The smectic ZA phase: Antiferroelectric smectic order as a prelude to the ferroelectric nematic.

We have structurally characterized the liquid crystal (LC) phase that can appear as an intermediate state when a dielectric nematic, having polar disorder of its molecular dipoles, transitions to the almost perfectly polar-ordered ferroelectric nematic. This intermediate phase, which fills a 100-y-old void in the taxonomy of smectic LCs and which we term the "smectic ZA," is antiferroelectric, with the nematic director and polarization oriented parallel to smectic layer planes, and the polarization alternating in sign from layer to layer with a 180 Å period. A Landau free energy, originally derived from the Ising model of ferromagnetic ordering of spins in the presence of dipole-dipole interactions, and applied to model incommensurate antiferroelectricity in crystals, describes the key features of the nematic-SmZA-ferroelectric nematic phase sequence.

Observation of a uniaxial ferroelectric smectic A phase.

We report the observation of the smectic AF, a liquid crystal phase of the ferroelectric nematic realm. The smectic AF is a phase of small polar, rod-shaped molecules that form two-dimensional fluid layers spaced by approximately the mean molecular length. The phase is uniaxial, with the molecular director, the local average long-axis orientation, normal to the layer planes, and ferroelectric, with a spontaneous electric polarization parallel to the director. Polarization measurements indicate almost complete polar ordering of the ∼10 Debye longitudinal molecular dipoles, and hysteretic polarization reversal with a coercive field ∼2 × 105 V/m is observed. The SmAF phase appears upon cooling in two binary mixtures of partially fluorinated mesogens: 2N/DIO, exhibiting a nematic (N)-smectic ZA (SmZA)-ferroelectric nematic (NF)-SmAF phase sequence, and 7N/DIO, exhibiting an N-SmZA-SmAF phase sequence. The latter presents an opportunity to study a transition between two smectic phases having orthogonal systems of layers.

Superfluid Edge Dislocation: Transverse Quantum Fluid.

Recently, it was argued [Kuklov et al., Phys. Rev. Lett. 128, 255301 (2022)PRLTAO0031-900710.1103/PhysRevLett.128.255301] that unusual features associated with the superflow-through-solid effect observed in solid ^{4}He can be explained by unique properties of dilute distribution of superfluid edge dislocations. We demonstrate that stability of supercurrents controlled by quantum phase slips (instantons), and other exotic infrared properties of the superfluid dislocations readily follow from a one-dimensional quantum liquid distinguished by an effectively infinite compressibility (in the absence of Peierls potential) associated with the edge dislocation's ability to climb. This establishes a new class of quasi-one-dimensional superfluid states that remain stable and long-range ordered despite their dimensionality. Our theory is consistent with the existing experimental data, and we propose an experiment to test the mass-current-pressure characteristic prediction.

First-principles experimental demonstration of ferroelectricity in a thermotropic nematic liquid crystal: Polar domains and striking electro-optics.

We report the experimental determination of the structure and response to applied electric field of the lower-temperature nematic phase of the previously reported calamitic compound 4-[(4-nitrophenoxy)carbonyl]phenyl2,4-dimethoxybenzoate (RM734). We exploit its electro-optics to visualize the appearance, in the absence of applied field, of a permanent electric polarization density, manifested as a spontaneously broken symmetry in distinct domains of opposite polar orientation. Polarization reversal is mediated by field-induced domain wall movement, making this phase ferroelectric, a 3D uniaxial nematic having a spontaneous, reorientable polarization locally parallel to the director. This polarization density saturates at a low temperature value of ∼6 µC/cm2, the largest ever measured for a fluid or glassy material. This polarization is comparable to that of solid state ferroelectrics and is close to the average value obtained by assuming perfect, polar alignment of molecular dipoles in the nematic. We find a host of spectacular optical and hydrodynamic effects driven by ultralow applied field (E ∼ 1 V/cm), produced by the coupling of the large polarization to nematic birefringence and flow. Electrostatic self-interaction of the polarization charge renders the transition from the nematic phase mean field-like and weakly first order and controls the director field structure of the ferroelectric phase. Atomistic molecular dynamics simulation reveals short-range polar molecular interactions that favor ferroelectric ordering, including a tendency for head-to-tail association into polar, chain-like assemblies having polar lateral correlations. These results indicate a significant potential for transformative, new nematic physics, chemistry, and applications based on the enhanced understanding, development, and exploitation of molecular electrostatic interaction.

Thermal Buckling Transition of Crystalline Membranes in a Field.

Two-dimensional crystalline membranes in isotropic embedding space exhibit a flat phase with anomalous elasticity, relevant, e.g., for graphene. Here we study their thermal fluctuations in the absence of exact rotational invariance in the embedding space. An example is provided by a membrane in an orientational field, tuned to a critical buckling point by application of in-plane stresses. Through a detailed analysis, we show that the transition is in a new universality class. The self-consistent screening method predicts a second-order transition, with modified anomalous elasticity exponents at criticality, while the RG suggests a weakly first-order transition.

Quantum indistinguishability in chemical reactions.

Quantum indistinguishability plays a crucial role in many low-energy physical phenomena, from quantum fluids to molecular spectroscopy. It is, however, typically ignored in most high-temperature processes, particularly for ionic coordinates, implicitly assumed to be distinguishable, incoherent, and thus well approximated classically. We explore enzymatic chemical reactions involving small symmetric molecules and argue that in many situations a full quantum treatment of collective nuclear degrees of freedom is essential. Supported by several physical arguments, we conjecture a "quantum dynamical selection" (QDS) rule for small symmetric molecules that precludes chemical processes that involve direct transitions from orbitally nonsymmetric molecular states. As we propose and discuss, the implications of the QDS rule include (i) a differential chemical reactivity of para- and orthohydrogen, (ii) a mechanism for inducing intermolecular quantum entanglement of nuclear spins, (iii) a mass-independent isotope fractionation mechanism, (iv) an explanation of the enhanced chemical activity of "reactive oxygen species", (v) illuminating the importance of ortho-water molecules in modulating the quantum dynamics of liquid water, and (vi) providing the critical quantum-to-biochemical linkage in the nuclear spin model of the (putative) quantum brain, among others.

Quantum Smectic Gauge Theory.

We present a gauge theory formulation of a two-dimensional quantum smectic and its relatives, motivated by their realizations in correlated quantum matter. The description gives a unified treatment of phonons and topological defects, respectively, encoded in a pair of coupled gauge fields and corresponding charges. The charges exhibit subdimensional constrained quantum dynamics and anomalously slow highly anisotropic diffusion of disclinations inside a smectic. This approach gives a transparent description of a multistage quantum melting transition of a two-dimensional commensurate crystal (through an incommensurate crystal-a supersolid) into a quantum smectic, which subsequently melts into a quantum nematic and isotropic superfluids, all in terms of a sequence of Higgs transitions.

Fractons from Vector Gauge Theory.

Motivated by the prediction of fractonic topological defects in a quantum crystal, we utilize a reformulated elasticity duality to derive a description of a fracton phase in terms of coupled vector U(1) gauge theories. The fracton order and restricted mobility emerge as a result of an unusual Gauss law where electric field lines of one gauge field act as sources of charge for others. At low energies this vector gauge theory reduces to the previously studied fractonic symmetric tensor gauge theory. We construct the corresponding lattice model and a number of generalizations, which realize fracton phases via a condensation of stringlike excitations built out of charged particles, analogous to the p-string condensation mechanism of the gapped X-cube fracton phase.

Symmetry-Enriched Fracton Phases from Supersolid Duality.

Motivated by the recently established duality between elasticity of crystals and a fracton tensor gauge theory, we combine it with boson-vortex duality, to explicitly account for bosonic statistics of the underlying atoms. We thereby derive a hybrid vector-tensor gauge dual of a supersolid, which features both crystalline and superfluid order. The gauge dual describes a fracton state of matter with full dipole mobility endowed by the superfluid order, as governed by "mutual" axion electrodynamics between the fracton and vortex sectors of the theory, with an associated generalized Witten effect. Vortex condensation restores U(1) symmetry, confines dipoles to be subdimensional (recovering the dislocation glide constraint of a commensurate quantum crystal), and drives a phase transition between two distinct fracton phases. Meanwhile, condensation of elementary fracton dipoles and charges, respectively, provide a gauge dual description of the superhexatic and ordinary superfluid. Consistent with conventional wisdom, in the absence of crystalline order, U(1)-symmetric phases are prohibited at zero temperature via a mechanism akin to deconfined quantum criticality.

Fracton-Elasticity Duality.

Motivated by recent studies of fractons, we demonstrate that elasticity theory of a two-dimensional quantum crystal is dual to a fracton tensor gauge theory, providing a concrete manifestation of the fracton phenomenon in an ordinary solid. The topological defects of elasticity theory map onto charges of the tensor gauge theory, with disclinations and dislocations corresponding to fractons and dipoles, respectively. The transverse and longitudinal phonons of crystals map onto the two gapless gauge modes of the gauge theory. The restricted dynamics of fractons matches with constraints on the mobility of lattice defects. The duality leads to numerous predictions for phases and phase transitions of the fracton system, such as the existence of gauge theory counterparts to the (commensurate) crystal, supersolid, hexatic, and isotropic fluid phases of elasticity theory. Extensions of this duality to generalized elasticity theories provide a route to the discovery of new fracton models. As a further consequence, the duality implies that fracton phases are relevant to the study of interacting topological crystalline insulators.

Multiply Quantized Vortices in Fermionic Superfluids: Angular Momentum, Unpaired Fermions, and Spectral Asymmetry.

We compute the orbital angular momentum L_{z} of an s-wave paired superfluid in the presence of an axisymmetric multiply quantized vortex. For vortices with a winding number |k|>1, we find that in the weak-pairing BCS regime, L_{z} is significantly reduced from its value ℏNk/2 in the Bose-Einstein condensation (BEC) regime, where N is the total number of fermions. This deviation results from the presence of unpaired fermions in the BCS ground state, which arise as a consequence of spectral flow along the vortex subgap states. We support our results analytically and numerically by solving the Bogoliubov-de Gennes equations within the weak-pairing BCS regime.

Anomalous Energetics and Dynamics of Moving Vortices.

Motivated by the general problem of moving topological defects in an otherwise ordered state and specifically, by the anomalous dynamics observed in vortex-antivortex annihilation and coarsening experiments in freely suspended smectic-C films, I study the deformation, energetics, and dynamics of moving vortices in an overdamped XY model and show that their properties are significantly and qualitatively modified by the motion.

Lattice-induced resonances in one-dimensional bosonic systems.

We study the resonant effects produced when a Feshbach dimer crosses a scattering continuum band of atoms in an optical lattice. We numerically obtain the exact spectrum of two particles in a one-dimensional lattice and develop an effective atom-dimer Hamiltonian that accurately captures resonant effects. The lattice-induced resonances lead to the formation of bound states simultaneously above and below the scattering continuum and significantly modify the curvature of the dimer dispersion relation. The nature of the atom-dimer coupling depends strongly on the parity of the dimer state leading to a novel coupling in the case of negative parity dimers.

Liquid crystal cells with "dirty" substrates.

We explore liquid crystal order in a cell with a "dirty" substrate imposing a random surface pinning. Modeling such systems by a random-field xy model with surface heterogeneity, we find that orientational order in the three-dimensional system is marginally unstable to such surface pinning. We compute the Larkin length scale, and the corresponding surface and bulk distortions. On longer scales we calculate correlation functions using the functional renormalization group and matching methods, finding a universal logarithmic and double-logarithmic roughness in two and three dimensions, respectively. For a finite thickness cell, we explore the interplay of homogeneous-heterogeneous substrate pair and detail crossovers as a function of disorder strength and cell thickness.

Conical soliton escape into a third dimension of a surface vortex.

We present an exact three-dimensional solitonic solution to a sine-Gordon-type Euler-Lagrange equation that describes a configuration of a three-dimensional vector field n constrained to a surface p-vortex, with a prescribed polar tilt angle on a planar substrate and escaping into the third dimension in the bulk. The solution is relevant to characterization of a schlieren texture in nematic liquid-crystal films with tangential (in-plane) substrate alignment. The solution is identical to a section of a point defect discovered many years ago by Saupe [Mol. Cryst. Liq. Cryst. 21, 211 (1973)], when latter is restricted to a surface.

Phases and transitions in phantom nematic elastomer membranes.

Motivated by recently discovered unusual properties of bulk nematic elastomers, we study a phase diagram of liquid-crystalline polymerized phantom membranes, focusing on in-plane nematic order. We predict that such membranes should generically exhibit five phases, distinguished by their conformational and in-plane orientational properties: namely, isotropic-crumpled, nematic-crumpled, isotropic-flat, nematic-flat, and nematic-tubule phases. In the nematic-tubule phase, the membrane is extended along the direction of spontaneous nematic order and is crumpled in the other. The associated spontaneous symmetries breaking guarantees that the nematic tubule is characterized by a conformational-orientational soft (Goldstone) mode and the concomitant vanishing of the in-plane shear modulus. We show that long-range orientational order of the nematic tubule is maintained even in the presence of harmonic thermal fluctuations. However, it is likely that tubule's elastic properties are qualitatively modified by these fluctuations, which can be studied using a nonlinear elastic theory for the nematic tubule phase that we derive at the end of this paper.

Theory of bent-core liquid-crystal phases and phase transitions.

We study phases and phase transitions that can take place in the recently discovered bow-shaped or bent-core liquid-crystal molecules. We show that to completely characterize phases exhibited by such bent-core molecules a third-rank tensor T(ijk) order parameter is necessary in addition to the vector and the nematic (second-rank) tensor order parameters. We present an exhaustive list of possible liquid phases, characterizing them by their space-symmetry group and order parameters, and catalog the universality classes of the corresponding phase transitions that we expect to take place in such bent-core molecular liquid crystals. In addition to the conventional liquid-crystal phases such as the nematic phase, we predict the existence of other liquid phases, including the spontaneously chiral nematic (N(T)+2)(*) and chiral polar (V(T)+2)(*) phases, the orientationally ordered but optically isotropic tetrahedratic T phase, and a nematic N(T) phase with D(2d) symmetry that is neither uniaxial nor biaxial. Interestingly, the isotropic-tetrahedratic transition is continuous in mean-field theory, but is likely driven first order by thermal fluctuations. We conclude with a discussion of smectic analogs of these phases and their experimental signatures.

Fluctuating nematic elastomer membranes.

We study the flat phase of nematic elastomer membranes with rotational symmetry spontaneously broken by an in-plane nematic order. Such a state is characterized by a vanishing elastic modulus for simple shear and soft transverse phonons. At harmonic level, the in-plane orientational (nematic) order is stable to thermal fluctuations that lead to short-range in-plane translational (phonon) correlations. To treat thermal fluctuations and relevant elastic nonlinearities, we introduce two generalizations of two-dimensional membranes in a three-dimensional space to arbitrary D-dimensional membranes embedded in a d-dimensional space and analyze their anomalous elasticities in an expansion about D=4. We find a stable fixed point that controls long-scale properties of nematic elastomer membranes. It is characterized by singular in-plane elastic moduli that vanish as a power law eta(lambda)=4-D of a relevant inverse length scale (e.g., wave vector) and a finite bending rigidity. Our predictions are asymptotically exact near four dimensions.

Symmetries and elasticity of nematic gels.

A nematic liquid-crystal gel is a macroscopically homogeneous elastic medium with the rotational symmetry of a nematic liquid crystal. In this paper, we develop a general approach to the study of these gels that incorporates all underlying symmetries. After reviewing traditional elasticity and clarifying the role of broken rotational symmetries in both the reference space of points in the undistorted medium and the target space into which these points are mapped, we explore the unusual properties of nematic gels from a number of perspectives. We show how symmetries of nematic gels formed via spontaneous symmetry breaking from an isotropic gel enforce soft elastic response characterized by the vanishing of a shear modulus and the vanishing of stress up to a critical value of strain along certain directions. We also study the phase transition from isotropic to nematic gels. In addition to being fully consistent with approaches to nematic gels based on rubber elasticity, our description has the important advantages of being independent of a microscopic model, of emphasizing and clarifying the role of broken symmetries in determining elastic response, and of permitting easy incorporation of spatial variations, thermal fluctuations, and gel heterogeneity, thereby allowing a full statistical-mechanical treatment of these materials.

Smectic order, pinning, and phase transition in a smectic-liquid-crystal cell with a random substrate.

We study smectic-liquid-crystal order in a cell with a heterogeneous substrate imposing surface random positional and orientational pinnings. Proposing a minimal random elastic model, we demonstrate that, for a thick cell, the smectic state without a rubbed substrate is always unstable at long scales and, for weak random pinning, is replaced by a smectic glass state. We compute the statistics of the associated substrate-driven distortions and the characteristic smectic domain size on the heterogeneous substrate and in the bulk. We find that for weak disorder, the system exhibits a three-dimensional temperature-controlled phase transition between a weakly and strongly pinned smectic glass states akin to the Cardy-Ostlund phase transition. We explore experimental implications of the predicted phenomenology and suggest that it provides a plausible explanation for the experimental observations on polarized light microscopy and x-ray scattering.