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.

Size dependence of exchange bias in Co/CoO nanostructures.

In Co/CoO nanostructures, of dimensions l×3l, at small Co thickness (≈6,10 nm), a strong increase in the bias field and the associated coercive field are found as the nanostructure size is reduced from l=120 nm to l=30 nm. This property indicates that the characteristic length D(AF) within the antiferromagnet which governs exchange-bias effects is the nanostructure size. By contrast, at larger Co thickness (≈23 nm), the exchange-bias field does not depend on the nanostructure size, implying that D(AF) is smaller than the nanostructure size. The results are discussed in the framework of the Malozemoff model, taking into account that the coupling between CoO grains is weak. Exchange bias is dominated either by coupling within the antiferromagnetic layer (6- and 10-nm-thick Co samples) or by ferromagnetic-antiferromagnetic interfacial coupling (23-nm-thick Co sample).

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

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

The conundrum of hot mitochondria.

The mitochondrion is often referred as the cellular powerhouse because the organelle oxidizes organic acids and NADH derived from nutriments, converting around 40% of the Gibbs free energy change of these reactions into ATP, the major energy currency of cell metabolism. Mitochondria are thus microscopic furnaces that inevitably release heat as a by-product of these reactions, and this contributes to body warming, especially in endotherms like birds and mammals. Over the last decade, the idea has emerged that mitochondria could be warmer than the cytosol, because of their intense energy metabolism. It has even been suggested that our own mitochondria could operate under normal conditions at a temperature close to 50 °C, something difficult to reconcile with the laws of thermal physics. Here, using our combined expertise in biology and physics, we exhaustively review the reports that led to the concept of a hot mitochondrion, which is essentially based on the development and use of a variety of molecular thermosensors whose intrinsic fluorescence is modified by temperature. Then, we discuss the physical concepts of heat diffusion, including mechanisms like phonons scattering, which occur in the nanoscale range. Although most of approaches with thermosensors studies present relatively sparse data and lack absolute temperature calibration, overall, they do support the hypothesis of hot mitochondria. However, there is no convincing physical explanation that would allow the organelle to maintain a higher temperature than its surroundings. We nevertheless proposed some research directions, mainly biological, that might help throw light on this intriguing conundrum.

Inducing micromechanical motion by optical excitation of a single quantum dot.

Hybrid quantum optomechanical systems1 interface a macroscopic mechanical degree of freedom with a single two-level system such as a single spin2-4, a superconducting qubit5-7 or a single optical emitter8-12. Recently, hybrid systems operating in the microwave domain have witnessed impressive progress13,14. Concurrently, only a few experimental approaches have successfully addressed hybrid systems in the optical domain, demonstrating that macroscopic motion can modulate the two-level system transition energy9,10,15. However, the reciprocal effect, corresponding to the backaction of a single quantum system on a macroscopic mechanical resonator, has remained elusive. In contrast to an optical cavity, a two-level system operates with no more than a single energy quantum. Hence, it requires a much stronger hybrid coupling rate compared to cavity optomechanical systems1,16. Here, we build on the large strain coupling between an oscillating microwire and a single embedded quantum dot9. We resonantly drive the quantum dot's exciton using a laser modulated at the mechanical frequency. State-dependent strain then results in a time-dependent mechanical force that actuates microwire motion. This force is almost three orders of magnitude larger than the radiation pressure produced by the photon flux interacting with the quantum dot. In principle, the state-dependent force could constitute a strategy to coherently encode the quantum dot quantum state onto a mechanical degree of freedom1.

Nanowire forest of pnictogen-chalcogenide alloys for thermoelectricity.

Pnictogen and chalcogenide compounds have been seen as high-potential materials for efficient thermoelectric conversion over the past few decades. It is also known that with nanostructuration, the physical properties of these pnictogen-chalcogenide compounds can be further enhanced towards a more efficient heat conversion. Here, we report the reduced thermal conductivity of a large ensemble of Bi2Te3 alloy nanowires (70 nm in diameter) with selenium for n-type and antimony for p-type (Bi2Te3-ySey and Bi2-xSbxTe3 respectively). The nanowire growth was carried out through electrodeposition in nanoporous aluminium oxide templates with high aspect ratios leading to a forest (109 per centimetre square) of nearly identical nanowires. The temperature dependence of thermal conductivity for the nanowire ensembles was acquired through a highly sensitive 3ω measurement technique. The change in the thermal conductivity of nanowires is largely affected by the roughness in addition to the size effect due to enhanced boundary scattering. The major factor that influences the thermal conductivity was found to be the ratio of the rms roughness to the correlation length of the nanowire. With a high Seebeck coefficient and electrical conductivity at room temperature, the overall thermoelectric figure of merit ZT allows the consideration of such forests of nanowires as efficient potential building blocks of future TE devices.

Heat conduction measurements in ballistic 1D phonon waveguides indicate breakdown of the thermal conductance quantization.

Emerging quantum technologies require mastering thermal management, especially at the nanoscale. It is now accepted that thermal metamaterial-based phonon manipulation is possible, especially at sub-kelvin temperatures. In these extreme limits of low temperatures and dimensions, heat conduction enters a quantum regime where phonon exchange obeys the Landauer formalism. Phonon transport is then governed by the transmission coefficients between the ballistic conductor and the thermal reservoirs. Here we report on ultra-sensitive thermal experiments made on ballistic 1D phonon conductors using a micro-platform suspended sensor. Our thermal conductance measurements attain a power sensitivity of 15 attoWatts [Formula: see text] around 100 mK. Ballistic thermal transport is dominated by non-ideal transmission coefficients and not by the quantized thermal conductance of the nanowire itself. This limitation of heat transport in the quantum regime may have a significant impact on modern thermal management and thermal circuit design.

Measuring Frequency Fluctuations in Nonlinear Nanomechanical Resonators.

Advances in nanomechanics within recent years have demonstrated an always expanding range of devices, from top-down structures to appealing bottom-up MoS2 and graphene membranes, used for both sensing and component-oriented applications. One of the main concerns in all of these devices is frequency noise, which ultimately limits their applicability. This issue has attracted a lot of attention recently, and the origin of this noise remains elusive to date. In this article we present a very simple technique to measure frequency noise in nonlinear mechanical devices, based on the presence of bistability. It is illustrated on silicon-nitride high-stress doubly clamped beams, in a cryogenic environment. We report on the same T/ f dependence of the frequency noise power spectra as reported in the literature. But we also find unexpected damping fluctuations, amplified in the vicinity of the bifurcation points; this effect is clearly distinct from already reported nonlinear dephasing and poses a fundamental limit on the measurement of bifurcation frequencies. The technique is further applied to the measurement of frequency noise as a function of mode number, within the same device. The relative frequency noise for the fundamental flexure δ f/ f0 lies in the range 0.5-0.01 ppm (consistent with the literature for cryogenic MHz devices) and decreases with mode number in the range studied. The technique can be applied to any type of nanomechanical structure, enabling progress toward the understanding of intrinsic sources of noise in these devices.

Measurement of anisotropic thermal conductivity of a dense forest of nanowires using the 3ω method.

The 3ω method is a dynamic measurement technique developed for determining the thermal conductivity of thin films or semi-infinite bulk materials. A simplified model is often applied to deduce the thermal conductivity from the slope of the real part of the ac temperature amplitude as a function of the logarithm of frequency, which in-turn brings a limitation on the kind of samples under observation. In this work, we have measured the thermal conductivity of a forest of nanowires embedded in nanoporous alumina membranes using the 3ω method. An analytical solution of 2D heat conduction is then used to model the multilayer system, considering the anisotropic thermal properties of the different layers, substrate thermal conductivity, and their thicknesses. Data treatment is performed by fitting the experimental results with the 2D model on two different sets of nanowires (silicon and BiSbTe) embedded in the matrix of nanoporous alumina templates, having thermal conductivities that differ by at least one order of magnitude. These experimental results show that this method extends the applicability of the 3ω technique to more complex systems having anisotropic thermal properties.

Quantum criticality at the superconductor-insulator transition revealed by specific heat measurements.

The superconductor-insulator transition (SIT) is considered an excellent example of a quantum phase transition that is driven by quantum fluctuations at zero temperature. The quantum critical point is characterized by a diverging correlation length and a vanishing energy scale. Low-energy fluctuations near quantum criticality may be experimentally detected by specific heat, cp, measurements. Here we use a unique highly sensitive experiment to measure cp of two-dimensional granular Pb films through the SIT. The specific heat shows the usual jump at the mean field superconducting transition temperature marking the onset of Cooper pairs formation. As the film thickness is tuned towards the SIT, is relatively unchanged, while the magnitude of the jump and low-temperature specific heat increase significantly. This behaviour is taken as the thermodynamic fingerprint of quantum criticality in the vicinity of a quantum phase transition.

Specific heat measurement set-up for quench condensed thin superconducting films.

We present a set-up designed for the measurement of specific heat of very thin or ultra-thin quench condensed superconducting films. In an ultra-high vacuum chamber, materials of interest can be thermally evaporated directly on a silicon membrane regulated in temperature from 1.4 K to 10 K. On this membrane, a heater and a thermometer are lithographically fabricated, allowing the measurement of heat capacity of the quench condensed layers. This apparatus permits the simultaneous thermal and electrical characterization of successively deposited layers in situ without exposing the deposited materials to room temperature or atmospheric conditions, both being irreversibly harmful to the samples. This system can be used to study specific heat signatures of phase transitions through the superconductor to insulator transition of quench condensed films.

Specific heat measurement of thin suspended SiN membrane from 8 K to 300 K using the 3ω-Völklein method.

We present a specific heat measurement technique adapted to thin or very thin suspended membranes from low temperature (8 K) to 300 K. The presented device allows the measurement of the heat capacity of a 70 ng silicon nitride membrane (50 or 100 nm thick), corresponding to a heat capacity of 1.4 × 10(-10) J/K at 8 K and 5.1 × 10(-8) J/K at 300 K. Measurements are performed using the 3ω method coupled to the Völklein geometry. This configuration allows the measurement of both specific heat and thermal conductivity within the same experiment. A transducer (heater/thermometer) is used to create an oscillation of the heat flux on the membrane; the voltage oscillation appearing at the third harmonic which contains the thermal information is measured using a Wheatstone bridge set-up. The heat capacity measurement is performed by measuring the variation of the 3ω voltage over a wide frequency range and by fitting the experimental data using a thermal model adapted to the heat transfer across the membrane. The experimental data are compared to a regular Debye model; the specific heat exhibits features commonly seen for glasses at low temperature.

Inverse proximity effect in a strongly correlated electron system.

An anomalous superconducting proximity effect between a strongly correlated electron system and a normal metal is demonstrated. The model system is a 2D ultrathin superconducting quench-condensed Pb film. Such a highly disordered film has a reduced transition temperature (T(c) = 1.7 K) due to the strong e(-)-e(-) interaction. Instead of weakening the superconductivity, an overlayer of Ag on Pb induces an increase of both the T(c) and the gap. The restoration of the electron screening brought about by the quasiparticles from the normal metal can explain this striking inverse proximity effect.