Low-temperature Properties Of Amorphous Solids Research Articles

Anomalous low-energy properties in amorphous solids and the interplay of electric and elastic interactions of tunneling two-level systems

Tunneling two-level systems (TLSs), generic to amorphous solids, dictate the low-temperature properties of amorphous solids and dominate noise and decoherence in quantum nano-devices. The properties of the TLSs are generally described by the phenomenological standard tunneling model. Yet, significant deviations from the predictions of this model found experimentally suggest the need for a more precise model in describing TLSs. Here we show that the temperature dependence of the sound velocity, dielectric constant, specific heat, and thermal conductivity, can be explained using an energy-dependent TLS density of states reduced at low energies due to TLS-TLS interactions. This reduction is determined by the ratio between the strengths of the TLS-TLS interactions and the random potential, which is enhanced in systems with dominant electric dipolar interactions.

Spatial structure of quasilocalized vibrations in nearly jammed amorphous solids

The low-temperature properties of amorphous solids are widely believed to be controlled by low-frequency quasi-localized modes. What governs their spatial structure and density is however debated. We study these questions numerically in very large systems as the jamming transition is approached and the pressure p vanishes. We find that these modes consist of an unstable core in which particles undergo the buckling motions and decrease the energy, and a stable far-field component which increases the energy and prevents the buckling of the core. The size of the core diverges as $p^{-1/4}$ and its characteristic volume as $p^{-1/2}$ These features are precisely those of the anomalous modes known to cause the Boson peak in the vibrational spectrum of weakly-coordinated materials. From this correspondence we deduce that the density of quasi-localized modes must go as $g_{\mathrm{loc}}(\omega) \sim \omega^4/p^2$ , in agreement with previous observations. Our analysis thus unravels the nature of quasi-localized modes in a class of amorphous materials.

Growing timescales and lengthscales characterizing vibrations of amorphous solids

Low-temperature properties of crystalline solids can be understood using harmonic perturbations around a perfect lattice, as in Debye's theory. Low-temperature properties of amorphous solids, however, strongly depart from such descriptions, displaying enhanced transport, activated slow dynamics across energy barriers, excess vibrational modes with respect to Debye's theory (i.e., a boson peak), and complex irreversible responses to small mechanical deformations. These experimental observations indirectly suggest that the dynamics of amorphous solids becomes anomalous at low temperatures. Here, we present direct numerical evidence that vibrations change nature at a well-defined location deep inside the glass phase of a simple glass former. We provide a real-space description of this transition and of the rapidly growing time- and lengthscales that accompany it. Our results provide the seed for a universal understanding of low-temperature glass anomalies within the theoretical framework of the recently discovered Gardner phase transition.

“Tunneling Two-Level Systems” Model of the Low-Temperature Properties of Glasses: Are “Smoking-Gun” Tests Possible?

Following a brief review of the "two-level (tunneling) systems" model of the low-temperature properties of amorphous solids ("glasses"), we ask whether it is in fact the unique explanation of these properties as is usually assumed, concluding that this is not necessarily the case. We point out that (a) one specific form of the model is already experimentally refuted and (b) that a definitive test of the model in its most general form, while not yet carried out, would appear to be now experimentally feasible.

Beyond the tunneling model: quantum phenomena in ultracold glasses

The low-temperature properties of amorphous solids are governed by atomic tunneling systems, the parameters of which are widely distributed due to the irregular structure of these materials. The standard tunneling model (STM) approximates such tunneling systems by particles moving in a double-well potential. Furthermore it assumes a constant distribution of the relevant parameters and in this way allows an understanding of many low-temperature properties of glasses on a phenomenological basis. However, a number of recent experiments show that the STM in its present form fails to explain some essential aspects of the physics of glasses at temperatures below about 100 mK . As examples we mention the rapid decay of spontaneous polarization echoes, the temperature dependence of the elastic and dielectric properties, the observation of various memory effects and the occurrence of an unexpected magnetic field dependence of the dielectric properties. A possible cause for the shortcomings of the STM might be the interaction between tunneling systems via their elastic and electric moments, which have not been considered in the original formulation of the STM. We will summarize the new findings and will discuss their implications.

Ultrasound Studies of Clathrate Thermoelectrics

ABSTRACTResonant Ultrasound Spectroscopy and low-temperature ultrasonic attenuation measurements are reported for filled and unfilled skutterudites and for Ge-clathrates. These data reveal that an unusual elastic behavior complements the thermal properties of the filled skutterudites and indicate the presence of low-energy vibrational modes. The attenuation at low-temperatures in the single-crystalline Ge-clathrate is glasslike and can be described by the same phenomenological Tunneling Model that has been developed to describe the low-temperature properties of amorphous solids.

The Physics of Phonons

Elements of crystal symmetry: Direct lattice Reciprocal lattice Brillouin zone Crystal structure Point groups Space groups Symmetry of the Brillouin zone Jones zone Surface Brillouin zone Matrix representations of point groups. Lattice dynamics in harmonic approximation - semiclassical treatment: Introduction Lattice dynamics of a linear chain Lattice dynamics of three-dimensional crystals - phenomenological models Density of normal modes Numerical calculation of g(w) Lattice heat capacity. Lattice dynamics in the harmonic approximation - ab initio treatment: Introduction The frozen-phonon approach The linear response approach The planar force constant method. Anharmonicity: Introduction Hamiltonian of a general three-dimensional crystal Effect of anharmonicity on phonon states Effects of the selection rules on three-phonon processes Hamiltonian of an anharmonic elastic continuum Evaluation of three-phonon scattering strengths The quasi-harmonic approximation and Grueneisen's constant. Theory of lattice thermal conductivity: Introduction Relaxation-time methods Gree-Kubo linear response theory Second sound and Poiseuille flow of phonons. Phonon scattering in solids: Boundary scattering Scattering by static imperfections Phonon scattering in alloys Anharmonic scattering Phonon-electron scattering in doped semiconductors Phonon scattering due to magnetic impurities in semiconductors Phonon scattering from tunnelling states of impurities Phonon-photon interaction. Analysis of phonon relaxation and thermal conductivity results: Anharmonic decay of phonons Lattice thermal conductivity of undoped semiconductors and insulators Non-metallic crystals with high thermal conductivity Thermal conductivity of complex crystals Low-temperature thermal conductivity of doped semiconductors. Phonons in low dimensional solids: Introduction Surface vibrational modes Attenuation of surface phonons Phonons in superlattices Thermal conductivity of superlattices. Phonons in impure and mixed crystals: Introduction Localised vibrational modes in semiconductors Experimental studies of long-wavelength optical phonons in mixed crystals Theoretical models for long-wavelength optical phonons in mixed crystals Phonon conductivity of mixed crystals. Phonons in quasi-crystalline and amorphous solids: Introduction Phonons in quasi-crystals Structure and vibrational excitations of amorphous solids Vibrational properties of amorphous solids Low-temperature properties of amorphous solids. Phonon spectroscopy: Introduction Heat pulse technique Superconducting tunnel junction technique Optical techniques Phonons from Landau levels in 2DEG Phonon focusing and imaging Frequency crossing phonon spectroscopy Phonon echoes. Phonons in liquid helium: Introduction Dispersion curve and elementary excitations Specific heat Interactions between the excitations Kapitza resistance Quantum evaporation. Appendices: Density functional formalism The pseudopotential method Evaluation of integrals in sections 6.4.1.4 Negative-definitenss of the phonon off-diagonal operator ^D*L. References. Index.

Tunneling models and the experimental thermal expansivities of fused silica and poly(methylmethacrylate) (PMMA) below 4 K

Linear-thermal-expansivity data are given to 1.5 K for the two different amorphous solids, fused silica (amorphous Si${\mathrm{O}}_{2}$) and PMMA [poly(methylmethacrylate)]. Both solids exhibit a negative expansivity contribution at low temperatures which is linear in the absolute temperature and which corresponds to a common Gr\uneisen parameter, ${\ensuremath{\gamma}}_{1}=\ensuremath{-}16$. A calculation is given for the corresponding expansivity which would be expected for a continuous distribution in energy of two-level states using both symmetric and asymmetric tunneling models. Inconsistencies between the postulates which must be made to explain the present results and those required to explain other low-temperature properties of amorphous solids lend support to the conclusion from other experiments that the tunneling model does not explain satisfactorily the low-temperature properties of amorphous solids.