Electrodynamics of amorphous media at low temperatures

Towards understanding two-level-systems in amorphous solids: insights from quantum circuits

Amorphous solids show surprisingly universal behaviour at low temperatures. The prevailing wisdom is that this can be explained by the existence of two-state defects within the material. The so-called standard tunneling model has become the established framework to explain these results, yet it still leaves the central question essentially unanswered-what are these two-level defects (TLS)? This question has recently taken on a new urgency with the rise of superconducting circuits in quantum computing, circuit quantum electrodynamics, magnetometry, electrometry and metrology. Superconducting circuits made from aluminium or niobium are fundamentally limited by losses due to TLS within the amorphous oxide layers encasing them. On the other hand, these circuits also provide a novel and effective method for studying the very defects which limit their operation. We can now go beyond ensemble measurements and probe individual defects-observing the quantum nature of their dynamics and studying their formation, their behaviour as a function of applied field, strain, temperature and other properties. This article reviews the plethora of recent experimental results in this area and discusses the various theoretical models which have been used to describe the observations. In doing so, it summarises the current approaches to solving this fundamentally important problem in solid-state physics.

Molecular binoculars: how to spatially resolve environmental fluctuations by following two or more single-molecule spectral trails at a time

We propose a novel type of spectral diffusion experiment that enables one to decouple spatial characteristics of the environmental fluctuations, such as their concentration, from the interaction with the chromophore. Traditional hole broadening experiments do not allow for such decoupling in the common case when the chromophore-environment interaction is scale invariant. Here we propose to simultaneously follow the spectral trails of a small number of nearby chromophores--two or more--which thereby sense a highly overlapping set of the fluctuations. To this end, we estimate the combined probability distribution for the frequencies of a set of chromophores contained within the same sample. The present setup introduces a new length scale, i.e., the interchromophore distance, which breaks the aforementioned scale invariance and enables one to determine independently the concentration of the environmental fluctuations and their coupling to the chromophores, by monitoring the time after which spectral diffusion of distinct chromophores becomes uncorrelated. We illustrate these results with structural excitations in low temperature glasses.

"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.

Stress distribution and the fragility of supercooled melts

We formulate a minimal ansatz for local stress distribution in a solid that includes the possibility of strongly anharmonic short-length motions. We discover a broken-symmetry metastable phase that exhibits an aperiodic, frozen-in stress distribution. This aperiodic metastable phase is characterized by many distinct, nearly degenerate configurations. The activated transitions between the configurations are mapped onto the dynamics of a long-range classical Heisenberg model with 6-component spins and anisotropic couplings. We argue the metastable phase corresponds to a deeply supercooled nonpolymeric, nonmetallic liquid and further establish an order parameter for the glass-to-crystal transition. The spin model itself exhibits a continuous range of behaviors between two limits corresponding to frozen-in shear and uniform compression/dilation, respectively. The two regimes are separated by a continuous transition controlled by the anisotropy in the spin-spin interaction, which is directly related to the Poisson ratio sigma of the material. The latter ratio and the ultraviolet cutoff of the theory determine the liquid configurational entropy. Our results suggest that liquid's fragility depends on the Poisson ratio in a nonmonotonic way. The present ansatz provides a microscopic framework for computing the configurational entropy and relaxational spectrum of specific substances.

Charge and momentum transfer in supercooled melts: Why should their relaxation times differ?

The steady-state values of the viscosity and the intrinsic ionic conductivity of quenched melts are computed, in terms of independently measurable quantities. The frequency dependence of the ac dielectric response is estimated. The discrepancy between the corresponding characteristic relaxation times is only apparent; it does not imply distinct mechanisms, but stems from the intrinsic barrier distribution for alpha-relaxation in supercooled fluids and glasses. This type of intrinsic "decoupling" is argued not to exceed four orders in magnitude for known glassformers. The origin of the discrepancy between the stretching exponent beta, as extracted from epsilon(omega) and the dielectric modulus data, is explained. The actual width of the barrier distribution always grows with lowering the temperature. The contrary is an artifact of the large contribution of the dc-conductivity component to the modulus data. The methodology allows one to single out other contributions to the conductivity, as in "superionic" liquids or when charge carriers are delocalized, implying that in those systems, charge transfer does not require structural reconfiguration.

Theory of Structural Glasses and Supercooled Liquids

We review the random first-order transition theory of the glass transition, emphasizing the experimental tests of the theory. Many distinct phenomena are quantitatively predicted or explained by the theory, both above and below the glass transition temperature T(g). These include the following: the viscosity catastrophe and heat-capacity jump at T(g), and their connection; the nonexponentiality of relaxations and their correlation with the fragility; dynamic heterogeneity in supercooled liquids owing to the mosaic structure; deviations from the Vogel-Fulcher law, connected with strings or fractal cooperative rearrangements; deviations from the Stokes-Einstein relation close to T(g); aging and its correlation with fragility; and the excess density of states at cryogenic temperatures owing to two-level tunneling systems and the Boson peak.

A Universal Criterion of Melting

Melting is analyzed dynamically as a problem of localization at a liquid-solid interface. A Lindemann-like criterion of melting is derived in terms of particular vibrational amplitudes, which turn out to equal a universal quotient (about one-tenth) of the molecular spacing, at the interface. The near universality of the Lindemann ratio apparently arises owing to strongly overdamped dynamics near melting, and despite the anharmonic interactions being system-specific. A similar criterion is derived for structural displacements in the bulk of the solid, in particular the premelted layer; the criterion is no longer strictly universal, but still depends only on the harmonic properties of the solid. We further compute the dependence of the magnitude of the elemental molecular translations, in deeply supercooled fluids, on the temperature and the high frequency elastic constants. We show explicitly that the surface tension between distinct liquid states, near the glass transition of a supercooled liquid, is nearly evenly split between entropic and energetic contributions.