Phase sensitive absolute amplitude detection of surface vibrations using homodyne interferometry without active stabilization

A detection scheme for obtaining phase and absolute amplitude information of surface vibrations on microacoustic components using homodyne laser interferometry is described. The scheme does not require active stabilization of the optical path length of the interferometer. The detection setup is realized in a homodyneMichelson interferometer configuration, and selected measurements on a 374 MHz surface acoustic wave fan-shaped filter and two different piezoelectrically actuated micromechanical resonators are presented to demonstrate the performance of the instrument. With the current detection electronics, the interferometer is capable of detecting out-of-plane surface vibrations up to 2 GHz with a lateral resolution of better than 1 μm and with a minimum detectable vibration amplitude of ∼1 pm.Peer reviewe

Characterization of energy trapping in a bulk acoustic wave resonator

Acoustic wave fields both within the active electrode area of a solidly mounted 1.8 GHz bulk acoustic waveresonator, and around it in the surrounding region, are measured using a heterodyne laser interferometer. Plate-wave dispersion diagrams for both regions are extracted from the measurement data. The experimental dispersion data reveal the cutoff frequencies of the acoustic vibration modes in the region surrounding the resonator, and, therefore, the energy trapping range of the resonator can readily be determined. The measureddispersionproperties of the surrounding region, together with the abruptly diminishing amplitude of the dispersion curves in the resonator, signal the onset of acoustic leakage from the resonator. This information is important for verifying and further developing the simulation tools used for the design of the resonators. Experimental wave field images, dispersion diagrams for both regions, and the threshold for energy leakage are discussed.Peer reviewe

Gap Anisotropy and de Haas-van Alphen Effect in Type-II Superconductors

We present a theoretical study on the de Haas-van Alphen (dHvA) oscillation in the vortex state of type-II superconductors, with a special focus on the connection between the gap anisotropy and the oscillation damping. Numerical calculations for three different gap structures clearly indicate that the average gap along extremal orbits is relevant for the magnitude of the extra damping, thereby providing a support for experimental efforts to probe gap anisotropy through the dHvA signal. We also derive an analytic formula for the extra damping which gives a good fit to the numerical results.Comment: 5 pages, 1 figure, changes in Introductio

Quasiparticle Density of States of Clean and Dirty s-Wave Superconductors in the Vortex State

The quasiparticle density of states (DOS) in the vortex state has been probed by specific heat measurements under magnetic fields (H) for clean and dirty s-wave superconductors, Y(Ni1-xPtx)2B2C and Nb1-xTaxSe2. We find that the quasiparticle DOS per vortex is appreciably H-dependent in the clean-limit superconductors, while it is H-independent in the dirty superconductors as expected from a conventional rigid normal electron core picture. We discuss possible origins for our observations in terms of the shrinking of the vortex core radius with increasing H.Comment: 5 pages, 4 figures, to appear in J. Phys. Soc. Jpn. Vol. 68 No.

Evidence for a Second Order Phase Transition in Glasses at Very Low Temperatures -- A Macroscopic Quantum State of Tunneling Systems

Dielectric measurements at very low temperature indicate that in a glass with the eutectic composition BaO-Al$_2$O$_3$-SiO$_2$ a phase transition occurs at 5.84 mK. Below that temperature small magnetic fields of the order of 10 $\mu$T cause noticeable changes of the dielectric constant although the glass is insensitive to fields up to 20 T above 10 mK. The experimental findings may be interpreted as the signature of the formation of a new phase in which many tunneling systems perform a coherent motion resulting in a macroscopic wave function.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let

Extraction of lateral eigenmode properties in thin film bulk acoustic wave resonator from interferometric measurements

A heterodyne laser interferometer is used to study acoustic wave fields excited in a 1.8 GHz AlN thin film bulk acoustic waveresonator. The electrical response of the resonator exhibits a strong thickness resonance onto which spurious modes, caused by lateral standing plate waves, are superposed. Optical interferometermeasurements are used to extract dispersion curves of the laterally propagating waves responsible for the spurious responses. A discrete eigenmode spectrum due to the finite lateral dimensions of the resonator is observed. An equivalent circuit model for a multimode resonator is fitted to the mechanical resonator response extracted along a single curve in the dispersion diagram, and is used to determine properties, such as Q-values, of the individual lateral eigenmodes.Measuredwave field images, extracted dispersion curves, and the eigenmode spectrum with the model fitting results are presented.Peer reviewe

Local density of states in the vortex lattice in a type II superconductor

Local density of states (LDOS) in the triangular vortex lattice is investigated based on the quasi-classical Eilenberger theory. We consider the case of an isotropic s-wave superconductor with the material parameter appropriate to NbSe_2. At a weak magnetic field, the spatial variation of the LDOS shows cylindrical structure around a vortex core. On the other hand, at a high field where the core regions substantially overlap each other, the LDOS is sixfold star-shaped structure due to the vortex lattice effect. The orientation of the star coincides with the experimental data of the scanning tunneling microscopy. That is, the ray of the star extends toward the nearest-neighbor (next nearest-neighbor) vortex direction at higher (lower) energy.Comment: 10 pages, RevTex, 32 figure

Glass-Like Heat Conduction in High-Mobility Crystalline Semiconductors

The thermal conductivity of polycrystalline semiconductors with type-I clathrate hydrate crystal structure is reported. Ge clathrates (doped with Sr and/or Eu) exhibit lattice thermal conductivities typical of amorphous materials. Remarkably, this behavior occurs in spite of the well-defined crystalline structure and relatively high electron mobility ($\sim 100 cm^2/Vs$). The dynamics of dopant ions and their interaction with the polyhedral cages of the structure are a likely source of the strong phonon scattering.Comment: 4 pages, 3 postscript figures, to be published, Phys. Rev. Let

Ginzburg-Landau-Gor'kov Theory of Magnetic oscillations in a type-II 2-dimensional Superconductor

We investigate de Haas-van Alphen (dHvA) oscillations in the mixed state of a type-II two-dimensional superconductor within a self-consistent Gor'kov perturbation scheme. Assuming that the order parameter forms a vortex lattice we can calculate the expansion coefficients exactly to any order. We have tested the results of the perturbation theory to fourth and eight order against an exact numerical solution of the corresponding Bogoliubov-de Gennes equations. The perturbation theory is found to describe the onset of superconductivity well close to the transition point $H_{c2}$. Contrary to earlier calculations by other authors we do not find that the perturbative scheme predicts any maximum of the dHvA-oscillations below $H_{c2}$. Instead we obtain a substantial damping of the magnetic oscillations in the mixed state as compared to the normal state. We have examined the effect of an oscillatory chemical potential due to particle conservation and the effect of a finite Zeeman splitting. Furthermore we have investigated the recently debated issue of a possibility of a sign change of the fundamental harmonic of the magnetic oscillations. Our theory is compared with experiment and we have found good agreement.Comment: 39 pages, 8 figures. This is a replacement of supr-con/9608004. Several sections changed or added, including a section on the effect of spin and the effect of a conserved number of particles. To be published in Phys. Rev.

The crossover from propagating to strongly scattered acoustic modes of glasses observed in densified silica

Spectroscopic results on low frequency excitations of densified silica are presented and related to characteristic thermal properties of glasses. The end of the longitudinal acoustic branch is marked by a rapid increase of the Brillouin linewidth with the scattering vector. This rapid growth saturates at a crossover frequency Omega_co which nearly coincides with the center of the boson peak. The latter is clearly due to additional optic-like excitations related to nearly rigid SiO_4 librations as indicated by hyper-Raman scattering. Whether the onset of strong scattering is best described by hybridization of acoustic modes with these librations, by their elastic scattering (Rayleigh scattering) on the local excitations, or by soft potentials remains to be settled.Comment: 14 pages, 6 figures, to be published in a special issue of J. Phys. Condens. Matte