Solids and crystals spontaneously break the translation symmetry of space, and their slow dynamics is governed by the resulting Goldstone modes, the phonons. In real materials these symmetries are often only approximate – broken weakly by impurities or by an underlying lattice – which gives the Goldstone modes a small mass and damping. With collaborators, I have developed hydrodynamic theories of viscoelastic materials, charge density waves and plastic deformations in electronic crystals, and studied how approximate symmetries and pseudo-Goldstone modes are constrained by the second law of thermodynamics.
Viscoelasticity extends elasticity to time-dependent effects, capturing how materials gradually recover their shape or keep deforming under sustained stress. Its hydrodynamics can equivalently be written as that of a superfluid with higher-form symmetries (arXiv:1908.01175).
Papers
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Fractonic solids
Fractons are exotic quasiparticles that cannot move on their own, only in pairs or larger groups. The symmetries behind this are at odds with those of space and time: theories with them cannot, for instance, be coupled to gravity. Yet in real materials, such as crystals with defects, fractons should be stuck to the material rather than to space itself. I propose a symmetry that restricts their motion relative to a crystal, which can itself move and deform. This removes the conflicts with space and time, and I also build a holographic model of such fractonic solids.
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Approximate higher-form symmetries, topological defects, and dynamical phase transitions
Higher-form symmetries, whose charges are extended objects such as magnetic field lines, help classify phases of matter. In real materials they are rarely exact: topological defects, such as vortices or charges on which field lines end, break them slightly. We build effective theories and hydrodynamics for such approximate higher-form symmetries and the ways they can be broken. The framework captures phase transitions driven by a proliferation of defects, from the melting of liquid crystals and the ionisation of a gas into a plasma to spin ice and the Meissner effect in superconductors.
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Hydrodynamics of plastic deformations in electronic crystals
When electrons repel each other strongly enough, they can freeze into a crystal of their own, such as a Wigner crystal or a charge density wave. These electronic crystals are fragile and hard to observe: impurities pin them in place and defects disrupt their order. We build a hydrodynamic theory of such crystals that includes pinning, vacancies and plastic deformations caused by moving dislocations. As dislocations multiply, the crystal’s conduction comes unpinned until it melts, giving way to a new phase: a pinned electronic liquid. We also suggest experiments to detect these signatures.
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Approximate symmetries, pseudo-Goldstones, and the second law of thermodynamics
Symmetries are useful even when they are only approximate: pions, for instance, are nearly massless ripples of an approximate symmetry of the strong force. Similar “pseudo-Goldstone” ripples appear in materials where impurities pin crystals, charge density waves or superfluids in place. We build a general hydrodynamic theory of such systems and show that the second law of thermodynamics alone implies their relaxation, along with a universal relation between how quickly the ripples die out and how fast they diffuse. We also find new effects that are sensitive to how the symmetry is broken.
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Hydrodynamics for charge density waves and their holographic duals
In materials such as the cuprate superconductors, electrons can arrange into a crystal-like pattern called a charge density wave. Since the electrons interact strongly, such phases are often studied using hydrodynamics or holography, which models them with black holes. We formulate their hydrodynamics and point out an ingredient missed before, the lattice pressure, which captures the crystal’s strain and thermal expansion. Holographic models must include it, and we use them to compute, for the first time, how such a crystal expands with temperature and charge.
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On the Hydrodynamic Description of Holographic Viscoelastic Models
Holographic models, which describe strongly interacting matter using black holes, are popular tools for studying strange metals and solid-like materials. Yet their behaviour did not quite match the hydrodynamics expected to describe them. We show that the missing ingredient is the “strain pressure”, a recently proposed transport coefficient: once it is included, hydrodynamics reproduces all the slow vibrations of these black holes. Even when the strain pressure vanishes in equilibrium, its change with temperature still matters, completing the match between the two descriptions.
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Viscoelastic hydrodynamics and holography
Most materials respond to being deformed partly like a solid, springing back, and partly like a liquid, flowing: they are viscoelastic. Despite a century of study, it has mostly been described by models built from springs and dashpots. We derive the nonlinear theory of viscoelastic crystals and liquid crystals from first principles, including all dissipative effects at leading order, and recover the classic Kelvin–Voigt model as a special case. We show that the same physics can be described as a superfluid of a higher-form symmetry, and build holographic models for both descriptions.
Talks
Pinned viscoelastic hydrodynamics
Generalised global symmetries and viscoelastic hydrodynamics
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Conference talk
Hydrodynamics at All Length Scales Workshop, Lorentz Center, Netherlands
