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.

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.

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 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.

Critical transport in weakly disordered semiconductors and semimetals

Motivated by Weyl semimetals and weakly doped semiconductors, we study transport in a weakly disordered semiconductor with a power-law quasiparticle dispersion ξ_{k}∝k^{α}. We show, that in 2α dimensions short-correlated disorder experiences logarithmic renormalization from all energies in the band. We study the case of a general dimension d using a renormalization group, controlled by an ϵ=2α-d expansion. Above the critical dimensions, conduction exhibits a localization-delocalization phase transition or a sharp crossover (depending on the symmetries of the Hamiltonian) as a function of disorder strength. We utilize this analysis to compute the low-temperature conductivity in Weyl semimetals and weakly doped semiconductors near and below the critical disorder point.

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.

Reentrant BCS-BEC crossover and a superfluid-insulator transition in optical lattices

We study the thermodynamics of a two-species Feshbach-resonant atomic Fermi gas in a periodic potential, focusing in a deep optical potential where a tight binding model is applicable. We show that for a more than half-filled band the gas exhibits a reentrant crossover with decreased detuning (increased attractive interaction), from a paired BCS superfluid to a Bose-Einstein condensate (BEC) of molecules of holes, back to the BCS superfluid, and finally to a conventional BEC of diatomic molecules. This behavior is associated with the nonmonotonic dependence of the chemical potential on detuning and the concomitant Cooper-pair or molecular size, larger in the BCS and smaller in the BEC regimes. For a single filled band we find a quantum phase transition from a band insulator to a BCS-BEC superfluid, and map out the corresponding phase diagram.

Frustrated quantum critical theory of putative spin-liquid phenomenology in 6H-B-Ba(3)NiSb(2)O(9)

A recently discovered material, 6H-B-Ba(3)NiSb(2)O(9) was found to display unusual low-temperature phenomenology, interpreted as a quantum spin liquid with spin S=1 on a triangular lattice. We study a spin S=1 exchange model on an AB stacked triangular lattice near its quantum paramagnet-to-spiral transition, driven by easy-plane single-ion anisotropy. We demonstrate that the frustrated inter- and intralayer exchanges induce contour lines of low-energy excitations that lead to a broad crossover regime of linear-temperature dependence of the specific heat. Based on this and various other predictions, we argue that the observed phenomenology can be understood in terms of a conventional picture of a proximity to this frustrated critical point.

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.

Nonlinear smectic elasticity of helical state in cholesteric liquid crystals and helimagnets

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 or 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.

Stability and distortions of liquid crystal order in a cell with a heterogeneous substrate

We study stability and distortions of liquid crystal nematic order in a cell with a random heterogeneous substrate. Modeling this system as a bulk xy model with quenched disorder confined to a surface, we find that nematic order is marginally unstable to such surface pinning. We compute the length scale beyond which nematic distortions become large and calculate orientational correlation functions using the functional renormalization-group and matching methods, finding universal logarithmic and double-logarithmic distortions in two and three dimensions, respectively. We extend these results to a finite-thickness liquid crystal cell with a second homogeneous substrate, detailing crossovers as a function of random pinning strength and cell thickness. We conclude with analysis of experimental signatures of these distortions in a conventional crossed-polarizer-analyzer light microscopy.

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.

p-wave resonant bose gas: a finite-momentum spinor superfluid

We show that a degenerate gas of two-species bosonic atoms interacting through a p-wave Feshbach resonance (as realized in, e.g., a (85)Rb -- (87)Rb mixture) exhibits a finite-momentum atomic-molecular superfluid (AMSF), sandwiched by a molecular p-wave (orbital spinor) superfluid and by an s-wave atomic superfluid at large negative and positive detunings, respectively. The magnetic field can be used to tune the modulation wave vector of the AMSF state, as well as to drive quantum phase transitions in this rich system.

Quantum liquid crystals in an imbalanced Fermi gas: fluctuations and fractional vortices in Larkin-Ovchinnikov states

We develop a low-energy model of an unidirectional Larkin-Ovchinnikov (LO) state. Because the underlying rotational and translational symmetries are broken spontaneously, this gapless superfluid is a smectic liquid crystal, that exhibits fluctuations that are qualitatively stronger than in a conventional superfluid, thus requiring a fully nonlinear description of its Goldstone modes. Consequently, at nonzero temperature the LO superfluid is an algebraic phase even in 3D. It exhibits half-integer vortex-dislocation defects, whose unbinding leads to transitions to a superfluid nematic and other phases. In 2D at nonzero temperature, the LO state is always unstable to a nematic superfluid. We expect this superfluid liquid-crystal phenomenology to be realizable in imbalanced resonant Fermi gases trapped isotropically.

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.

Thermal fluctuations and rubber elasticity

The effects of thermal elastic fluctuations in rubbery materials are examined. It is shown that, due to their interplay with the incompressibility constraint, these fluctuations qualitatively modify the large-deformation stress-strain relation, compared to that of classical rubber elasticity. To leading order, this mechanism provides a simple and generic explanation for the peak structure of Mooney-Rivlin stress-strain relation and shows good agreement with experiments. It also leads to the prediction of a phonon correlation function that depends on the external deformation.

Superfluid transition in a rotating fermi gas with resonant interactions

We study a rotating atomic Fermi gas near a narrow s-wave Feshbach resonance in a uniaxial trap with frequencies Omega perpendicular, Omega z. We predict the upper-critical angular velocity, omega c2(delta,T), as a function of temperature T and detuning delta across the BEC-BCS crossover. The suppression of superfluidity at omega c2 is distinct in the BCS and BEC regimes, with the former controlled by depairing and the latter by the dilution of bosonic molecules. At low T and Omega z << Omega perpendicular, in the BCS and crossover regimes of 0 less similar delta less similar delta c, omega c2 is implicitly given by [formula: see text], vanishing as omega c2 approximately Omega perpendicular(1 - delta/delta c)(1/2) near [formula: see text] (with Delta the BCS gap and gamma the resonance width), and extending the bulk result variant Planck's over 2pi omega c2 approximately 2Delta2/epsilonF to a trap. In the BEC regime of delta < 0 we find omega c2-->Omega perpendicular-, where molecular superfluidity is destroyed only by large quantum fluctuations associated with comparable boson and vortex densities.

BEC-BCS crossover in "magnetized" Feshbach-resonantly paired superfluids

We map out the detuning-magnetization phase diagram for a magnetized (unequal number of atoms in two pairing hyperfine states) gas of fermionic atoms interacting via an s-wave Feshbach resonance (FR). The phase diagram is dominated by the coexistence of a magnetized normal gas and a singlet-paired superfluid with the latter exhibiting a BCS-Bose Einstein condensate crossover with reduced FR detuning. On the BCS side of strongly overlapping Cooper pairs, a sliver of finite-momentum paired Fulde-Ferrell-Larkin-Ovchinnikov magnetized phase intervenes between the phase-separated and normal states. In contrast, for large negative detuning a uniform, polarized superfluid, that is, a coherent mixture of singlet Bose-Einstein-condensed molecules and fully magnetized single-species Fermi sea, is a stable ground state.

Quantum decoupling transition in a one-dimensional Feshbach-resonant superfluid

We study a one-dimensional gas of fermionic atoms interacting via an s-wave molecular Feshbach resonance. At low energies the system is characterized by two Josephson-coupled Luttinger liquids, corresponding to paired atomic and molecular superfluids. We show that, in contrast to higher dimensions, the system exhibits a quantum phase transition from a phase in which the two superfluids are locked together to one in which, at low energies, quantum fluctuations suppress the Feshbach resonance (Josephson) coupling, effectively decoupling the molecular and atomic superfluids. Experimental signatures of this quantum transition include the appearance of an out-of-phase gapless mode (in addition to the standard gapless in-phase mode) in the spectrum of the decoupled superfluid phase and a discontinuous change in the molecular momentum distribution function.

Quantum phase transitions across a p-wave Feshbach resonance

We study a single-species polarized Fermi gas tuned across a narrow p-wave Feshbach resonance. We show that in the course of a Bose-Einstein condensation (BEC)-BCS crossover, the system can undergo a magnetic-field-tuned quantum phase transition from a px-wave to a px+ipy-wave superfluid. The latter state, that spontaneously breaks time-reversal symmetry, furthermore undergoes a topological px+ipy to px+ipy transition at zero chemical potential mu. In two dimensions, for mu > 0 it is characterized by a Pfaffian ground state exhibiting topological order and non-Abelian excitations familiar from fractional quantum Hall systems.

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.

Nonequilibrium dynamics and thermodynamics of a degenerate fermi gas across a feshbach resonance

We consider a two-species degenerate Fermi gas coupled by a diatomic Feshbach resonance. We show that the resulting superfluid can exhibit a form of coherent BEC-to-BCS oscillations in response to a nonadiabatic change in the system's parameters, such as, for example, a sudden shift in the position of the Feshbach resonance. In the narrow resonance limit, the resulting solitonlike collisionless dynamics can be calculated analytically. In equilibrium, the thermodynamics can be accurately computed across the full range of BCS-BEC crossover, with corrections controlled by the ratio of the resonance width to the Fermi energy.

Superfluid transitions in bosonic atom-molecule mixtures near a Feshbach resonance

We study bosonic atoms near a Feshbach resonance and predict that, in addition to standard normal and atomic superfluid phases, this system generically exhibits a distinct phase of matter: a molecular superfluid, where molecules are superfluid while atoms are not. We explore zero- and finite-temperature properties of the molecular superfluid (a bosonic, strong-coupling analog of a BCS superconductor), and study quantum and classical phase transitions between the normal, molecular superfluid, and atomic superfluid states.

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.

Universal elasticity and fluctuations of nematic gels

We study elasticity of spontaneously orientationally ordered amorphous solids, characterized by a vanishing transverse shear modulus, as realized by nematic elastomers and gels. We show that local heterogeneities and elastic nonlinearities conspire to lead to anomalous nonlocal universal elasticity controlled by a nontrivial infrared fixed point. Namely, such solids are characterized by universal shear and bending moduli that, respectively, vanish and diverge at long scales, are universally incompressible, and exhibit a universal negative Poisson ratio and a non-Hookean elasticity down to arbitrarily low strains. Based on expansion about five dimensions, we argue that the nematic order is stable to thermal fluctuation and local heterogeneities down to d(lc)<3.

Liquid-crystal-solid interface structure at the antiferroelectric-ferroelectric phase transition

Total internal reflection is used to probe the molecular organization at the surface of a tilted chiral smectic liquid crystal at temperatures in the vicinity of the bulk antiferroelectric-ferroelectric phase transition. Data are interpreted using an exact analytical solution of a real model for ferroelectric order at the surface. In the mixture T3, ferroelectric surface order is expelled with the bulk ferroelectric-antiferroelectric transition. The conditions for ferroelectric order at the surface of an antiferroelectric bulk are presented.

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.

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.

Theory of quantum Hall nematics

Transport measurements on two-dimensional electron systems in moderate magnetic fields suggest the existence of a spontaneously orientationally ordered, compressible liquid state. We develop and analyze a microscopic theory of such a "quantum Hall nematic" (QHN) phase, predict the existence of a novel, highly anisotropic q(3) density-director mode, find that the T = 0 long-range orientational order is unstable to weak disorder, and compute the tunneling into such a strongly correlated state. This microscopic approach is supported and complemented by a hydrodynamic model of the QHN, which, in the dissipationless limit, reproduces the modes of the microscopic model.

Pseudospin canting transition and stripes in bilayer quantum Hall ferromagnets: a self-charging capacitor

We predict that in nu(T) = 1 bilayer quantum Hall (QH) pseudoferromagnets, an in-plane magnetic field can induce a reentrant pseudospin "canting" transition between interlayer charge balanced (planar) to imbalanced (canted) QH states. At T = 0 ( T>0) this quantum (classical) transition is in a new, anisotropic, compressible (2+1)D (2D) Ising universality class. The striking experimental signatures are the universal nonlinear charge-voltage and in-plane field relations, and the divergence of the differential bilayer capacitance at the transition, resulting in a bilayer capacitor that spontaneously charges itself, even in the absence of an applied interlayer voltage.

Universality and scaling in the disordering of a smectic liquid crystal

We present experimental and theoretical studies of the effects of quenched disorder on one-dimensional crystal ordering in three dimensions. This fragile smectic liquid crystal layering, the material with the simplest positional order, is also the most easily deformed periodic structure and is, therefore, profoundly affected by disorder, introduced here by confinement in silica aerogel. Theory and experiment combine to characterize this system to an extraordinary degree, their close accord producing a coherent picture: crystal ordering is lost, giving way to extended short-range correlations that exhibit universal structure and scaling, anomalous layer elasticity, and glassy dynamics.

Novel phases and reentrant melting of two-dimensional colloidal crystals

We investigate two-dimensional (2D) melting in the presence of a one-dimensional (1D) periodic potential as, for example, realized in recent experiments on 2D colloids subjected to two interfering laser beams. The topology of the phase diagram is found to depend primarily on two factors: the relative orientation of the 2D crystal and the periodic potential troughs, which selects a set of Bragg planes running parallel to the troughs, and the commensurability ratio p=a(')/d of the spacing a(') between these Bragg planes to the period d of the periodic potential. The complexity of the phase diagram increases with the magnitude of the commensurabilty ratio p. Rich phase diagrams, with "modulated liquid," "floating," and "locked floating" solid and smectic phases are found. Phase transitions between these phases fall into two broad universality classes, roughening and melting, driven by the proliferation of discommensuration walls and dislocations, respectively. We discuss correlation functions and the static structure factor in these phases, and make detailed predictions about the universal features close to the phase boundaries. We predict that for charged systems with highly screened short-range interactions, these melting transitions are generically reentrant as a function of the strength of the periodic potential, a prediction that is in accord with recent 2D colloid experiments. Implications of our results for future experiments are also discussed.

Interlayer tunneling in double-layer quantum hall pseudoferromagnets

We show that the interlayer tunneling I-V in double-layer quantum Hall states displays a rich behavior which depends on the relative magnitude of sample size, voltage length scale, current screening, disorder, and thermal lengths. For weak tunneling, we predict a negative differential conductance of a power-law shape crossing over to a sharp zero-bias peak. An in-plane magnetic field splits this zero-bias peak, leading instead to a "derivative" feature at V(B)(B(parallel)) = 2 pi Planck's over 2 pi upsilon B(parallel)d/e phi(0), which gives a direct measurement of the dispersion of the Goldstone mode corresponding to the spontaneous symmetry breaking of the double-layer Hall state.

A discotic disguised as a smectic: A hybrid columnar bragg glass

We show that discotics, lying deep in the columnar phase, can exhibit an x-ray scattering pattern which mimics that of a somewhat unusual smectic liquid crystal. This exotic, new glassy phase of columnar liquid crystals, which we call a "hybrid columnar Bragg glass," can be achieved by confining a columnar liquid crystal in an anisotropic random environment of, e.g., strained aerogel. Long-ranged orientational order in this phase makes single-domain x-ray scattering possible, from which a wealth of information could be extracted. We give detailed quantitative predictions for the scattering pattern in addition to exponents characterizing anomalous elasticity of the system.

Ring-pattern dynamics in smectic-C* and smectic-C*A freely suspended liquid crystal films

Ring patterns of concentric 2pi solitons in molecular orientation form in freely suspended chiral smectic-C films in response to an in-plane rotating electric field. We present measurements of the driven dynamics of ring formation under conditions of synchronous winding and of the zero-field relaxation of ring patterns, and propose a simple model which enables their quantitative description in low polarization DOBAMBC. In smectic-C*A TFMHPOBC we observe an odd-even layer number effect, with odd layer number films exhibiting order of magnitude slower relaxation rates than even layer films. We show that this rate difference is due to a much larger spontaneous polarization in odd layer number films.