Correlation-hole induced paired quantum Hall states in the lowest Landau level

A theory is developed for the paired even-denominator fractional quantum Hall states in the lowest Landau level. We show that electrons bind to quantized vortices to form composite fermions, interacting through an exact instantaneous interaction that favors chiral p-wave pairing. There are two canonically dual pairing gap functions related by the bosonic Laughlin wave function (Jastrow factor) due to the correlation holes. We find that the ground state is the Moore-Read Pfaffian in the long-wavelength limit for weak Coulomb interactions, a new Pfaffian with an oscillatory pairing function for intermediate interactions, and a Read-Rezayi composite Fermi liquid beyond a critical interaction strength. Our findings are consistent with recent experimental observations of the 1/2 and 1/4 fractional quantum Hall effects in asymmetric wide quantum wells.     

Ballistic phonon studies in the lowest Landau level

We report time-resolved studies of ballistic phonon absorption in the fractional quantum Hall regime at Landau level filling factors of and . The technique used can resolve the interaction of the two-dimensional electron system with LA and TA phonons and has been used to measure the temperature variation of the heat capacity of a single layer of electrons at . The energy gaps at have also been measured and found to be in good agreement with theory. The roles of compressible and incompressible regions in the phonon absorption process are discussed. Angle resolved measurements at are also in good agreement with theory.     

Dissipation and criticality in the lowest Landau level of graphene

The lowest Landau level of graphene is studied numerically by considering a tight-binding Hamiltonian with disorder. The Hall conductance sigma_{xy} and the longitudinal conductance sigma_{xx} are computed. We demonstrate that bond disorder can produce a plateaulike feature centered at nu=0, while the longitudinal conductance is nonzero in the same region, reflecting a band of extended states between +/-E_{c}, whose magnitude depends on the disorder strength. The critical exponent corresponding to the localization length at the edges of this band is found to be 2.47+/-0.04. When both bond disorder and a finite mass term exist the localization length exponent varies continuously between approximately 1.0 and approximately 7/3.     

Exact density of states for lowest Landau level in white noise potential superfield representation for interacting systems

The density of states of two-dimensional electrons in a strong perpendicular magnetic field and white-noise potential is calculated exactly under the provision that only the states of the free electrons in the lowest Landau level are taken into account. It is used that the integral over the coordinates in the plane perpendicular to the magnetic field in a Feynman graph yields the inverse of the number of Euler trails through the graph, whereas the weight by which a Feynman graph contributes in this disordered system is times that of the corresponding interacting system. Thus the factors cancel which allows the reduction of thed dimensional disordered problem to a (d-2) dimensional ⁴ interaction problem. The inverse procedure and the equivalence of disordered harmonic systems with interacting systems of superfields is used to give a mapping of interacting systems withU(1) invariance ind dimensions to interacting systems with UPL(1,1) invariance in (d+2) dimensions. The partition function of the new systems is unity so that systems with quenched disorder can be treated by averaging exp(–H) without recourse to the replica trick.Supported in part by the DFG through SFB123 Stochastic Mathematical Models     

Rapidly rotating Bose-Einstein condensates in and near the lowest Landau level

We create rapidly rotating Bose-Einstein condensates in the lowest Landau level by spinning up the condensates to rotation rates Omega > 99% of the centrifugal limit for a harmonically trapped gas, while reducing the number of atoms. As a consequence, the chemical potential drops below the cyclotron energy 2 variant Planck's over 2pi Omega. While in this mean-field quantum-Hall regime we still observe an ordered vortex lattice, its elastic shear strength is strongly reduced, as evidenced by the observed very low frequency of Tkachenko modes. Furthermore, the gas approaches the quasi-two-dimensional limit. The associated crossover from interacting- to ideal-gas behavior along the rotation axis results in a shift of the axial breathing mode frequency.     

Possible reentrance of the fractional quantum Hall effect in the lowest Landau level

In the framework of a recently developed model of interacting composite fermions, we calculate the energy of different solid and Laughlin-type liquid phases of spin-polarized composite fermions. The liquid phases have a lower energy than the competing solids around the electronic filling factors nu = 4/11,6/17, and 4/19 and may thus be responsible for the fractional quantum Hall effect at nu = 4/11. The alternation between solid and liquid phases when varying the magnetic field may lead to reentrance phenomena in analogy with the observed reentrant integral quantum Hall effect.     

Possible pairing-induced even-denominator fractional quantum Hall effect in the lowest Landau level

We report on our theoretical investigations that point to the possibility of a fractional quantum Hall effect with partial spin polarization at nu = 3/8. The physics of the incompressible state proposed here involves p-wave pairing of composite fermions in the spin reversed sector. The temperature and magnetic field regimes for the realization of this state are estimated.     

Random-phase approximation for the grand-canonical potential of composite fermions in the half-filled lowest Landau level

We reconsider the theory of the half-filled lowest Landau level using the Chern-Simons formulation and study the grand-canonical potential in the random-phase approximation (RPA). Calculating the unperturbed response functions for current- and charge-density exactly, without any expansion with respect to frequency or wave vector, we find that the integral for the ground-state energy converges rapidly (algebraically) at large wave vectors k, but exhibits a logarithmic divergence at small k. This divergence originates in the k^-2 singularity of the Chern-Simons interaction and it is already present in lowest-order perturbation theory. A similar divergence appears in the chemical potential. Beyond the RPA, we identify diagrams for the grand-canonical potential (ladder-type, maximally crossed, or a combination of both) which diverge with powers of the logarithm. We expand our result for the RPA ground-state energy in the strength of the Coulomb interaction. The linear term is finite and its value compares well with numerical simulations of interacting electrons in the lowest Landau level. Received: 19 February 1998 / Revised: 25 March 1998 / Accepted: 17 April 1998     

Characterizing neutral modes of fractional states in the second Landau level

Fractionally charged quasiparticles, which obey non-abelian statistics, were predicted to exist in the ν=8/3, ν=5/2, and ν=7/3 fractional quantum Hall states (in the second Landau level). Here we present measurements of charge and neutral modes in these states. For both ν=7/3 and ν=8/3 states, we found a quasiparticle charge e=1/3 and an upstream neutral mode only in ν=8/3-excluding the possibility of non-abelian Read-Rezayi states and supporting Laughlin-like states. The absence of an upstream neutral mode in the ν=7/3 state also proves that edge reconstruction was not present in the ν=7/3 state, suggesting its absence also in ν=5/2 state, and thus may provide further support for the non-abelian anti-pfaffian nature of the ν=5/2 state.