Ballistic Phonon Propagation Research Articles

Search for fourth sound propagation in supersolid He4

A systematic study is carried out to search for fourth sound propagation solid He4 samples below 500mK down to 40mK between 25 and 56bar using the techniques of heat pulse generator and titanium superconducting transition edge bolometer. If solid He4 is endowed with superfluidity below 200mK, as indicated by recent torsional oscillator experiments, theories predict fourth sound propagation in such a supersolid state. If found, fourth sound would provide convincing evidence for superfluidity and a new tool for studying the new phase. The search for a fourth sound-like mode is based on the response of the bolometers to heat pulses traveling through cylindrical samples of solids grown with different crystal qualities. Bolometers with increasing sensitivity are constructed. The heater generator amplitude is reduced to the sensitivity limit to search for any critical velocity effects. The fourth sound velocity is expected to vary as ∝ρs∕ρ. Searches for a signature in the bolometer response with such a characteristic temperature dependence are made. The measured response signal has not so far revealed any signature of a new propagating mode within a temperature excursion of 5μK from the background signal shape. Possible reasons for this negative result are discussed. Prior to the fourth sound search, the temperature dependence of heat pulse propagation was studied as it transformed from “second sound” in the normal solid He4 to transverse ballistic phonon propagation. Our work extends the studies of [V. Narayanamurti and R. C. Dynes, Phys. Rev. B 12, 1731 (1975)] to higher pressures and to lower temperatures. The measured transverse ballistic phonon propagation velocity is found to remain constant (within the 0.3% scatter of the data) below 100mK at all pressures and reveals no indication of an onset of supersolidity. The overall dynamic thermal response of solid to heat input is found to depend strongly on the sample preparation procedure.

Preliminary Report: Heat Pulse Propagation in Solid 4He up to 56 bar Between 40 and 500 mK

Heat pulse propagation in the solid 4He has been studied between 40 and 500 mK. Response to heat pulses are detected by a titanium film superconducting transition edge bolometer. Crossover behavior from second sound in normal solid above 500 mK to ballistic propagation below 200 mK is observed. Detailed study is made to search for possible modification of this propagation behavior by the appearance of supersolidity. It is found, that the ballistic phonon propagation velocity remains constant, within 0.3% scatter of data, below 100 mK at all pressures measured between 25 and 56 bar. The temporal evolution of the detected pulse shape has not revealed any anomaly below 200 mK.

Thermal budget of superconducting digital circuits at subkelvin temperatures

Superconducting single-flux-quantum (SFQ) circuits have so far been developed and optimized for operation at or above helium temperatures. The SFQ approach, however, should also provide potentially viable and scalable control and readout circuits for Josephson-junction qubits and other applications with much lower, millikelvin, operating temperatures. This paper analyzes the overheating problem which becomes important in this temperature range. We suggest a thermal model of the SFQ circuits at subkelvin temperatures and present experimental results on overheating of electrons and silicon substrate which support this model. The model establishes quantitative limitations on the dissipated power both for “local” electron overheating in resistors and “global” overheating due to ballistic phonon propagation along the substrate. Possible changes in the thermal design of SFQ circuits in view of the overheating problem are also discussed.

Ballistic Phonon Thermal Transport in Multiwalled Carbon Nanotubes

We report electrical transport experiments, using the phenomenon of electrical breakdown to perform thermometry, that probe the thermal properties of individual multiwalled carbon nanotubes. Our results show that nanotubes can readily conduct heat by ballistic phonon propagation. We determine the thermal conductance quantum, the ultimate limit to thermal conductance for a single phonon channel, and find good agreement with theoretical calculations. Moreover, our results suggest a breakdown mechanism of thermally activated C-C bond breaking coupled with the electrical stress of carrying approximately 10(12) A/m2. We also demonstrate a current-driven self-heating technique to improve the conductance of nanotube devices dramatically.

Nondiffracting waves in anisotropic media.

Recently the physics of ballistic phonon propagation in anisotropic crystals has been studied with new phonon-imaging methods. In this paper we consider nondiffracting waves that can propagate in anisotropic crystals and analyze their properties that emerge specifically due to the anisotropy. We further present a detailed generation and detection scheme for the experimental verification of the wave modes considered.

Sound and heat absorption by a two-dimensional electron gas in an odd-integer quantized Hall regime

The absorption of bulk acoustic phonons in a two-dimensional (2D) GaAs/AlGaAs heterostructure is studied (in the clean limit) where the 2D electron-gas (2DEG), being in an odd-integer quantum-Hall state, is in fact a spin dielectric. Of the two channels of phonon absorption associated with excitation of spin waves, one, which is due to the spin-orbit (SO) coupling of electrons, involves a change of the spin state of the system and the other does not. We show that the phonon-absorption rate corresponding to the former channel (in the paper designated as the second absorption channel) is finite at zero temperature ($T$), whereas that corresponding to the latter (designated as the first channel) vanishes for $T\to 0$. The long-wavelength limit, being the special case of the first absorption channel, corresponds to sound (bulk and surface) attenuation by the 2DEG. At the same time, the ballistic phonon propagation and heat absorption are determined by both channels. The 2DEG overheat and the attendant spin-state change are found under the conditions of permanent nonequilibrium phonon pumping.

Real space resolved investigation of ballistic electron transport in Bi single crystals

In pure single crystals at low temperatures the mean free path l * of electrons can reach values of several 100 μm. The propagation of these so-called ballistic electrons can be probed by local excitation and subsequent detection within a distance of the order l *. In our experiment a small spot on the sample surface is illuminated by laser light. Thermally excited electrons propagate from the illuminated spot (source) into the crystal. A Cu point contact is fixed to the opposite sample surface as a detector (collector). By measuring the voltage at the point contact as a function of the source position the highly anisotropic flux of electrons can be probed in real space. A calculation taking into account the band structure of bismuth is in good agreement with the experiment. In addition to a contribution due to electronic transport, the signal shows a contribution associated with ballistic phonon propagation. The electron and phonon contributions can be distinguished by their response to an applied magnetic field. In a second experiment, a Cu point contact is used as the electron source. Here the collector signal shows only the contribution of electrons but no phonon contributions.

Investigation of Ballistic Phonon Propagation in Quartz by the Time‐of‐Flight Method

AbstractThe ballistic phonon propagation in α‐quartz is measured in directions z and y, for different bolometer currents, by the time‐of‐flight method. For higher currents on time‐dependent bolometer signal curves more singularities are observed than it was reported earlier. On the basis of calculations the observed singularities are explained as separately detected phonon modes and the increase of their number is connected with a diminution of the bolometer active area by increase of bolometer current for very thin aluminium bolometers.

Transmission of high-frequency ballistic phonons in superconducting In, Sn, and Pb films.

Phonon transmission through superconducting In, Sn, and Pb films (with thicknesses of 4 and 8 \ensuremath{\mu}m) is studied with a heat-pulse technique using a semiconductor Si:P detachable bolometer as the phonon detector. Below the critical temperature of the films, ballistic-phonon propagation is observed. From the dependence of the phonon transmission on the incident power and film thickness, we calculate the mean free path of phonons at the gap frequency. The phonon transmission amount changes when a magnetic field is applied and is also different if the field is parallel or perpendicular to the film. By a simple model based on the Landau laminar model for intermediate states, the critical field for the films can be calculated. Good agreement (for In and Sn) with the theoretical values is obtained.

Detection of elementary particles using silicon crystal acoustic detectors with titanium transition edge phonon sensors

We are developing silicon crystal acoustic detectors (SiCADs), which operate at cryogenic temperatures and use thin-films of superconducting titanium ( T c = 435 mK) to sense phonons generated when an incident particle scatters off a nucleus or electron in pure and cold (< 1 K) silicon. Our motivation for developing SiCADs includes their many direct applications to neutrino physics (e.g. to perform neutrino oscillation experiments), particle astrophysics (e.g. to measure the solar neutrino spectrum or search for the hypothetical dark matter in the universe) and solid state physics (e.g. to study phonon dynamics and focusing effects). We have fabricated and characterized multi-channel SiCADs with phonon sensors instrumented on both sides of a Si wafer substrate, and have used these devices to detect radioactive sources of gamma and X-rays, alpha particles and neutrons with incident energies of < 6 keV to 10 MeV. We discuss our results in terms of ballistic and quasi-diffusive phonon propagation, and show evidence for ballistic phonon focusing effects in [100] silicon.

Nonequilibrium phonon detectors

Many experiments in nuclear and particle physics would benefit from a device capable of detecting nonionizing events with a low energy threshold. We report on experimental tests of a low-temperature detector based on the registration of nonequilibrium phonons. The device is composed of a silicon single crystal with superconducting tunnel junctions (Al/Al2O3/Al) evaporated onto its surface. In first experiments a 20×10×3 mm3 crystal at an operating temperature of T = 0.37 K was tested with 5.5-MeV α particles. Pulse-height analysis and the timing of pulses in different junctions is shown to yield position and energy resolution. An energy threshold of 250 keV was estimated for absorption anywhere in the crystal. A position resolution of 0.6 mm was determined over a sensitive length of 10 mm. Though phonon focusing effects were registered in the vicinity of the [001] direction, scattered and reflected phonons dominate the signals in the general case. The experimental results are discussed in terms of ballistic and quasidiffuse phonon propagation. To improve the energy threshold, the operating temperature was lowered to 60 mK in order to increase junction sensitivity and a weak thermal coupling of the absorber to the heat bath was introduced to force phonons to leave the crystal via the detecting junctions. Si crystals of up to 20×20×10 mm3 size were used in these second experiments. With a 4 cm3 crystal a threshold of 270 keV was obtained. The performance in these experiments at 60 mK, however, was limited by exceptionally high values of the normal conducting junction resistances. With a reasonable value of this parameter it should be possible to realize an energy threshold of 1 keV with absorbers of a volume of several cm3.

Observation of alpha-induced ballistic phonon time-of-flight using multi-channel silicon crystal acoustic detectors

We have developed a technique for producing double-sided multi-channel silicon crystal acoustic detectors (SiCADs). These detectors, which are operated at = 400 mK and use 40 nm thick films of supercond ucting Ti as the phonon sensors, have been used in time-coincidence experiments to study the propagation of alpha-induced ballistic phonons through 1 mm of crystalline Si.

Observation of alpha-induced ballistic phonon time-of-flight using multi-channel silicon crystal acoustic detectors

We have developed a technique for producing double-sided multi-channel silicon crystal acoustic detectors (SiCADs). These detectors, which are operated at = 400 mK and use 40 nm thick films of supercond ucting Ti as the phonon sensors, have been used in time-coincidence experiments to study the propagation of alpha-induced ballistic phonons through 1 mm of crystalline Si.

Ballistic phonon signal for imaging crystal properties

We present a summarizing overview of our recent experiments using the ballistic phonon signal generated by low temperature scanning electron microscopy for imaging defect structures and the anisotropic elastic properties (phonon-focusing effect) in single-crystal materials. Extensive studies have been performed with dielectric crystals (sapphire and α-quartz) and semiconductors (GaAs, silicon and germanium). With a single phonon detector of small area (superconducting bolometers of size between 2 μm × 2 μm and 10 μm × 10 μm), we have obtained two-dimensional images with a lateral resolution reaching about 5 μm. Using superconducting tunnel junctions as frequency-selective phonon detectors, dispersive effects in the ballistic phonon propagation have been observed. The application of more than one phonon detector placed at different locations allows stereoscopic observations and yields information on the defect structure in all three dimensions. Using computer-controlled electron beam scanning and digital data processing, techniques for contrast enhancement in the three-dimensional acoustic imaging of defect structures have been developed. A three-dimensional acoustic tomography principle based on the ballistic phonon signal in combination with a detector array is outlined. Our present experiments indicate that a spatial resolution of about 20 μm in all three dimensions can be achieved with this acoustic imaging principle.

Characterization of single-crystalline GaAs by imaging with ballistic phonons

Ballistic phonon propagation in single-crystalline [001]-oriented gallium arsenide has been studied using low-temperature scanning electron microscopy for imaging. Deviations in the phonon focusing pattern due to dispersion effects were found by comparing the phonon images to theoretical calculations of the long-wavelength limit. The phonon propagation behavior in, samples cut from differently prepared wafers has been investigated. For highly impure crystals we found a pronounced increase of the diffusive signal component at the expense of the ballistic one. Samples with varying dislocation densities also showed a sensitive dependence, of the ballistic phonon propagation on these crystal defects. For focusing calculations considering elastic scattering processes the diffusivity of the phonons could be determined as a function of the mean scattering length. We have found phonon mean free paths of 0.35 mm to 0.80 mm for the various GaAs crystals.

Dispersive anisotropic ballistic phonon propagation in [100] GaAs

We report experimental observations of the phonon focusing pattern in [100] GaAs using low temperature electron beam scanning for phonon generation. The typical dispersive effects for high-frequency phonons expected from the calculations by Tamura have clearly been observed using PbIn tunnel junctions for phonon detection. The quantitative comparison of our experimental results with the frequency dependent calculations by Tamura allowed to determine the dominant phonon frequencies contributing to the detector signal in our different experiments. Above the temperature of the λ-point the dominant phonon frequencies appear to be shifted considerably to lower values, which could be explained by a heating effect in the liquid-He layer adjacent to the tunnel junction detector. By comparing the observed magnitude of the detector signal with different theoretical treatments of the detector response, we have found satisfactory agreement for a model where the perturbation due to the high-frequency phonons is restricted to the base electrode of the detector reached first by the phonons following their passage through the crystal.

Propagation of ballistic phonons in crystals and their detection with a detachable bolometer

Ballistic phonons were generated in single-crystalline sapphire samples by scanning the crystal surface with the electron beam in a scanning electron microscope equipped with a low-temperature stage. The phonons were detected using a superconducting thin film (granular Al) bolometer configuration which could be detached from the sample crystal (allowing repeated use). We have applied these experimental techniques for obtaining phonon images of laser-drilled holes in the sample crystals, achieving a spatial resolution of better than 10 μm.

A new detector of nuclear radiation based on ballistic phonon propagation in single crystals at low temperatures

The absorption of 5.5 MeV α-particles in a silicon single crystal kept at T=0.38 K was detected by an array of superconducting tunnel diodes evaporated onto the surface of the crystal. Signals were mediated by phonons propagating ballistically within the crystal. The phon flux proved anisotropic due to phonon focusing effects. This anisotropy and the study of time resolved signal correlations between the diodes allowed us to distinguish two spots of α-absorption separated by 0.75 mm. This detection principle might be applicable in a variety of experiments in nuclear and elementary particle physics.

Imaging of spatial structures in crystals with ballistic phonons

Ballistic phonon propagation in single crystals has been used for imaging defect structures in bulk material. We have realized this principle by means of low-temperature scanning electron microscopy. As model cases we have imaged laser drilled holes in single-crystalline sapphire and α-quartz samples. Comparing the acoustic images with those obtained by optical transmission microscopy, we found that fine structure seen optically was well reproduced acoustically. In addition strain fields due to plastic deformations could clearly be imaged acoustically. The spatial resolution of our imaging technique is estimated to be a few micrometer. By using two or more phonon detectors, three-dimensional imaging of spatial inhomogeneities becomes possible.

Imaging of oxide precipitates in silicon with ballistic phonons

Ballistic phonons were generated at low temperatures in nearly single-crystalline silicon by scanning the specimen surface with an electron beam. At the opposite sample surface the ballistic phonons were detected with two small-area bolometers placed at different locations. For a Si specimen which had been annealed for 150 h at 1050 °C, the ballistic phonon image contained fine structure which could be attributed to oxide precipitates. Comparing the phonon images obtained with the two bolometers, we concluded that the structural inhomogeneities affecting the ballistic phonon propagation were located far from the specimen surface scanned by the electron beam. With these experiments a new principle of three-dimensional tomography based on ballistic phonons has been demonstrated.