Strongly correlated phases in rapidly rotating Bose gases

We consider a system of trapped spinless bosons interacting with a repulsive potential and subject to rotation. In the limit of rapid rotation and small scattering length, we rigorously show that the ground state energy converges to that of a simplified model Hamiltonian with contact interaction projected onto the Lowest Landau Level. This effective Hamiltonian models the bosonic analogue of the Fractional Quantum Hall Effect (FQHE). For a fixed number of particles, we also prove convergence of states; in particular, in a certain regime we show convergence towards the bosonic Laughlin wavefunction. This is the first rigorous justification of the effective FQHE Hamiltonian for rapidly rotating Bose gases. We review previous results on this effective Hamiltonian and outline open problems.Comment: AMSLaTeX, 23 page

The excitation spectrum for weakly interacting bosons in a trap

We investigate the low-energy excitation spectrum of a Bose gas confined in a trap, with weak long-range repulsive interactions. In particular, we prove that the spectrum can be described in terms of the eigenvalues of an effective one-particle operator, as predicted by the Bogoliubov approximation.Comment: LaTeX, 32 page

The Transition to a Giant Vortex Phase in a Fast Rotating Bose-Einstein Condensate

We study the Gross-Pitaevskii (GP) energy functional for a fast rotating Bose-Einstein condensate on the unit disc in two dimensions. Writing the coupling parameter as 1 / \eps^2 we consider the asymptotic regime \eps \to 0 with the angular velocity $\Omega$ proportional to (\eps^2|\log\eps|)^{-1} . We prove that if \Omega = \Omega_0 (\eps^2|\log\eps|)^{-1} and $\Omega_0 > 2(3\pi)^{-1}$ then a minimizer of the GP energy functional has no zeros in an annulus at the boundary of the disc that contains the bulk of the mass. The vorticity resides in a complementary `hole' around the center where the density is vanishingly small. Moreover, we prove a lower bound to the ground state energy that matches, up to small errors, the upper bound obtained from an optimal giant vortex trial function, and also that the winding number of a GP minimizer around the disc is in accord with the phase of this trial function.Comment: 52 pages, PDFLaTex. Minor corrections, sign convention modified. To be published in Commun. Math. Phy

Anisotropic transport in unidirectional lateral superlattice around half-filling of the second Landau level

We have observed marked transport anisotropy in short period (a=92 nm) unidirectional lateral superlattices around filling factors nu=5/2 and 7/2: magnetoresistance shows a sharp peak for current along the modulation grating while a dip appears for current across the grating. By altering the ratio a/l (with l=sqrt{hbar/eB_perp} the magnetic length) via changing the electron density n_e, it is shown that the nu=5/2 anisotropic features appear in the range 6.6 alt a/l alt 7.2 varying their intensities, becoming most conspicuous at a/l simeq 6.7. The peak/dip broadens with temperature roughly preserving its height/depth up to 250 mK. Tilt experiments reveal that the structures are slightly enhanced by an in-plane magnetic field B_| perpendicular to the grating but are almost completely destroyed by B_| parallel to the grating. The observations suggest the stabilization of a unidirectional charge-density-wave or stripe phase by weak external periodic modulation at the second Landau level.Comment: REVTeX, 5 pages, 3 figures, Some minor revisions, Added notes and reference

New insulating phases of two-dimensional electrons in high Landau levels: observation of sharp thresholds to conduction

The intriguing re-entrant integer quantized Hall states recently discovered in high Landau levels of high-mobility 2D electron systems are found to exhibit extremely non-linear transport. At small currents these states reflect insulating behavior of the electrons in the uppermost Landau level. At larger currents, however, a discontinuous and hysteretic transition to a conducting state is observed. These phenomena, found only in very narrow magnetic field ranges, are suggestive of the depinning of a charge density wave state, but other explanations can also be constructed.Comment: 5 pages, 5 figure

Theory of the Quantum Hall Smectic Phase II: Microscopic Theory

We present a microscopic derivation of the hydrodynamic theory of the Quantum Hall smectic or stripe phase of a two-dimensional electron gas in a large magnetic field. The effective action of the low energy is derived here from a microscopic picture by integrating out high energy excitations with a scale of the order the cyclotron energy.The remaining low-energy theory can be expressed in terms of two canonically conjugate sets of degrees of freedom: the displacement field, that describes the fluctuations of the shapes of the stripes, and the local charge fluctuations on each stripe.Comment: 20 pages, RevTex, 3 figures, second part of cond-mat/0105448 New and improved Introduction. Final version as it will appear in Physical Review

A cluster theory for a Janus fluid

Recent Monte Carlo simulations on the Kern and Frenkel model of a Janus fluid have revealed that in the vapour phase there is the formation of preferred clusters made up of a well-defined number of particles: the micelles and the vesicles. A cluster theory is developed to approximate the exact clustering properties stemming from the simulations. It is shown that the theory is able to reproduce the micellisation phenomenon.Comment: 27 pages, 8 figures, 6 table

The Effects of Disorder on the ν=1\nu=1 Quantum Hall State

A disorder-averaged Hartree-Fock treatment is used to compute the density of single particle states for quantum Hall systems at filling factor $\nu=1$. It is found that transport and spin polarization experiments can be simultaneously explained by a model of mostly short-range effective disorder. The slope of the transport gap (due to quasiparticles) in parallel field emerges as a result of the interplay between disorder-induced broadening and exchange, and has implications for skyrmion localization.Comment: 4 pages, 3 eps figure