Periodic Reporting for period 4 - GlassUniversality (Universal explanation of low-temperature glass anomalies)
Reporting period: 2022-03-01 to 2023-02-28
Amorphous solids, in which atoms are organized in a disordered way, constitute most of the solid matter found in Nature: think to window glasses (typically silicates), plastics and rubbers (typically polymers), and even foods such as hard candy or mayonnaise. Their understanding is much poorer than for crystalline solids, such as diamond or quartz, in which atoms are organized in a periodic pattern. This extends up to the point that most solid state textbooks are entirely focused on crystals. The reason underlying this uncomfortable situation is that amorphous solids display all kinds of anomalies with respect to the textbook description of crystals, formulated in terms of “phonon” (plane wave) vibrations around a perfect lattice. In particular, amorphous solids show an excess of low-frequency vibrational modes, their specific heat and thermal conductivity behave differently from crystals, they respond non-linearly to arbitrarily small strains, and have highly cooperative dynamics. Traditionally, each of these aspects has been studied independently of the others, by almost distinct communities, and in terms of microscopic elements that are specific to a given material.
Developing a more detailed understanding of amorphous solids is important for society. First of all, because we would like to understand all phases of matter that we observe around us. It is very frustrating, from a purely cultural point of view, that our understanding of amorphous solids is so poor. Second, because amorphous solids are used in many diverse technological applications, and being able to understand their fundamental properties should allow us to design better materials, with mechanical, optical or thermodynamic properties well optimized for the required applications.
The original objective of the GlassUniversality project was to establish a universal explanation of all the anomalies of amorphous solids, in terms of criticality associated with a new phase transition between two distinct glass phases, called the “Gardner transition” in honor of its discoverer, Elisabeth Gardner. Such a phase transition has been theoretically predicted to exist on rigorous grounds, in an abstract limit of infinite spatial dimensions (a limit often used by physicists to simplify complex problems); and its existence allows one to compute the critical exponents that characterize the jamming of hard balls under compression, in strikingly good agreement with numerical simulations. More specifically, the goal is to firmly establish the universal nature of the transition in realistic models of glasses; to connect it to the experimentally observed anomalies through concrete analytical and numerical calculations; and to design precise experimental tests of the theory.
Developing a more detailed understanding of amorphous solids is important for society. First of all, because we would like to understand all phases of matter that we observe around us. It is very frustrating, from a purely cultural point of view, that our understanding of amorphous solids is so poor. Second, because amorphous solids are used in many diverse technological applications, and being able to understand their fundamental properties should allow us to design better materials, with mechanical, optical or thermodynamic properties well optimized for the required applications.
The original objective of the GlassUniversality project was to establish a universal explanation of all the anomalies of amorphous solids, in terms of criticality associated with a new phase transition between two distinct glass phases, called the “Gardner transition” in honor of its discoverer, Elisabeth Gardner. Such a phase transition has been theoretically predicted to exist on rigorous grounds, in an abstract limit of infinite spatial dimensions (a limit often used by physicists to simplify complex problems); and its existence allows one to compute the critical exponents that characterize the jamming of hard balls under compression, in strikingly good agreement with numerical simulations. More specifically, the goal is to firmly establish the universal nature of the transition in realistic models of glasses; to connect it to the experimentally observed anomalies through concrete analytical and numerical calculations; and to design precise experimental tests of the theory.
During the project, substantial progress has been achieved.
First of all, a rather complete understanding of the Gardner transition was obtained. We now understand that, while the transition is common to all amorphous solids in the abstract limit of infinite spatial dimensions, in physical three-dimensional systems it is only observed in the vicinity of the “jamming” transition, which is characteristics of soft emulsions, colloids and grains. As a consequence, the vibrations of these systems are strongly anomalous: all atoms vibrate together in a “collective” way, but strongly different from the plane waves that characterize crystals. On the contrary, structural glasses (such as window glasses) do not show the transition. Their vibrations are mostly plane waves as in crystals, but occasionally, rare “localized” defects constituted by a few atoms can scatter these waves and induce anomalies. The distinction between “collective” and “localized” excitations is a crucial property of glasses, and the interplay of these two kinds of excitations can lead to a very rich phenomenology, as we discussed in Nature Communications 10, 5102 (2019).
Additional progress has been made by developing a theory for the vibration of non-spherical particles (such as M&M’s candies) around their jammed state, published in PNAS 115, 11736 (2018). This problem, which might look very academic, is actually very important because most granular systems are composed of non-spherical particles. Furthermore, friction originates from rough surface interactions between particles, and is potentially described by the same non-spherical framework, as we discuss in Physical Review Letters 124, 208001 (2020).
We also investigated quantum effects in very low-temperature glasses, which are dominated by localized defects that tunnel between two locally stable states because of quantum mechanical dynamics. We have presented, for the first time, a direct observation of tunnelling defects in a model for structural glass simulated in the computer, in Physical Review Letters 124, 225901 (2020). We confirmed that such defects are strongly suppressed in ultra-stable glasses prepared by slow annealing or vapor deposition, in quantitative agreement with experiment. This work opens the way for a more direct investigation of such defects, which are very important for quantum decoherence in glasses and thus relevant for applications, e.g. in quantum computing.
Finally, we worked on understanding the failure of glasses subjected to external loads, which happens at the so-called “yielding transition”. We extended mean field theory to describe a characteristic two-step yielding process observed in attractive colloids. We made progress in understand the universality class of yielding, by investigating variants of the random field Ising model that should belong to that class, which should provide important insight on the basic mechanisms for glass failure, again with important potential applications, see Physical Review Letters 129, 228002 (2022).
First of all, a rather complete understanding of the Gardner transition was obtained. We now understand that, while the transition is common to all amorphous solids in the abstract limit of infinite spatial dimensions, in physical three-dimensional systems it is only observed in the vicinity of the “jamming” transition, which is characteristics of soft emulsions, colloids and grains. As a consequence, the vibrations of these systems are strongly anomalous: all atoms vibrate together in a “collective” way, but strongly different from the plane waves that characterize crystals. On the contrary, structural glasses (such as window glasses) do not show the transition. Their vibrations are mostly plane waves as in crystals, but occasionally, rare “localized” defects constituted by a few atoms can scatter these waves and induce anomalies. The distinction between “collective” and “localized” excitations is a crucial property of glasses, and the interplay of these two kinds of excitations can lead to a very rich phenomenology, as we discussed in Nature Communications 10, 5102 (2019).
Additional progress has been made by developing a theory for the vibration of non-spherical particles (such as M&M’s candies) around their jammed state, published in PNAS 115, 11736 (2018). This problem, which might look very academic, is actually very important because most granular systems are composed of non-spherical particles. Furthermore, friction originates from rough surface interactions between particles, and is potentially described by the same non-spherical framework, as we discuss in Physical Review Letters 124, 208001 (2020).
We also investigated quantum effects in very low-temperature glasses, which are dominated by localized defects that tunnel between two locally stable states because of quantum mechanical dynamics. We have presented, for the first time, a direct observation of tunnelling defects in a model for structural glass simulated in the computer, in Physical Review Letters 124, 225901 (2020). We confirmed that such defects are strongly suppressed in ultra-stable glasses prepared by slow annealing or vapor deposition, in quantitative agreement with experiment. This work opens the way for a more direct investigation of such defects, which are very important for quantum decoherence in glasses and thus relevant for applications, e.g. in quantum computing.
Finally, we worked on understanding the failure of glasses subjected to external loads, which happens at the so-called “yielding transition”. We extended mean field theory to describe a characteristic two-step yielding process observed in attractive colloids. We made progress in understand the universality class of yielding, by investigating variants of the random field Ising model that should belong to that class, which should provide important insight on the basic mechanisms for glass failure, again with important potential applications, see Physical Review Letters 129, 228002 (2022).
The methodology of the project consists in building a microscopic understanding of amorphous solids by moving away from exactly solvable limits in a controlled way. We started from two well understood limits: infinite spatial dimensions, where rigorous analytic computations are possible, and zero temperature, where jamming is a sharply defined phase transition. During the project, important methodological developments have been achieved beyond the state of the art in what concerns the solution in infinite dimensions. In particular, a general method to derive Dynamical Mean Field Theory (DMFT) equations has been developed [J.Phys.A: Math.Theor. 52, 144002 (2019)]. The resulting equations are very broadly applicable, in particular to describe the non-equilibrium dynamics of liquids due to active self-propulsion, an applied shear strain, or a lack of equilibration with the thermal bath. In parallel, we also developed methods to systematically investigate the excitations and defects of glasses at jamming and away from it.
Thanks to these developments, we have been able to deepen our understanding of the dynamics of dense liquids and glasses in a variety of out-of-equilibrium situations (thanks to DMFT equations), of the excitations and defects in glasses (following up on our work on two-level systems), and on the yielding and failure of glasses under an external load.
Thanks to these developments, we have been able to deepen our understanding of the dynamics of dense liquids and glasses in a variety of out-of-equilibrium situations (thanks to DMFT equations), of the excitations and defects in glasses (following up on our work on two-level systems), and on the yielding and failure of glasses under an external load.