The Microscopic Quantum Theory of Low Temperature Amorphous Solids

Microscopic observation of two-level systems in a metallic glass model

The low-temperature quasi-universal behavior of amorphous solids has been attributed to the existence of spatially localized tunneling defects found in the low-energy regions of the potential energy landscape. Computational models of glasses can be studied to elucidate the microscopic nature of these defects. Recent simulation work has demonstrated the means of generating stable glassy configurations for models that mimic metallic glasses using the swap Monte Carlo algorithm. Building on these studies, we present an extensive exploration of the glassy metabasins of the potential energy landscape of a variant of the most widely used model of metallic glasses. We carefully identify tunneling defects and reveal their depletion with increased glass stability. The density of tunneling defects near the experimental glass transition temperature appears to be in good agreement with experimental measurements.

Glass Dynamics Deep in the Energy Landscape

When a liquid is cooled, progress down the energy landscape is arrested near the glass transition temperature T_g. In principle, lower energy states can be accessed by waiting for further equilibration, but the rough energy landscape of glasses quickly leads to kinetics on geologically slow time scales below T_g. Over the past decade, progress has been made probing deeper into the energy landscape via several techniques. By looking at bulk and surface diffusion, using layered deposition that promotes equilibration, imaging glass surfaces with faster dynamics below T_g, and optically exciting glasses, experiments have moved into a regime of ultrastable, low energy glasses that was difficult to access in the past. At the same time, both simulations and energy landscape theory based on a random first order transition (RFOT) have tackled systems that include surfaces, optical excitation, and interfacial dynamics. Here we review some of the recent experimental work, and how energy landscape theory illuminates glassy dynamics well below the glass transition temperature by making direct connections between configurational entropy, energy landscape barriers, and the resulting dynamics.

Quantum polyamorphism in compressed distinguishable helium-4

We demonstrate that two amorphous solid states can exist in ⁴He consisting of distinguishable Boltzmann atoms under compressed conditions. The isothermal compression of normal or supercritical fluid ⁴He was conducted at 3-25 K using the isobaric-isothermal path integral centroid molecular dynamics simulation. The compression of fluid first produced the low-dispersion amorphous (LDA) state possessing modest extension of atomic necklaces. Further isothermal compression up to the order of 10 kbar to 1 Mbar or an isobaric cooling of LDA induced the transition to the high-dispersion amorphous (HDA) state. The HDA was characterized by long quantum wavelengths of atoms extended over several Angstroms and the promotion of atomic residual diffusion. They were related to the quantum tunneling of atoms bestriding the potential saddle points in this glass. The change in pressure or temperature induced the LDA-HDA transition reversibly with hysteresis, while it resembled the coil-globule transition of classical polymers. The HDA had lower kinetic and higher Gibbs free energies than the LDA at close temperature. The HDA was absent at T ≥ 13 K, while the LDA-HDA transition pressure significantly decreased with lowering temperature. The LDA and HDA correspond to the trapped and tunneling regimes proposed by Markland et al. [J. Chem. Phys. 136, 074511 (2012)], respectively. The same reentrant behavior as they found was observed for the expansion factor of the quantum wavelength as well as for atomic diffusivity.

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.

Temperature-driven narrowing of the insulating gap as a precursor of the insulator-to-metal transition: Implications for the electronic structure of solids

We present a microscopic picture rationalizing the surprisingly steep decrease in the bandgap with temperature in insulators, crystalline or otherwise. The gap narrowing largely results from fluctuations of long-wavelength optical phonons-when the latter are present-or their disordered analogs if the material is amorphous. We elaborate on this notion to show that possibly with the exception of weakly bound solids made of closed-shell electronic configurations, the existence of an insulating gap or pseudogap in a periodic solid implies that optical phonons must be present, too. This means that in an insulating solid, the primitive cell must have at least two atoms and/or that a charge density wave is present, with the possible exception of weakly bonded solids such as rare-gas or ferromagnetic Wigner crystals. As a corollary, a (periodic) elemental solid held together by nonclosed shell interactions and whose primitive unit contains only one atom will ordinarily be a metal, consistent with observation. Consequences of the present picture for Wigner solids are discussed. A simple field theory of the metal-insulator transition is constructed that directly ties long-wavelength optical vibrations with fluctuations of an order parameter for the metal-insulator transition. The order parameter is shown to have at least two components, yet no Goldstone mode arises as a result of the transition.

Aging, Jamming, and the Limits of Stability of Amorphous Solids

Apart from not having crystallized, supercooled liquids can be considered as being properly equilibrated and thus can be described by a few thermodynamic control variables. In contrast, glasses and other amorphous solids can be arbitrarily far away from equilibrium and require a description of the history of the conditions under which they formed. In this paper we describe how the locality of interactions intrinsic to finite-dimensional systems affects the stability of amorphous solids far off equilibrium. Our analysis encompasses both structural glasses formed by cooling and colloidal assemblies formed by compression. A diagram outlining regions of marginal stability can be adduced which bears some resemblance to the quasi-equilibrium replica meanfield theory phase diagram of hard sphere glasses in high dimensions but is distinct from that construct in that the diagram describes not true phase transitions but kinetic transitions that depend on the preparation protocol. The diagram exhibits two distinct sectors. One sector corresponds to amorphous states with relatively open structures, the other to high density, more closely packed ones. The former transform rapidly owing to there being motions with no free energy barriers; these motions are string-like locally. In the dense region, amorphous systems age via compact activated reconfigurations. The two regimes correspond, in equilibrium, to the collisional or uniform liquid and the so-called landscape regime, respectively. These are separated by a spinodal line of dynamical crossovers. Owing to the rigidity of the surrounding matrix in the landscape, high-density part of the diagram, a sufficiently rapid pressure quench adds compressive energy which also leads to an instability toward string-like motions with near vanishing barriers. Conversely, a dilute collection of rigid particles, such as a colloidal suspension leads, when compressed, to a spatially heterogeneous structure with percolated mechanically stable regions. This jamming corresponds to the onset of activation when the spinodal line is traversed from the low density side. We argue that a stable glass made of sufficiently rigid particles can also be viewed as exhibiting sporadic and localized buckling instabilities that result in local jammed structures. The lines of instability we discuss resemble the Gardner transition of meanfield systems but, in contrast, do not result in true criticality owing to being short-circuited by activated events. The locally marginally stable modes of motion in amorphous solids correspond to secondary relaxation processes in structural glasses. Their relevance to the low temperature anomalies in glasses is also discussed.

Amorphous chalcogenides as random octahedrally bonded solids: I. Implications for the first sharp diffraction peak, photodarkening, and Boson peak

We develop a computationally efficient algorithm for generating high-quality structures for amorphous materials exhibiting distorted octahedral coordination. The computationally costly step of equilibrating the simulated melt is relegated to a much more efficient procedure, viz., generation of a random close-packed structure, which is subsequently used to generate parent structures for octahedrally bonded amorphous solids. The sites of the so-obtained lattice are populated by atoms and vacancies according to the desired stoichiometry while allowing one to control the number of homo-nuclear and hetero-nuclear bonds and, hence, effects of the mixing entropy. The resulting parent structure is geometrically optimized using quantum-chemical force fields; by varying the extent of geometric optimization of the parent structure, one can partially control the degree of octahedrality in local coordination and the strength of secondary bonding. The present methodology is applied to the archetypal chalcogenide alloys As_xSe_1-x. We find that local coordination in these alloys interpolates between octahedral and tetrahedral bonding but in a non-obvious way; it exhibits bonding motifs that are not characteristic of either extreme. We consistently recover the first sharp diffraction peak (FSDP) in our structures and argue that the corresponding mid-range order stems from the charge density wave formed by regions housing covalent and weak, secondary interactions. The number of secondary interactions is determined by a delicate interplay between octahedrality and tetrahedrality in the covalent bonding; many of these interactions are homonuclear. The present results are consistent with the experimentally observed dependence of the FSDP on arsenic content, pressure, and temperature and its correlation with photodarkening and the Boson peak. They also suggest that the position of the FSDP can be used to infer the effective particle size relevant for the configurational equilibration in covalently bonded glassy liquids, where the identification of the effective rigid molecular unit is ambiguous.

Probing Nanoscale Ion Dynamics in Ultrathin Films of Polymerized Ionic Liquids by Broadband Dielectric Spectroscopy

Continuous progress in energy storage and conversion technologies necessitates novel experimental approaches that can provide fundamental insights regarding the impact of reduced dimensions on the functional properties of materials. Here, we demonstrate a nondestructive experimental approach to probe nanoscale ion dynamics in ultrathin films of polymerized 1-vinyl-3-ethylimidazolium bis(trifluoromethylsulfonyl)imide over a broad frequency range spanning over 6 orders of magnitude by broadband dielectric spectroscopy. The approach involves using an electrode configuration with lithographically patterned silica nanostructures, which allow for an air gap between the confined ion conductor and one of the electrodes. We observe that the characteristic rate of ion dynamics significantly slows down with decreasing film thicknesses above the calorimetric glass transition of the bulk polymer. However, the mean rates remain bulk-like at lower temperatures. These results highlight the increasing influence of the polymer/substrate interactions with decreasing film thickness on ion dynamics.

Comparison of static length scales characterizing the glass transition

The dramatic dynamic slowing down associated with the glass transition is considered by many to be related to the existence of a static length scale that grows when temperature decreases. Defining, identifying, and measuring such a length is a subtle problem. Recently, two proposals, based on very different insights regarding the relevant physics, were put forward. One approach is based on the point-to-set correlation technique and the other on the scale where the lowest eigenvalue of the Hessian matrix becomes sensitive to disorder. Here we present numerical evidence that the two approaches might result in the same identical length scale. This provides mutual support for their relevance and, at the same time, raises interesting theoretical questions, discussed in the conclusion.

Microscopic calculation of the free energy cost for activated transport in glass-forming liquids

Activated transport in liquids--supercooled liquids in particular--occurs via mutual nucleation of alternative, aperiodic minima of the free energy. Xia and Wolynes [Proc. Natl. Acad. Sci. U.S.A. 97, 2990 (2000)] have made a general argument that at temperatures near the ideal glass transition, the surface penalty for this kind of nucleation is largely determined by the temperature and the logarithm of the size of the vibrational fluctuation of rigid molecular units about the local minimum. Here, we independently show how to estimate this surface tension and, hence, the activation barrier for the activated transport for several actual liquids, using their structure factors and knowledge of the finite-frequency elastic constants. In this estimate, the activation free energy, while depending on the configurational entropy, also depends on the elastic modulus as in the "shoving" models. The resulting estimates are however consistent with the estimate provided by Xia and Wolynes' argument near the glass transition and, in addition, reflect the barrier softening effects predicted earlier for fragile substances.