Session R62: Thermal Transport in Nanostructures I

Advanced Josephson junctions circuits and nanoscale devices: The phase-coherence in heat transport

The emerging field of phase-coherent caloritronics (from the Latin word calor, heat) [1] 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, I will initially report the first experimental realization of a heat interferometer. We investigate heat exchange between two normal metal electrodes kept at different temperatures and tunnel-coupled to each other through a thermal device in the form of a DC-SQUID. Heat transport in the system is found to be phase dependent, in agreement with the original prediction. After this initial demonstration, we have extended the concept of heat interferometry to various other devices, implementing the first quantum `diffractor’ for thermal fluxes, realizing the first balanced Josephson heat modulator, and the first tunable 0-π thermal Josephson junction. Finally, I will conclude by showing the realization of the first phase-tunable Josephson thermal router. Thanks to the Josephson effect, this latter structure allows to regulate the thermal gradient between the output electrodes until reaching its inversion, and represents an important step towards the realization of caloritronic logic components, and quantum thermal machines.

[1] A. Fornieri and F. Giazotto, Nat. Nanotechnol. 12, 944 (2017).   

Topological Quantum Thermocouple

The flows of charge and heat in an open quantum system coupled to three macroscopic electron reservoirs are studied. It is shown that even without particle-hole asymmetry in the electronic structure, thermoelectric effects can be induced topologically by the Aharonov-Bohm effect. The Peltier effect is calculated, and the conditions of maximum cooling power are determined. The Carnot bound on the refrigeration coefficient is verified, and in so doing, a generalized relationship between the Peltier and Seebeck effects in multi-terminal quantum devices is derived. An apparent thermodynamic paradox involving persistent Peltier cooling in equilibrium is resolved by a rigorous treatment of heat flow at the quantum level.   

Noise emitted by a temperature biased tunnel junction

Caloritronic in small systems has been of high interest in recent years since new ways to manipulate electronic heat currents at the nanoscale have been developed. The ability to make mesoscopic systems with well controlled temperature enables the study of quantum heat transport and out of equilibrium quantum thermodynamic, which is of fundamental interest. A tunnel barrier between two metallic electrodes forms the basic unit in the study of non-equilibrium physics and fluctuations. This system has been put to great use in the understanding of electronic transport whether at equilibrium where fluctuations are used as thermometer or in the presence of voltage bias where information on charge carrier can be accessed. In this talk we present calculations and measurements of the electrical noise in a metallic tunnel junction in presence of a thermal and voltage gradient, pushing farther our understanding of its non-equilibrium properties.   

Thermal Conductivity of Small Angle Twisted Bilayer Graphene

The effect of misorientation on the in-plane thermal conductivity of twisted BLG (TBG) is still poorly understood. The one experimental study found that interlayer misorientation could reduce the in-plane thermal conductivity by 50%. A recent theoretical study of TBG with the three smallest commensurate unit cells, 21.8^o, 32.2^o, and 13.2^o, found that the thermal conductivity decreased approximately linearly as the commensurate lattice constant increased. What happens at smaller misorientation angles of 10^o or less is still an open question. For this range of rotation angles, we perform large-scale, non-equilibrium molecular dynamics calculations of the thermal conductivity of TBG for twist angles down to 1.89^o. The picture that emerges from this study is that the misorientation reduces the shear elastic constant C44 which increases the wrinkling of the TBG. The increased out-of-plane wrinkling then reduces the thermal conductivity.   

Thermal Transport across hBN/Graphene Interfaces

Heterostructures of two-dimensional materials (2D) are a promising platform for the observation of phonon interface transport and coherent-phonon effects. Layer thickness and orientation can be tuned during heterostructure fabrication which provides a variety of ways to control the thermal-transport properties of the system. Using the 3ω method, we measure the interfacial thermal resistance between two common 2D materials, hexagonal boron nitride (hBN) and graphene (Gr), to be significantly lower than previously reported Raman thermometry values. The uncertainty of our measurement is limited by the uncertainty in the literature value for the bulk thermal conductivity of hBN. We aim to provide a precise measurement of the cross plane thermal resistance of hBN flakes from the bulk-like down to the ballistic phonon transport regime and demonstrate that a variety of geometries of 3ω wires including a semicircle with 750μm diameter, measure the same cross plane thermal resistance of a 70nm thick SiO₂ film with a standard deviation of 4.7 m² K GW^-1.   

Engineering ultrahigh thermal anisotropy in 2D van der Waals films

Thermally anisotropic materials, whose thermal conductivity differs depending on the direction of heat conduction, are technologically important for heat management and fundamentally intriguing in terms of their mechanism of heat transport. Previous studies have achieved thermal anisotropy through anisotropic bonding, fabricating heterostructures, and introducing low dimensional defects, giving rise to anisotropic ratios of 1-2 orders of magnitude. Herein we report an ultrahigh thermal anisotropy (~1000 at room temperature) in large-area thin films with tunable thicknesses made by stacking transition metal dichalcogenide (MoS₂ or WS₂) monolayers. We measure an ultralow cross-plane thermal conductivity comparable to that of air, which can be attributed to interlayer rotation and the lack of lattice order. In the in-plane direction, a high thermal conductivity close to that of the single crystal counterpart is maintained due to the long-range lattice order and grain connectivity in the polycrystalline monolayers. The overall thermal anisotropy ratio in our films is higher than that of any man-made or natural material, demonstrating interlayer structure as a new degree of freedom for engineering thermal anisotropy in matter.   

Phonon Localization in Ultrathin Silicon Membranes with Surface Nanostructures

Surface nanostructures have been shown to introduce new vibrational modes that locally couple with phonon modes of the base and impact in-plane phonon propagation. Nanoscopic surface imperfections have been experimentally and theoretically demonstrated to decrease the thermal conductivity (TC) of silicon (Si) membranes. However, the tunability of the coupling or hybridization mechanisms due to unique surface geometries, and the extent of their impact on phonon properties are not fully understood. Using direct non-equilibrium molecular dynamics (MD), we investigate the effect of periodic “nanofins” on the thermal properties of ultrathin Si membranes. Our study exhibits that these structures engender a distinct in-plane anisotropy in the TC of the membrane, and create unique localized temperature and phonon-induced strain profiles, in accordance with the surface structure periodicity. Further investigation, using lattice dynamics with the quasi-harmonic approximation, reveals a significant reduction in mode diffusivity, indicating phonon localization, approaching behavior similar to highly disordered solids, e.g., amorphous Si. These results further establish surface nanoengineering as a viable approach to meter and direct heat flow in future microelectronic/quantum technologies.   

Surface phonon mode remarkably limits heat conduction in a silicon ultra-thin film

Decrease of silicon channel thickness is efficient to suppress short channel effects, which is beneficial for further miniaturizing of MOS transistor. However, this causes larger reduction thermal conductivity, resulting in temperature rise of the channel region. Therefore, accurate analysis of heat conduction in thin film is needed for heat dissipation control. The Sondheimer model, which has been widely used, is known to be valid for reproducing heat conduction in the range of 50-100 nm thickness. However, since the Sondheimer model uses the bulk phonon property, the applicability of the model to ultra-thin film with several nanometers is doubtful. Here, in order to validate the model, we performed the anharmonic lattice dynamics explicitly considering atomic structure of the film to rigorously calculate thermal conductivity and phonon transport properties of the ultra-thin silicon film. Consequently we found that the Sondheimer model cannot reproduce spectral phonon transport properties of ultra-thin film because it ignores the change of phonon dispersion and presence of surface phonon. We will discuss this discrepancy in terms of surface phonon scattering to suggest the way to resolve this.   

Numerical study on the transition from coherent to incoherent phonon transport in a superlattice

Superlattice has been widely investigated due to its capability of modulating phonon dispersion and suppressing transport. However, increases of superlattice periodicity and temperature cause phonon decoherence and then suppress the reduction of lattice thermal conductivity [1], which is well known as the issue for developing heat conduction control by superlattice. Here a criterion for which phonon coherence is preserved needed to be identified. Ref. [2] derived the phonon coherence condition with respect to wavelength and temperature as λ≥(hv/kBT) with speed of sound (v), however, we addressed this issue from different viewpoint, namely, the uncertainty associated with energy and momentum conservations; it should be satisfied that not only the multiplication of phonon frequency ω and relaxation time τ is large enough (ωτ»1) but also fluctuation of momentum δ(hk/2π) is sufficiently smaller than reciprocal lattice vector G(=2π/a) (δ(hk/2π)«hG/2π), where a denotes periodicity. These discussions finally result in the relationship T≤(hvg/kBa), where vg denotes group velocity. By using molecular dynamics simulations, we will report the verification of this formula.
[1] Phys. Rev. Lett. 84, 927 (2000). [2] AIP Advances 6, 065024 (2016).   

Nonequilibrium phonon distribution in current-driven nanostructures

Electric energy of current flowing in materials or devices is dissipated mostly as Joule heat. However, in nanoscale systems, the generated phonons can escape before they thermalize, which can result in the breakdown of the Joule heating approximation.
We demonstrate a strongly non-equilibrium phonon distribution in current-driven metallic microwires, which cannot be described in terms of heat [1]. Our main observation is a linear dependence of resistance on current at cryogenic temperatures, qualitatively inconsistent with the effects of Joule heating, as confirmed by the simulations of heat flow. As the temperature is increased, the zero-current singularity becomes smoothed out, but the linear dependence remains apparent at sufficiently large currents even near ambient temperatures. A kinetic model based on the quasi-ballistic escape approximation for the nonequilibrium phonons generated by electron scattering reproduces our main observations. The demonstrated effects are important for optimizing thermal management in electronic and thermoelectric nanodevices, and for the analysis of current-induced thermal effects at nanoscale.

[1] G.X. Chen, R. Freeman, A. Zholud, S. Urazhdin, arXiv:1907.00224.   

New regimes of nanoscale thermal transport from nanostructured heat sources on diamond probed using coherent EUV beams

Nanostructured materials make it possible to engineer properties that are unattainable using conventional bulk materials, with applications in next-generation energy efficient devices. However, macroscopic, diffusive transport models break down at length scales comparable to a material’s dominant phonon mean free path. Moreover, there are few, if any, characterization techniques that can probe functional nanosystems. Here we use short wavelength (~30nm), ultrafast pulse (~10fs) extreme ultraviolet (EUV) beams to nondestructively probe nanoscale thermal transport in diamond. We first impulsively heat nickel nano-gratings fabricated on the diamond sample with an infrared pump laser and then extract thermal conductivity by monitoring surface relaxation with a time-delayed EUV probe. Diamond is an ideal candidate for validating emergent transport behaviors because its long phonon mean free path causes non-diffusive effects to appear at larger length scales. We compare our results to an advanced hydrodynamic transport model to isolate the contribution of viscous resistivity directly underneath the nanoheaters to thermal transport. Finally, we gain insight into non-diffusive cooling processes by examining the individual diffracted orders in the scattered EUV probe beam.   

Nanoelectronic thermometry and refrigeration for sub-millikelvin temperatures

It has recently been shown that magnetic refrigeration can be deployed on-chip to cool nanoelectronic devices below the base temperature of a dilution refrigerator [1, 2, 3]. This technique has the potential to unlock microkelvin electron temperatures in nanoscale structures and devices. However, there are still significant challenges in thermometry and thermal isolation to be overcome. In this talk, we present our recent work to lower the operating temperature of Coulomb blockade thermometers to ≈300µK, and to improve the base electron temperature reachable by demagnetisation refrigeration of on-chip copper.
[1] Bradley et al., Sci. Rep. 7, 45566 (2017)
[2] Palma, Scheller et al., Appl. Phys. Lett. 111, 253101 (2017)
[3] Yurttagül, Sarsby et al., Phys. Rev. Appl. 12, 011005 (2019)