RSC School Seminar - Dr. David Cortie

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From time crystals to time glasses

Lattice vibrations play a key role in the behavior of materials at finite temperatures. The phonon paradigm of treating lattice excitations as independent planewaves has been tremendously successful for describing conventional crystals with a well-defined Bravais lattice. The accuracy of this approach at lower temperatures is well established, where the independent quasiparticles have a long lifetime, and the atomic displacements are small, and this has led to the phonon paradigm becoming a cornerstone of modern condensed matter physics. Nevertheless, in recent years, there has been a growing interest in atomistic dynamics that cannot be described using standard phonon theory. For example, there has been great interest in achieving non-equilibrium Floquet states such as the time-crystal: a system with a well defined periodic motion, ordered discretely in time similar involving an “atomic” clock inside a material [1], which is a state that is forbidden in standard thermal equilibrium phononic systems [2] but can be achieved in driven systems [3]. Here I briefly develop a theory of the experimental signature of a hypothetical time-crystal using neutron spectroscopy as a probe of the coherent dynamics in a lattice system, assuming a suitable driving mechanism such as intense terahertz light. By extension, I also introduce the inverse concept of a time-glass: that is a material which has a well-ordered average crystal structure in the limit of infinite time, but a glassy low-symmetry structure when viewed at the instantaneous femtosecond timescale. Recent data demonstrates that, unlike time-crystals, time-glasses can occur under thermodynamic equilibrium and are relatively common in nature with experimental examples in molecular sieves [4], superionic thermoelectrics [5], and hybrid perovskite materials [6]. Ab initio molecular dynamics and lattice dynamics within the density-functional theory formalism can be used to provide a stronger set of criteria to identify time-glass materials with dynamics beyond the traditional phonon picture. A key indicator of a time-glass states the existence of imaginary instantaneous normal modes in the solid, similar but not identical to those found in liquids, which lead to a breakdown of traditional phonon dynamics, often in tandem with short-ranged confined diffusion around well-defined average positions. This manifests as a distinctive quasielastic contribution in neutron spectroscopy experiments.