann transport equation under gray approximation with full phonon dispersion is shown to be equivalent to the self-consistent heat bath model. We also study thermal transport through two-dimensional constrictions in square lattice and graphene and discuss the differences between the exact solution and linear approximations.

Scanning tunneling microscope-quartz crystal microbalance study of temperature gradients at an asperity contact

Investigations of atomic-scale friction frequently involve setups where a tip and substrate are initially at different temperatures. The temperature of the sliding interface upon contact has thus become a topic of interest. A method for detecting initial tip-sample temperature differences at an asperity contact is described, which consists of a scanning tunneling microscope (STM) tip in contact with the surface electrode of a quartz crystal microbalance (QCM). The technique makes use of the fact that a QCM is extremely sensitive to abrupt changes in temperature. In order to demonstrate the technique's capabilities, QCM frequency shifts were recorded for varying initial tip-substrate temperature differences as an STM tip was brought into and out of contact. The results are interpreted within the context of a recent model for thermal heat conduction at an asperity contact, and it is concluded that the transient frequency response is attributable to small changes in temperature close to the region of contact rather than a change in the overall temperature of the QCM itself. For the assumed model parameters, the results moreover reveal substantial temperature discontinuities at the boundary between the tip and the sample, for example, on the order of 10-15 °C for initial temperature differences of 20 °C.

Imaging the electron-phonon interaction at the atomic scale

Thin Pb films epitaxially grown on 7×7 reconstructed Si(111) represent an ideal model system for studying the electron-phonon interaction at the metal-insulator interface. For this system, using a combination of scanning tunneling microscopy and inelastic electron tunneling spectroscopy, we performed direct real-space imaging of the electron-phonon coupling parameter. We found that λ increases when the electron scattering at the Pb/Si(111) interface is diffuse and decreases when the electron scattering is specular. We show that the effect is driven by transverse redistribution of the electron density inside a quantum well.

Thermal conduction and interface effects in nanoscale Fermi-Pasta-Ulam conductors

We perform classical nonequilibrium molecular dynamics simulations to calculate heat flow through a microscopic junction connecting two larger reservoirs. In contrast to earlier papers, we also include the reservoirs in the simulated region to study the effect of the bulk-nanostructure interfaces and the bulk conductance. The scalar Fermi-Pasta-Ulam (FPU) model is used to describe the effects of anharmonic interactions in a simple manner. The temperature profile close to the junction in the low-temperature limit is shown to exhibit strong directional features that fade out when temperature increases. Simulating both the FPU chain and the two bulk regions is also shown to eliminate the nonmonotonous temperature variations found for simpler geometries and models. We show that, with sufficiently large reservoirs, the temperature profile in the chain does not depend on the details of thermalization used at the boundaries.

Heat exchange mediated by a quantum system

We consider heat transfer between two thermal reservoirs mediated by a quantum system using the generalized quantum Langevin equation. The thermal reservoirs are treated as ensembles of oscillators within the framework of the Drude-Ullersma model. General expressions for the heat current and thermal conductance are obtained for arbitrary coupling strength between the reservoirs and the mediator and for different temperature regimes. As an application of these results we discuss the origin of Fourier's law in a chain of large but finite subsystems coupled to each other by the quantum mediators. We also address a question of anomalously large heat current between the scanning tunneling microscope (STM) tip and substrate found in a recent experiment. The question of minimum thermal conductivity is revisited in the framework of scaling theory as a potential application of the developed approach.

Real-space imaging of inelastic Friedel-like surface oscillations emerging from molecular adsorbates

We report real space imaging measurements of inelastic Friedel oscillations. The inelastic electron tunneling spectroscopy, using scanning tunneling microscopy, around dimers of dichlorobenze adsorbates on Au(111) surface display clear spatial modulations that we attribute to inelastic scattering at the molecular sites caused by molecular vibrations. Due to local interactions between the adsorbate and the surface states, the molecular vibrations generate a redistribution of the charge density at energies in a narrow range around the inelastic mode. Our experimental findings are supported by theoretical arguments.