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We investigate thin film resistive thermometry based on metal-to-insulator-transition (niobium nitride) materials down to very low temperature. The variation of the NbN thermometer resistance have been calibrated versus temperature and magnetic field. High sensitivity in tempertaure variation detection is demonstrated through efficient temperature coefficient of resistance. The nitrogen content of the niobium nitride thin films can be tuned to adjust the optimal working temperature range. In the present experiment, we show the versatility of the NbN thin film technology through applications in very different low temperature use-cases. We demonstrate that thin film resistive thermometry can be extended to temperatures below 30 mK with low electrical impedance., Comment: Article accepted for publication in JLTP

Superconductivity in two dimensions is nontrivial. One way to achieve global superconductivity is via the Berezinskii-Kosterlitz-Thouless (BKT) transition due to proliferation of vortex-antivortex pairs. This transition is expected to have a clear signature on the specific heat. The singularity at the transition temperature ${T}_{\mathrm{BKT}}$ is predicted to be immeasurable, and a broad nonuniversal peak is expected at $Tg{T}_{\mathrm{BKT}}$. Up to date, this has not been observed in two-dimensional superconductors; this work is then dedicated to investigate ${c}_{p}$ signatures in the limit of ultrathin 2d superconductors. We use a unique highly sensitive technique to measure the specific heat of quench condensed ultrathin Pb films. We find that thick films exhibit a specific heat jump at ${T}_{C}$ that is consistent with BCS theory. As the film thickness is reduced below the superconducting coherence length and the systems enter the 2D limit, the specific heat reveals BKT-like behavior in what can appear as to be a continuous BCS-BKT crossover as a function of film thickness. However, a number of problems arise with this interpretation. We discuss the experimental results and the possible significance of various scenarios involving BKT physics.

Advances in nanomechanics within recent years have demonstrated an always expanding range of devices, from top-down structures to appealing bottom-up MoS$_2$ 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 up to date. In this Letter 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 {\it 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 $\delta f/f_0$ lies in the range $0.5 - 0.01~$ppm (consistent with literature for cryogenic MHz devices), and decreases with mode number in the range studied. The technique can be applied to {\it any types} of nano-mechanical structures, enabling progresses towards the understanding of intrinsic sources of noise in these devices., Comment: Published 7 may 2018

We report on microwave optomechanics measurements performed on a nuclear adiabatic demagnetization cryostat, whose temperature is determined by accurate thermometry from below 500$~\mu$K to about 1$~$Kelvin. We describe a method for accessing the on-chip temperature, building on the blue-detuned parametric instability and a standard microwave setup. The capabilities and sensitivity of both the experimental arrangement and the developed technique are demonstrated with a very weakly coupled silicon-nitride doubly-clamped beam mode of about 4$~$MHz and a niobium on-chip cavity resonating around 6$~$GHz. We report on an unstable intrinsic driving force in the coupled microwave-mechanical system acting on the mechanics that appears below typically 100$~$mK. The origin of this phenomenon remains unknown, and deserves theoretical input. It prevents us from performing reliable experiments below typically 10-30$~$mK; however no evidence of thermal decoupling is observed, and we propose that the same features should be present in all devices sharing the microwave technology, at different levels of strengths. We further demonstrate empirically how most of the unstable feature can be annihilated, and speculate how the mechanism could be linked to atomic-scale two level systems. The described microwave/microkelvin facility is part of the EMP platform, and shall be used for further experiments within and below the millikelvin range., Comment: 14 pages with appendix; plus Erratum 17, 049901 (2022)

with the emergence of quantum technologies mastering thermal management is required, especially at the nanoscale. It is now accepted that thermal metamaterials (phononic diodes, themo-crystals) based on phonon manipulation are made possible especially at sub-Kelvin temperatures. In these extreme limits of low temperature and low dimension, phonon heat conduction enters into a quantum regime where the phonon exchange obeys the Landauer formalism. In this regime, phonon transport is governed by the value of the transmission coefficients between the ballistic conductor and the thermal reservoirs. Here, we report an ultra-sensitive thermal experiments made on a ballistic 1D phonon conductor using a new micro-platform suspended sensor. We achieved the measurement of thermal conductance with a resolution of $\Delta \mathrm{K}=\mathrm{K}$ of 1.5% and an unprecedented power sensitivity of few attoWatts around 100 mK. We show that the ballistic thermal transport is dominated by non-ideal transmission coefficients and not by the quantized thermal conductance of the nanowire itself. The measurements reveal scattering mechanisms dominated by phonon diffusion in the reservoirs. Since amorphous silicon nitride are used in that experiment we suspect that scattering of phonons on tunneling two Level systems (TLS) may be at the origin of the reduction of thermal transport. Complementary specific heat experiments are confirming that hypothesis of significant phonon-TLS scattering. The demonstration of the breakdown of the thermal conductance quantization is a major result for the phonon physics, showing that optimized thermal coupling to reservoirs from a 1D structure might be difficult to obtain. This limitation of heat transport in the quantum regime may have significant impacts on the design of modern thermal circuits and nanoelectronics (Josephson junction, quantum solid state devices). This high resolution experimental achievement gives new insight of heat transport in the quantum regime, a scientific goal that has remained uncertain till now.

The superconductor-insulator transition (SIT) is considered an excellent example of a quantum phase transition which 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, $c_{\rm p}$, measurements. Here, we use a unique highly sensitive experiment to measure $c_{\rm p}$ of two-dimensional granular Pb films through the SIT. The specific heat shows the usual jump at the mean field superconducting transition temperature $T_{\rm c}^{\rm {mf}}$ marking the onset of Cooper pairs formation. As the film thickness is tuned toward the SIT, $T_{\rm c}^{\rm {mf}}$ 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., 9 pages, 5 figures, 1 table

We report on experiments performed within the Knudsen boundary layer of a low-pressure gas. The non-invasive probe we use is a suspended nano-electro-mechanical string (NEMS), which interacts with $^4$He gas at cryogenic temperatures. When the pressure $P$ is decreased, a reduction of the damping force below molecular friction $\propto P$ had been first reported in Phys. Rev. Lett. Vol 113, 136101 (2014) and never reproduced since. We demonstrate that this effect is independent of geometry, but dependent on temperature. Within the framework of kinetic theory, this reduction is interpreted as a rarefaction phenomenon, carried through the boundary layer by a deviation from the usual Maxwell-Boltzmann equilibrium distribution induced by surface scattering. Adsorbed atoms are shown to play a key role in the process, which explains why room temperature data fail to reproduce it., Comment: Article plus supplementary material

We report on experiments addressing the non-linear interaction between a nano-mechanical mode and position fluctuations. The Duffing non-linearity transduces the Brownian motion of the mode, and of other non-linearly coupled ones, into frequency noise. This mechanism, ubiquitous to all weakly-nonlinear resonators thermalized to a bath, results in a phase diffusion process altering the motion: two limit behaviors appear, analogous to motional narrowing and inhomogeneous broadening in NMR. Their crossover is found to depend non-trivially on the ratio of the frequency noise correlation time to its magnitude. Our measurements obtained over an unprecedented range covering the two limits match the theory of Y. Zhang and M. I. Dykman, Phys. Rev. B 92, 165419 (2015), with no free parameters. We finally discuss the fundamental bound on frequency resolution set by this mechanism, which is not marginal for bottom-up nanostructures., Article plus Supplementary Material

International audience; It has been proposed for a long time now that the reduction of the thermal conductivity by reducing the phonon mean free path is one of the best way to improve the current performance of thermoelectrics. By measuring the thermal conductance and thermal conductivity of nanowires and thin films, we show different ways of increasing the phonon scattering from low temperature up to room temperature experiments. It is shown that playing with the geometry (constriction, periodic structures, nano-inclusions), from the ballistic to the diffusive limit, the phonon thermal transport can be severely altered in single crystalline semiconducting structures; the phonon mean free path being in consequence reduced. The diverse implications on thermoelectric properties will be eventually discussed.; Reduction du libre parcours moyen des phonons : de la physique des basses températures aux applications en thermoélectricitésthermoélectricitésà l'ambiante. Il a ´ eté proposé depuis longtemps maintenant que dimi-nuer la conductivité thermique en réduisant le libre parcours moyen des phonons est une des meilleures facons d'améliorer les performances actuelles des matériaux thermoélectriques. En mesurant la conductance thermique et la conductivité thermique de nanofils et de couches minces, nous montrons différentesmanì eres d'augmenter la diffusion des phonons des basses températures jusqu'` a température ambiante. Il est montré qu'en jouant sur la géométrie (constriction, structures périodiques, nano-inclusions), ` a partir de la limite balistique jusqu'` a la limite diffusive, le transport thermique phononique peutêtrepeutêtre de facon significative altéré dans des structures monocris-tallines semiconductrices ; le libre parcours moyen des phononsétantphononsétant réduit en conséquence. Enfin, les diverses implications sur les propriétés thermoélectriques seront discutées.

Nanocalorimetry is a technique that deals with any thermal measurement methods in which either the samples to be studied have a size in the range of the nanometer scale or the measured energies involved are of the order of the nanojoule or below Garden et al (Acta 492:16–28, 2009). In this paper, we show the results of two nanocalorimetric experiments. The first one is related to the measurement of specific heat on ultra-thin small systems (thin films) at low temperature. It is shown that such measurement can be sensitive to less than one monolayer of materials. The second one illustrates the efficiency of calorimetric studies sensitive at the nanoJoule on complex system (polymeric glass) at room temperature. We then discuss the potentiality of these experimental methods in the field of security: the measurement of either a very small mass or very small quantity of energy for the detection of tiny thermal events.

Using microfabrication techniques, it has become possible to make mechanical devices with dimensions in the micro and even in the nano scale domain. Allied to low temperature techniques, these systems have opened a new path in physics with the ultimate goal of reaching the quantum nature of a macroscopic mechanical degree of freedom (LaHaye et al. in Science 304:74, 2004). Within this field, materials research plays a significant role. It ranges from the fundamental nature of the dissipation mechanisms at the lowest temperatures, to the non-linear behavior of mechanical oscillators. We present experimental results on cantilever structures mimicking the well known “vibrating wire” technique, which present many advantages as far as the mechanical studies are concerned: the measurement is phase-resolved, they can be magnetomotive and electrostatically driven, and support extremely large displacements. Moreover, these devices can be advantageously used to study quantum fluids, making the link with conventional low temperature physics.

International audience; Polytetrafluoroethylene can be considered as a model for calorimetric studies of complex systems with thermodynamics transitions at ambient temperature. This polymer exhibits two phase transitions of different nature at 292 K and 303 K. We show that sensitive ac-calorimetry measurements allow us to study the thermodynamic behaviour of polytetrafluoroethylene when it is brought out of thermodynamic equilibrium. Thanks to the thermal modelisation of our calorimetric device, the frequency dependent complex heat capacity of this polymer is extracted. The temperature and frequency variations of the real and imaginary parts of the complex heat capacity are obtained when polytetrafluoroethylene undergoes its first-order structural phase transition at 292 K.

We report on measurements performed at low temperatures on a nanoelectromechanical system (NEMS) under (capacitive) parametric pumping. The excitations and detection schemes are purely electrical, and enable in the present experiment the straightforward measurement of forces down to about a femtonewton, for displacements of an Angstr\"om, using standard room temperature electronics. We demonstrate that a small (linear) force applied on the device can be amplified up to more than a 100 times, while the system is {\it truly moving}. We explore the dynamics up to about 50$~$nm deflections for cantilevers about 200$~$nm thick by 3$~$$\mu$m long oscillating at a frequency of 7$~$MHz. We present a generic modeling of nonlinear parametric amplification, and give analytic theoretical solutions enabling the fit of experimental results. We finally discuss the practical limits of the technique, with a particular application: the measurement of {\it anelastic damping} in the metallic coating of the device with an exceptional resolution of about 0.5$~$\%.

We have measured the thermal properties of suspended membranes from 10 K to 300 K for two amplitudes of internal stress (about 0.1 GPa and 1 GPa) and for two different thicknesses (50 nm and 100 nm). The use of the original 3 \omega -Volklein method has allowed the extraction of both the specific heat and the thermal conductivity of each SiN membrane over a wide temperature range. The mechanical properties of the same substrates have been measured at helium temperatures using nanomechanical techniques. Our measurements show that the thermal transport in freestanding SiN membranes is not affected by the presence of internal stress. Consistently, mechanical dissipation is also unaffected even though Qs increase with increasing tensile stress. We thus demonstrate that the theory developed by Wu and Yu [Phys. Rev. B 84, 174109 (2011)] does not apply to this amorphous material in this stress range. On the other hand, our results can be viewed as a natural consequence of the "dissipation dilution" argument [Y. L. Huang and P. R. Saulson, Rev. Sci. Instrum. 69, 544 (1998)] which has been introduced in the context of mechanical damping., Comment: 15 pages, 6 figures. Submitted to PRB

We have measured the interaction between $^4$He gas at 4.2$~$K and a high-quality nano-electro-mechanical string device for its first 3 symmetric modes (resonating at 2.2$~$MHz, 6.7$~$MHz and 11$~$MHz with quality factor $Q > 0.1$ million) over almost 6 orders of magnitude in pressure. This fluid can be viewed as the best experimental implementation of an almost-ideal monoatomic and inert gas which properties are tabulated. The experiment ranges from high pressure where the flow is of laminar Stokes-type presenting slippage, down to very low pressures where the flow is molecular. In the molecular regime, when the mean-free-path is of the order of the distance between the suspended nano-mechanical probe and the bottom of the trench we resolve for the first time the signature of the boundary (Knudsen) layer onto the measured dissipation. Our results are discussed in the framework of the most recent theories investigating boundary effects in fluids (both analytic approaches and Monte-Carlo DSMC simulations)., Editor's suggestion

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 1.4x10$^{-10}$ J/K at 8 K and 5.1x10$^{-8}$ J/K at 300 K. Measurements are performed using the 3$\omega$ method coupled to the V$\ddot{o}$lklein 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 3$\omega$ 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.

hh; The thermal conductance of straight and corrugated monocrystalline silicon nanowires has been measured between 0.3~K and 5~K. The difference in the thermal transport between corrugated nanowires and straight ones demonstrates a strong reduction in the mean free path of the phonons. This averaged mean free path is remarkably smaller than the smaller diameter of the nanowire, evidencing a phonon thermal transport reduced below the Casimir limit. Monte Carlo simulations highlight that this effect can be attributed to significant multiple scattering of ballistic phonons occuring on the corrugated surfaces. This result suggests an original approach to transforming a monocrystalline material into a phonon glass.

International audience; We present a high-sensitivity measurement technique for mechanical nanoresonators. Due to intrinsic nonlinear effects, different flexural modes of a nanobeam can be coupled while driving each of them on resonance. This mode-coupling scheme is dispersive and one mode resonance shifts with respect to the motional amplitude of the other. The same idea can be implemented on a single mode, exciting it with two slightly detuned signals. This two-tone scheme is used here to measure the resonance lineshape of one mode through a frequency shift in the response of the device. The method acts as an amplitude-to-frequency transduction which ultimately suffers only from phase noise of the local oscillator used and of the nanomechanical device itself. We also present a theory which reproduces the data without free parameters

International audience; We have characterized the mechanical resonance properties (both linear and nonlinear) of various doubly-clamped silicon nitride nanomechanical resonators, each with a different intrinsic tensile stress. The measurements were carried out at 4 K and the magnetomotive technique was used to drive and detect the motion of the beams. The resonant frequencies of the beams are in the megahertz range, with quality factors of the order of 104.We also measure the dynamic range of the beams and their nonlinear (Duffing) behaviour

We report on experiments performed at low temperatures on aluminum covered silicon nanoelectromechanical resonators. The substantial difference observed between the mechanical dissipation in the normal and superconducting states measured within the same device unambiguously demonstrates the importance of normal-state electrons in the damping mechanism. The dissipative component becomes vanishingly small at very low temperatures in the superconducting state, leading to exceptional values for the quality factor of such small silicon structures. A critical discussion is given within the framework of the standard tunneling model., SI not provided

We introduce a calorimetric approach to probe persistent currents in normal metal rings. The heat capacity of a large ensemble of silver rings is measured by nanocalorimetry under a varying magnetic field at different temperatures (60, 100, and 150 mK). Periodic oscillations versus magnetic field are detected in the phase signal of the temperature oscillations, though not in the amplitude (both of them directly linked to the heat capacity). The period of these oscillations (${\ensuremath{\Phi}}_{0}/2$, with ${\ensuremath{\Phi}}_{0}=h/e$ the magnetic flux quantum) and their evolution with temperature are in agreement with theoretical predictions. In contrast, the amplitude of the corresponding heat capacity oscillations (several ${k}_{\mathrm{B}}$) is two orders of magnitude larger than predicted by theory.

Decoherence is an essential mechanism that defines the boundary between classical and quantum behaviours, while imposing technological bounds for quantum devices. Little is known about quantum coherence of mechanical systems, as opposed to electromagnetic degrees of freedom. But decoherence can also be thought of in a purely classical context, as the loss of phase coherence in the classical phase space. Indeed the bridge between quantum and classical physics is under intense investigation, using in particular classical nanomechanical analogues of quantum phenomena. In the present work, by separating pure dephasing from dissipation, we quantitatively model the classical decoherence of a mechanical resonator: through the experimental control of frequency fluctuations, we engineer artificial dephasing. Building on the fruitful analogy introduced between spins/quantum bits and nanomechanical modes, we report on the methods available to define pure dephasing in these systems, while demonstrating the intrinsic almost-ideal properties of silicon-nitride beams. These experimental and theoretical results, at the boundary between classical nanomechanics and quantum information fields, are prerequisite in the understanding of decoherence processes in mechanical devices, both classical and quantum., Comment: SI not provided

A suspended system for measuring the thermal properties of membranes is presented. The sensitive thermal measurement is based on the 3$\omega$ dynamic method coupled to a V$\ddot{o}$lklein geometry. The device obtained using micro-machining processes allows the measurement of the in-plane thermal conductivity of a membrane with a sensitivity of less than 10nW/K (+/-$5x10^{-3}$Wm$^{-1}K^{-1}$ at room temperature) and a very high resolution ($\Delta K/K =10^{-3}$). A transducer (heater/thermometer) centered on the membrane is used to create an oscillation of the heat flux and to measure the temperature oscillation at the third harmonic using a Wheatstone bridge set-up. Power as low as 0.1nanoWatt has been measured at room temperature. The method has been applied to measure thermal properties of low stress silicon nitride and polycrystalline diamond membranes with thickness ranging from 100 nm to 400 nm. The thermal conductivity measured on the polycrystalline diamond membrane support a significant grain size effect on the thermal transport., Comment: 17 pages

International audience; We report on experiments performed in vacuum and at cryogenic temperatures on a tri-port nano-electro-mechanical (NEMS) device. One port is a very non-linear capacitive actuation, while the two others implement the magnetomotive scheme with a linear input force port and a (quasilinear) output velocity port. We present an experimental method enabling a full characterization of the nanomechanical device harmonic response: the non-linear capacitance function C(x) is derived, and the normal parameters k and m (spring constant and mass) of the mode under study are measured through a careful definition of the motion (in meters) and of the applied forces (in Newtons). These results are obtained with a series of purely electric measurements performed without disconnecting/reconnecting the device, and rely only on known DC properties of the circuit, making use of a thermometric property of the oscillator itself: we use the Young modulus of the coating metal as a thermometer, and the resistivity for Joule heating. The setup requires only three connecting lines without any particular matching, enabling the preservation of a high impedance NEMS environment even at MHz frequencies. The experimental data are fit to a detailed electrical and thermal model of the NEMS device, demonstrating a complete understanding of its dynamics. These methods are quite general and can be adapted (as a whole, or in parts) to a large variety of elecromechanical devices

A significant reduction in the N\'eel temperature of CoO ultrathin films is revealed by highly sensitive specific heat measurement. It is found that the films consist of weakly coupled antiferromagnetic (AF) grains. The ${T}_{N}$ reduction from large to small grain samples scales with the grain size reduction, according to the Binder theory of critical phenomena in systems of reduced dimensions. In these finite AF nanosystems, the intergrain exchange interaction is reduced by the presence of surface Co spins, weakly coupled to Co moments inside the grains.

Microfabrication techniques have made possible the realization of mechanical devices with dimensions in the micro- and nano-scale domain. At low temperatures, one can operate and study these devices in well-controlled conditions, namely low electrical noise and cryogenic vacuum, with the ability to use high magnetic fields and superconducting coating metals (Collin et al. in J. Low Temp. Phys. 150(5–6):739, 2008). Moreover, the temperature turns out to be a control parameter in the experimental study of mechanical dissipation processes, with the cryogenic environment ensuring that only low energy states are thermally populated. Immersed in a quantum fluid, these MEMS and NEMS devices (micro and nano electro-mechanical systems) can probe the excitations of the liquid at a smaller scale, with higher frequencies and better resolution than “classical” techniques (Triqueneaux et al. in Physica B 284:2141, 2000). We present experimental results obtained in vacuum on cantilever NEMS structures which can be both magnetomotive and electrostatically driven. The device is extremely sensitive with resolved displacements down to 1 A using conventional room-temperature electronics. It is calibrated in situ, and frequency/non-linearity can be tuned electrostatically. The design should allow parametric amplification to be used.

International audience; We report on experiments performed on a cantilever-based tri-port nano-electro-mechanical (NEMS) device. Two ports are used for actuation and detection through the magnetomotive scheme, while the third port is a capacitively coupled gate electrode. By applying a low frequency voltage signal on the gate, we demonstrate mixing in the mechanical response of the device, even for {\it low magnetomotive drives, without resorting to conduction measurements through the NEMS}. The technique can thus be used in particular in the linear regime, as an alternative to nonlinear mixing, for normal conducting devices. An analytic theory is presented reproducing the data without free parameters

By introducing a serpentine structure in a straight silicon nanowire, we have experimentally achieved a significant reduction in its phonon thermal conductance at low temperature $(Tl5\text{ }\text{K}.)$ The magnitude of this effect is one order of magnitude larger than expected based on a thermal resistors picture. With a more refined theoretical model that considers the frequency dependence of phonon transport, we are able to quantitatively account for the experimental results of straight and serpentine nanowires in the whole temperature range. This experimental demonstration of a large, purely geometry induced effect on nanoscale thermal conductance contrasts strikingly with the negligible effects reported on a different nanoscale system in a previous publication.

We report the microfabrication and operation of a highly sensitive ac-calorimeter designed to characterize small mass magnetic systems operating at very low frequencies (from 0.1 to 5 Hz) in a temperature range from 20 to 300 K. The calorimetric cell is built in the center of a 500 nm thick polymeric membrane of parylene C held up by a Cu frame. On both sides of the membrane defining a three layer structure, electrical leads, heater, and thermometer are deposited as thin film layers of NbN(x), with different nitrogen contents, taking benefit of the poor thermal conductance of niobium nitride to thermally isolate the system. This suspended structure ensures very low heat capacity addenda with values in the microJ/K over the 1 mm(2) area of the measurement cell. The structuring of the membrane along with suspending of the sensing part only by the parylene bridges leads to a highly reduced thermal link. The calorimeter has been characterized as a function of frequency, temperature, and magnetic field. The thermal link measured is really small reaching values well below 10(-8) W/K at 50 K. With these characteristics the frequency of adiabaticity is typically around few hertz and energy exchanges as small as 1 pJ can be detected. Measurements have been performed on Co/Au thin films and on the GdAl(2) microcrystal where the ferromagnetic phase transition is clearly evidenced.

HAL version : paper title is "Temperature fluctuations in the Ultimate Regime of Convection"; International audience; In 1997, a new turbulent regime has been observed in a Rayleigh-B'enard cell and has been interpreted as the "Ultimate Regime" of convection. This observation was based on global heat transfer measurements at very high Rayleigh numbers (Ra). Using a set-up similar to the one used in 1997, we examine the signature of this regime from within the flow itself. A systematic study of probe-size corrections shows that the earlier local temperature measurements within the flow were altered by an excessive size of thermometer, but not according to a theoretical model proposed in the literature. Using a probe one order of magnitude smaller than the one used previously, we find evidence that the transition to the very-high-Ra regime is indeed accompanied with a clear change in the statistics of temperature fluctuations in the flow

We report the measurement of thermal conductance of silicon nanowires at low temperature. It is demonstrated that the roughness at the nanometer scale plays a crucial role for the phonon transport in low-dimensional samples. To this end, using e-beam lithography, nanowires of size 200 nm by 100 nm and 10 microm long have been nanofabricated. Their thermal properties have been measured using the 3 omega method between 0.3 and 6 K. The change in the temperature behavior of the thermal conductance (quadratic temperature dependence of K(T)) is a signature of an intermediate regime lying between the classical Casimir regime and the quantum regime. The Casimir-Ziman model is used to show that this specific behavior originates in mesoscopic samples where the dominant phonon wavelength becomes commensurate to the characteristic length of the roughness of the nanowire surfaces.

We report on the dynamic measurements of thermal properties of nanosystems at very low temperatures. These techniques are based on the modulation of the temperature and hence leads to highly sensitive measurements. We will discuss the intrinsic limitations of these methods when the thermal properties of nano-objects are studied at very low temperatures, much below 1 K. Firstly, we will present thermal conductance measurements using the 3ω method. This technique is limited at low temperatures due to the significant increase of the mean free path. Secondly, heat capacity measurements using ac calorimetry are outlined, and again restrictions occur due to the continuous temperature gradient inherent to that technique. Propositions are made in order to overcome these limitations.

International audience; Membrane based nanocalorimeters have been developed for ac calorimetry experiments. It has allowed highly sensitive measurements of heat capacity from solid state physics to complex systems like polymers and proteins. In this article we review what has been developed in ac calorimetry toward the measurement of very small systems. Firstly, at low temperature ac calorimetry using silicon membrane permits the measurement of superconducting sample having geometry down to the nanometer scale. New phase transitions have been found in these nanosystems illustrated by heat capacity jumps versus the applied magnetic field. Secondly, a sensor based on ultra-thin polymer membrane will be presented. It has been devoted to thermal measurements of nanomagnetic systems at intermediate temperature (20K to 300K). Thirdly, three specific polyimide membrane based sensors have been designed for room temperature measurements. One is devoted to phase transitions detection in polymer, the second one to protein folding/unfolding studies and the third one will be used for the study of heat release in living cells. The possibility of measuring systems out of equilibrium will be emphasized.

International audience; In 1991 and 2001, two groups reported a qualitative change in the second order statistics of local temperature fluctuations in Rayleigh-Bénard cells for Rayleigh numbers in the range Ra ~ 10^{12} - 10^{13}. In the second group, this change was accompanied by an abrupt increase of the heat transfer, and these concomitant observations were interpreted as two signatures of the transition to Kraichnan's ''Ultimate Regime'' of convection. In the first group, a second change on temperature statistics was reported at lower Ra but no heat transfer enhancement was found. The 1991 observations have been questioned putting forward a finite size cut-off of the probe . If this finite size argument was valid, it should also hold for the 2001 study, as the probes had the same size (200 microns) and the cell heights used in 1991 and 2001 were respectively 40 and 20 cm. In this case, the only signature of the transition to the Ultimate Regime in the 2001 study would be the increase in heat transfer. To test the finite size argument, we designed a third experiment in a 40 cm-high cell using a specially developed probe 10 times smaller than the ones used previously. A micro-machining process was developed to produce NbN micro-thermometers with temperature-sensitive spot of typical size 20 microns x 1 microns deposited on a poorly conducting glass fiber of diameter 17 microns (or less) and few mm in length. Following the 2001 study, the temperature fluctuations were monitored using the exponent of the increments of the second order structure function. This quantity, which is formally equivalent to the traditional spectral density, provides in practice a more accurate observable thanks to a better immunity to noise. This new experiment shows a heat transfer transition between Ra=10^{12} and 10^{13} and, concomitantly, a qualitative change in the statistics of temperature fluctuations. The nature of this change is very similar to the one reported in 2001 with larger probes. Both present observations are consistent with the 2001 observation.

The study of thermal and thermodynamic properties at the nanoscale requires the development of samples with well controlled small scale structure, but also ultrasensitive and innovative experimental techniques for handling such samples. The challenge is to measure very small amounts of energy, and to control the flow of these energies on very small length scales. Such measurements generally depend on very precise temperature control made possible by ultrasensitive thermometry. From this point of view, electrical measurements afford unique solutions, because they are easily adapted to small scales by exploiting experimental techniques developed to measure electrical resistances. With the help of technologies transferred from micro- and nanoelectronics, devices and sensors can be designed to measure the physical properties of small systems. In this chapter, we begin by calculating the thermodynamic properties expected for condensed matter at low temperatures. The temperature dependence of the specific heat and the thermal conductivity are calculated for each type of heat carrier, viz., phonons and electrons. Special attention is paid to the specificities of low-dimensional systems: quantum effects on the thermal conductance and the heat capacity. We then describe the experimental aspects (techniques and instrumentation), by reviewing the various solutions available in thermometry, and methods for measuring the specific heat and thermal conductivity, in either steady state or dynamical contexts. We will see how to apply each technique on the submicron scale, illustrating with different suspended systems in the case of membranes and nanowires.

We study the influence of superconducting correlations on the electronic specific heat in a diffusive superconductor-normal metal-superconductor Josephson junction. We present a description of this system in the framework of the diffusive-limit Green's function theory, taking into account finite temperatures, phase difference as well as junction parameters. We find that proximity effect may lead to a substantial deviation of the specific heat as compared to that in the normal state, and that it can be largely tuned in magnitude by changing the phase difference between the superconductors. A measurement setup to confirm these predictions is also suggested., Comment: 4+ pages, 4 figures

International audience; The heat capacity $C_{p}$ of an array of independent aluminum rings has been measured under an external magnetic field $\vec{H}$ using highly sensitive ac-calorimetry based on a silicon membrane sensor. Each superconducting vortex entrance induces a phase transition and a heat capacity jump and hence $C_{p}$ oscillates with $\vec{H}$. This oscillatory and non-stationary behaviour measured versus the magnetic field has been studied using the Wigner-Ville distribution (a time-frequency representation). It is found that the periodicity of the heat capacity oscillations varies significantly with the magnetic field; the evolution of the period also depends on the sweeping direction of the field. This can be attributed to a different behavior between expulsion and penetration of vortices into the rings. A variation of more than 15\% of the periodicity of the heat capacity jumps is observed as the magnetic field is varied. A description of this phenomenon is given using an analytical solution of the Ginzburg-Landau equations of superconductivity.

A sensor for thermal and thermodynamic measurements of small magnetic systems has been designed and built. It is based on a 5 μ m -thick suspended polymer membrane, which has a very low heat capacity ( ≈ 10 - 6 J / K at nitrogen temperature), and on which a heater and a highly sensitive thermometer are deposited. The sensor properties have been characterized as a function of temperature and frequency. Energy exchanges as small as 1 picojoule ( 10 - 12 J ) were detected in the 40–300 K temperature range. Such values correspond to those required for measuring the thermal signatures occurring during magnetization reversal in very thin samples (typically 10 nm thick), which would be deposited on the membrane. It is expected that this method will constitute a powerful tool in view of analyzing magnetization reversal processes in magnetic nanosystems, e.g. exhibiting the exchange–spring and exchange–bias phenomena.

We have performed thermal conductance measurements on individual single crystalline silicon suspended nanowires. The nanowires (130 nm thick and 200 nm wide) are fabricated by e-beam lithography and suspended between two separated pads on Silicon On Insulator (SOI) substrate. We measure the thermal conductance of the phonon wave guide by the 3 method. The cross-section of the nanowire approaches the dominant phonon wavelength in silicon which is of the order of 100 nm at 1K. Above 1.3K the conductance behaves as T3, but a deviation is measured at the lowest temperature which can be attributed to the reduced geometry.

We present the first measurements of thermal signatures of the Little-Parks effect using a highly sensitive nanocalorimeter. Small variations of the heat capacity $C\_p$ of 2.5 millions of non interacting micrometer-sized superconducting rings threaded by a magnetic flux $\Phi$ have been measured by attojoule calorimetry. This non-invasive method allows the measurement of thermodynamic properties -- and hence the probing of the energy levels -- of nanosystems without perturbing them electrically. It is observed that $C\_p$ is strongly influenced by the fluxoid quantization (Little-Parks effect) near the critical temperature $T\_c$. The jump of $C\_p$ at the superconducting phase transition is an oscillating function of $\Phi$ with a period $\Phi\_0=h/2e$, the magnetic flux quantum, which is in agreement with the Ginzburg-Landau theory of superconductivity., Comment: To be published in Physical Review B, Rapid Communications

We report the first experimental evidence of nontrivial thermal behavior of the simplest mesoscopic system - a superconducting loop. By measuring the specific heat C of an array of 450,000 noninteracting aluminum loops with very high accuracy of ~20 fJ/K, we show that the loops go through a periodic sequence of phase transitions (with period of an integer number of magnetic flux quanta) as the magnetic flux threading each loop is increased. The transitions are well described by the Ginzburg-Landau theory and are accompanied by discontinuities of C of only several thousands of Boltzmann constants k_B., Comment: RevTeX, 4 pages, 4 figures

We have measured the ground state of ferromagnetic Josephson junctions using a single dc SQUID (superconducting quantum interference device).We show that the Josephson coupling is either positive (0 coupling) or negative ($\ensuremath{\pi}$ coupling) depending on the ferromagnetic layer thickness. As expected, the sign change of the Josephson coupling is observed as a shift of half a quantum flux in the SQUID diffraction pattern when operating in the linear limit.

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.

International audience; The thermal properties of suspended thin films prepared by the micro-machining process have been measured using the 3! dynamic method coupled to a Volklein geometry. A transducer (heater/thermometer) centered on the membrane is driven by an ac current causingperiodic thermal oscillations. The measurement of the temperature oscillation on the membrane is made at the third harmonic using a Wheatstone bridge set up. Here by coupling the 3! method to a Voolklein geometry (suspended membrane) we obtained a highly sensitive techniqueto measure the thermal conductance with a resolution of (..K=K = 10-3) and a sensitivity of the order of nanoWatt/K, thanks to a very sensitive niobium nitride thermometry. This method is applied to measure the in-plane thermal conductivity of 100 nm silicon nitride membrane, inthe temperature range of 10-275 K

International audience; Asymmetry in the magnetization reversal processes of exchange bias Co/CoO rectangular nanodot arrays is revealed by magnetic force microscopy. One-step switching is found along the descending branch of the hysteresis cycle whereas rotational or multidomain processes are involved along the ascending branch. From a statistical analysis of the environment of each dot during reversal, it is concluded that dipolar interactions do not significantly influence the magnetization reversal processes.

Thermal conductance measurements are presented on nanostructured individual single crystalline Si suspended nanowires at low temperature. The mechanically suspended silicon nanowires with different sizes (130nm by 100nm and 130 nm by 200nm) are fabricated by e-beam lithography from Silicon On Insulator (SOI) substrate. The thermal conductance of the ballistic phonon wave guides is measured by means of an ac technique, the 3 ω method, using a niobium nitride transducer deposited on top. The geometry of the nanowire is chosen to match the order of magnitude of the dominant phonon wave length in silicon at low temperature which is of the order of 100 nm at 1K. A regular cubic law is observed at high temperature, but a deviation is measured at the lowest temperature with a saturation of thermal conductance which is attributed to the reduced geometry of the nanowire. The experimental results are in agreement with the Casimir theory taking into account the surface state (roughness) of the silicon wire. The deviation observed at low temperature is a clear signature of the consequence of the low dimentionality of the wire as well as the surface effects on the phonon transport.

International audience; Phase transitions in superconducting mesoscopic disks have been studied over the $H-T$ phase diagram through heat capacity measurement of an array of independent aluminium disks. These disks exhibit non periodic modulations versus $H$ of the height of the heat capacity jump at the superconducting to normal transition. This behaviour is attributed to giant vortex states characterized by their vorticity $L$. A crossover from a bulk-like to a mesoscopic behaviour is demonstrated. $C_{\rm p}$ versus $H$ plots exhibit cascades of phase transitions as $L$ increases or decreases by one unity, with a strong hysteresis. Phase diagrams of giant vortex states inside the superconducting region are drawn in the vortex penetration and expulsion regimes and phase transitions driven by temperature between vortex states are thus predicted in the zero field cooled regime before being experimentally evidenced.