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Register a new userActive cholesterics: odder than odd elasticity
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In equilibrium liquid crystals, chirality leads to a variety of spectacular three-dimensional structures, but chiral and achiral phases with the same broken continuous symmetries have identical long-time, large-scale dynamics. In this paper, we demonstrate that chirality qualitatively modifies the dynamics of layered liquid crystals in active systems in both two and three dimensions due to an active odder elasticity. In three dimensions, we demonstrate that the hydrodynamics of active cholesterics differs fundamentally from smectic-A liquid crystals, unlike their equilibrium counterpart. This distinction can be used to engineer a columnar array of vortices, with anti-ferromagnetic vorticity alignment, that can be switched on and off by external strain. A two-dimensional chiral layered state -- an array of lines on an incompressible, free-standing film of chiral active fluid with a preferred normal direction -- is generically unstable. However, this instability can be tuned in easily realisable experimental settings, when the film is either on a substrate or in an ambient fluid.
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Odd viscosity arises in systems with time reversal symmetry breaking, which creates non-dissipative effects. One method to probe changes in viscosity is to examine the dynamics of a single probe particle driven though a medium, a technique known as active rheology. We show that active rheology in a system with odd viscosity and no quenched disorder reveals a variety of novel effects, including a speed up of the probe particle with increasing system density when the background medium creates a velocity boost of the driven particle due to the Magnus effect. In contrast, the probe particle velocity in the dissipation-dominated limit monotonically decreases with increasing system density. We also show that the odd viscosity imparts a Hall angle to the probe particle, and that both the Hall angle and the velocity boost depend strongly on the drive. These results should be general to other systems with odd viscosity, including skyrmions in chiral magnets.
General symmetry arguments, dating back to de Gennes dictate that at scales longer than the pitch, the low-energy elasticity of a chiral nematic liquid crystal (cholesteric) and of a Dzyaloshinskii-Morya (DM) spiral state in a helimagnet with negligible crystal symmetry fields (e.g., MnSi, FeGe) is identical to that of a smectic liquid crystal, thereby inheriting its rich phenomenology. Starting with a chiral Frank free-energy (exchange and DM interactions of a helimagnet) we present a transparent derivation of the fully nonlinear Goldstone mode elasticity, which involves an analog of the Anderson-Higgs mechanism that locks the spiral orthonormal (director/magnetic moment) frame to the cholesteric (helical) layers. This shows explicitly the reduction of three orientational modes of a cholesteric down to a single phonon Goldstone mode that emerges on scales longer than the pitch. At a harmonic level our result reduces to that derived many years ago by Lubensky and collaborators.
We establish non-Hermitian topological mechanics in one dimensional (1D) and two dimensional (2D) lattices consisting of mass points connected by meta-beams that lead to odd elasticity. Extended from the non-Hermitian skin effect in 1D systems, we demonstrate this effect in 2D lattices in which bulk elastic waves exponentially localize in both lattice directions. We clarify a proper definition of Berry phase in non-Hermitian systems, with which we characterize the lattice topology and show the emergence of topological modes on lattice boundaries. The eigenfrequencies of topological modes are complex due to the breaking of $mathcal{PT}$-symmetry and the excitations could exponentially grow in time in the damped regime. Besides the bulk modes, additional localized modes arise in the bulk band and they are easily affected by perturbations. These distinguishing features may manifest themselves in various active materials and biological systems.
The properties of crystals consisting of several components can be widely tuned. Often solid solutions are produced, where substitutional or interstitional disorder determines the crystal thermodynamic and mechanical properties. The chemical and structural disorder impedes the study of the elasticity of such solid solutions, since standard procedures like potential expansions cannot be applied. We present a generalization of a density-functional based approach recently developed for one-component crystals to multi-component crystals. It yields expressions for the elastic constants valid in solid solutions with arbitrary amounts of point defects and up to the melting temperature. Further, both acoustic and optical phonon eigenfrequencies can be computed in linear response from the equilibrium particle densities and established classical density functionals. As a proof of principle, dispersion relations are computed for two different binary crystals: A random fcc crystal as an example for a substitutional, and a disordered sodium chloride structure as an example of an interstitial solid solution. In cases where one of the components couples only weakly to the others, the dispersion relations develop characteristic signatures. The acoustic branches become flat in much of the first Brillouin zone, and a crossover between acoustic and optic branches takes place at a wavelength which can far exceed the lattice spacing.*
Active chiral viscoelastic materials exhibit elastic responses perpendicular to the applied stresses, referred to as odd elasticity. We use a covariant formulation of viscoelasticity combined with an entropy production analysis to show that odd elasticity is not only present in active systems but also in broad classes of passive chiral viscoelastic fluids. In addition, we demonstrate that linear viscoelastic chiral solids do require activity in order to manifest odd elastic responses. In order to model the phenomenon of passive odd viscoelasticity we propose a chiral extension of Jeffreys model. We apply our covariant formalism in order to derive the dispersion relations of hydrodynamic modes and obtain clear imprints of odd viscoelastic behavior.
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