arXiv subjects

Leo Radzihovsky

Publications and source records attributed to Leo Radzihovsky.

At least 109 records · Page 6Linked to original sources

arXiv2002

Velocity-force characteristics of an interface driven through a periodic potential

We study the creep dynamics of a two-dimensional interface driven through a periodic potential using dynamical renormalization group methods. We find that the nature of weak-drive transport depends qualitatively on whether the temperature $T$ is above or below the equilibrium roughening transition temperature $T_c$. Above $T_c$, the velocity-force characteristics is Ohmic, with linear mobility exhibiting a jump discontinuity across the transition. For $T \le T_c$, the transport is highly nonlinear, exhibiting an interesting crossover in temperature and weak external force $F$. For intermediate drive, $F>F_*$, we find near $T_c^{-}$ a power-law velocity-force characteristics $v(F)\sim F^σ$, with $σ-1\propto \tilde{t}$, and well-below $T_c$, $v(F)\sim e^{-(F_*/F)^{2\tilde{t}}}$, with $\tilde{t}=(1-T/T_c)$. In the limit of vanishing drive ($F\ll F_*$) the velocity-force characteristics crosses over to $v(F)\sim e^{-(F_0/F)}$, and is controlled by soliton nucleation.

cond-mat.stat-mech↗

arXiv2002

Theory of Banana Liquid Crystal Phases and Phase Transitions

We study phases and phase transitions that can take place in the newly discovered banana (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 novel 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 novel nematic $N_T$ phase with $D_{2d}$ symmetry that is neither uniaxial nor biaxial. Interestingly, the Isotropic-Tetrahedratic transition is {\em 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.

cond-mat.soft↗

arXiv2001

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 novel materials.

cond-mat.soft↗

arXiv2001

Persistent Currents and Dissipation in Narrow Bilayer Quantum Hall Bars

Bilayer quantum Hall states support a flow of nearly dissipationless staggered current which can only decay through collective channels. We study the dominant finite-temperature dissipation mechanism which in narrow bars is driven by thermal nucleation of pseudospin solitons. We find the finite-temperature resistivity, predict the resulting staggered current-voltage characteristics, and calculate the associated zero-temperature critical staggered current and gate voltage.

cond-mat.mes-hall↗

arXiv2001

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.

cond-mat.mes-hall↗

arXiv2001

"Soft" Anharmonic Vortex Glass in Ferromagnetic Superconductors

Ferromagnetic order in superconductors can induce a {\em spontaneous} vortex (SV) state. For external field ${\bf H}=0$, rotational symmetry guarantees a vanishing tilt modulus of the SV solid, leading to drastically different behavior than that of a conventional, external-field-induced vortex solid. We show that quenched disorder and anharmonic effects lead to elastic moduli that are wavevector-dependent out to arbitrarily long length scales, and non-Hookean elasticity. The latter implies that for weak external fields $H$, the magnetic induction scales {\em universally} like $B(H)\sim B(0)+ c H^α$, with $α\approx 0.72$. For weak disorder, we predict the SV solid is a topologically ordered vortex glass, in the ``columnar elastic glass'' universality class.

cond-mat.soft↗

arXiv2001

Pseudo-spin canting transition in bilayer quantum Hall ferromagnets: a self-charging capacitor

For sufficiently strong in-plane magnetic field a $ν_T=1$ bilayer quantum Hall pseudo-ferromagnet is expected to exhibit a soliton lattice. For sufficiently close layers and large in-plane field, we predict this incommensurate ``planar'' phase $P_I$ to undergo a reentrant pseudo-spin canting transition to an incommensurate state $C_I$, with a finite out-of-plane pseudo-magnetization component, corresponding to an interlayer charge imbalance in regions between solitons. At $T>0$ the transition is in the 2d compressible Ising universality class, and at T=0, the quantum transition is in heretofore unexplored 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.

cond-mat.mes-hall↗

arXiv2000

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 {\em 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.

cond-mat.soft↗

arXiv2000

Fluctuation-Driven 1st-Order Isotropic-to-Tetrahedratic Phase Transition

Motivated in part by recent experiments on liquid crystals with bent-core molecules, which are observed to display a spontaneous chiral symmetry breaking, we introduce a field theory of a 3rd-rank tensor order parameter T^{ijk} to describe the isotropic-to-tetrahedratic phase transition that we predict to take place in these materials. We study the critical properties of the corresponding phase transition and find that this transition, continuous at the mean-field level, is generically driven 1st-order by thermal fluctuations.

cond-mat.soft↗

arXiv2000

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 select 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 diagram, 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 of 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, prediction that is in accord with recent 2d colloid experiments. Implications of our results for future experiments are also discussed.

cond-mat.soft↗

arXiv2000

Interlayer tunneling in double-layer quantum Hall pseudo-ferromagnets

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 $V_B(B_{||})=2π\hbar v B_{||}d/eϕ_0$, which gives a direct measure of the dispersion of the Goldstone mode corresponding to the spontaneous symmetry breaking of the double-layer Hall state.

cond-mat.mes-hall↗

arXiv1999

Interstitials, Vacancies and Dislocations in Flux-Line Lattices: A Theory of Vortex Crystals, Supersolids and Liquids

We study a three dimensional Abrikosov vortex lattice in the presence of an equilibrium concentration of vacancy, interstitial and dislocation loops. Vacancies and interstitials renormalize the long-wavelength bulk and tilt elastic moduli. Dislocation loops lead to the vanishing of the long-wavelength shear modulus. The coupling to vacancies and interstitials - which are always present in the liquid state - allows dislocations to relax stresses by climbing out of their glide plane. Surprisingly, this mechanism does not yield any further independent renormalization of the tilt and compressional moduli at long wavelengths. The long wavelength properties of the resulting state are formally identical to that of the ``flux-line hexatic'' that is a candidate ``normal'' hexatically ordered vortex liquid state.

cond-mat.soft↗

arXiv1999

Smectic Liquid Crystals in Random Environments

We study smectic liquid crystals in random environments, e.g., aerogel. A low temperature analysis reveals that even arbitrarily weak quenched disorder (i.e., arbitrarily low aerogel density) destroys translational (smectic) order. A harmonic approximation to the elastic energy suggests that there is no ``smectic Bragg glass'' phase in this system: even at zero temperature, it is riddled with dislocation loops induced by the quenched disorder. This result implies the destruction of orientational (nematic) order as well, and that the thermodynamically sharp Nematic-Smectic-A transition is destroyed by disorder, in agreement with recent experimental results. We also show that the anharmonic elastic terms neglected in the above treatment are important (i.e., are ``relevant'' in the renormalization group sense); whether they alter the above conclusions about the smectic Bragg glass, orientational disorder, and the existence of sharp transitions, remains an open question. However, they do not alter our conclusion that translational (smectic) order is always destroyed. In contrast, we expect that weak annealed disorder should have no qualitative effects on the smectic order.

cond-mat.soft↗

arXiv1999

Light Induced Melting of Colloidal Crystals in Two Dimensions

We demonstrate that particles confined to two dimensions (2d) and subjected to a one-dimensional (1d) periodic potential exhibit a rich phase diagram, with both ``locked floating solids'' and smectic phases. The resulting phases and phase transitions are studied as a function of temperature and potential strength. We find reentrant melting as a function of the potential strength. Our results lead to universal predictions consistent with recent experiments on 2d colloids in the presence of a laser-induced 1d periodic potential.

cond-mat.soft↗

arXiv1999

Two new topologically ordered glass phases of smectics confined in anisotropic random media

We show that smectic liquid crystals confined in_anisotropic_ porous structures such as e.g.,_strained_ aerogel or aerosil exhibit two new glassy phases. The strain both ensures the stability of these phases and determines their nature. One type of strain induces an ``XY Bragg glass'', while the other creates a novel, triaxially anisotropic ``m=1 Bragg glass''. The latter exhibits anomalous elasticity, characterized by exponents that we calculate to high precision. We predict the phase diagram for the system, and numerous other experimental observables.

cond-mat.soft↗

arXiv1998

Transversely Driven Charge Density Waves and Striped Phases of High-T$_c$ Superconductors: The Current Effect Transistor

We show that a normal (single particle) current density $J_x$ {\em transverse} to the ordering wavevector $2k_F{\bf\hat{z}}$ of a charge density wave (CDW) has dramatic effects both above and {\em below} the CDW depinning transition. It exponentially (in $J_x$) enhances CDW correlations, and exponentially suppresses the longitudinal depinning field. The intermediate longitudinal I-V relation also changes, acquiring a {\em linear} regime. We propose a novel ``current effect transistor'' whose CDW channel is turned on by a transverse current. Our results also have important implications for the recently proposed ``striped phase'' of the high-T$_c$ superconductors.

cond-mat.soft↗

arXiv1997

Elasticity, Shape Fluctuations and Phase Transitions in the New Tubule Phase of Anisotropic Tethered Membranes

We study the shape, elasticity and fluctuations of the recently predicted (cond-mat/9510172) and subsequently observed (in numerical simulations) (cond-mat/9705059) tubule phase of anisotropic membranes, as well as the phase transitions into and out of it. This novel phase lies between the previously predicted flat and crumpled phases, both in temperature and in its physical properties: it is crumpled in one direction, and extended in the other. Its shape and elastic properties are characterized by a radius of gyration exponent $ν$ and an anisotropy exponent $z$. We derive scaling laws for the radius of gyration $R_G(L_\perp,L_y)$ (i.e. the average thickness) of the tubule about a spontaneously selected straight axis and for the tubule undulations $h_{rms}(L_\perp,L_y)$ transverse to its average extension. For phantom (i.e. non-self-avoiding) membranes, we predict $ν=1/4$, $z=1/2$ and $η_κ=0$, exactly, in excellent agreement with simulations. For membranes embedded in the space of dimension $d<11$, self-avoidance greatly swells the tubule and suppresses its wild transverse undulations, changing its shape exponents $ν$ and $z$. We give detailed scaling results for the shape of the tubule of an arbitrary aspect ratio and compute a variety of correlation functions, as well as the anomalous elasticity of the tubules. Finally we present a scaling theory for the shape of the membrane and its specific heat near the continuous transitions into and out of the tubule phase and perform detailed renormalization group calculations for the crumpled-to-tubule transition for phantom membranes.

cond-mat.soft↗

arXiv1997

Nematic--to--Smectic-A Transition in Aerogel

We study a model for the Nematic--Smectic-A (NA) transition in aerogel, and find that even arbitrarily weak quenched disorder (i.e., low aerogel density) destroys translational (smectic) order. Ignoring elastic anharmonicities, but keeping anharmonic couplings to disorder, leads to the prediction that there is no ``Bragg glass'' phase in this system: it is riddled with dislocation loops induced by the quenched disorder. Orientational (nematic) order is destroyed as well, as is the thermodynamically sharp NA transition, in agreement with recent experimental results.

cond-mat.soft↗