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.

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.

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.

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.

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.

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.

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.