Broken Symmetry and Josephson-like Tunneling in Quantum Hall Bilayers

I review recent novel experimental and theoretical advances in the physics of quantum Hall effect bilayers. Of particular interest is a broken symmetry state which optimizes correlations by putting the electrons into a coherent superposition of the two different layers.Comment: to be published in Proc. 11th International Conf. on Recent Progress in Many-Body Theories, ed. R.F. Bishop, T. Brandes, K.A. Gernoth, N.R. Walet, and Y. Xian, to appear in the series "Advances in Quantum Many-Body Theory" (World Scientific). 12 pages, 4 figure

DC Transformer and DC Josephson(-like) Effects in Quantum Hall Bilayers

In the early days of superconductivity, Ivar Giaver discovered that it was possible to make a novel DC transformer by using one superconductor to drag vortices through another. An analogous effect was predicted to exist in quantum Hall bilayers and has recently been discovered experimentally by Eisenstein's group at Caltech. Similarly, new experiments from the Caltech group have demonstrated the existence of a Josephson-like `supercurrent' branch for electrons coherently tunnelling between the two layers.Comment: To Appear in Proceedings of the Nobel Symposium on Quantum Coherence, Goteborg, Sweden, December, 2001 (Physica Scripta) Revision: references update

Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes

Starting from the graphene lattice tight-binding Hamiltonian with an on-site U and long-range Coulomb repulsion, we derive an interacting continuum Dirac theory governing the low-energy behavior of graphene in an applied magnetic field. Initially, we consider a clean graphene system within this effective theory and explore integer quantum Hall ferromagnetism stabilized by exchange from the long-range Coulomb repulsion. We study in detail the ground state and excitations at nu = 0 and nu = \pm 1, taking into account small symmetry-breaking terms that arise from the lattice-scale interactions, and also explore the ground states selected at nu = \pm 3, \pm 4, and \pm 5. We argue that the ferromagnetic regime may not yet be realized in current experimental samples, which at the above filling factors perhaps remain paramagnetic due to strong disorder. In an attempt to access the latter regime where the role of exchange is strongly suppressed by disorder, we apply Hartree theory to study the effects of interactions. Here, we find that Zeeman splitting together with symmetry-breaking interactions can in principle produce integer quantum Hall states in a paramagnetic system at nu = 0, \pm 1 and \pm 4, but not at nu = \pm 3 or \pm 5, consistent with recent experiments in high magnetic fields. We make predictions for the activation energies in these quantum Hall states which will be useful for determining their true origin.Comment: 13 pages, 2 figure

Superfluid-insulator transitions of two-species Bosons in an optical lattice

We consider a realization of the two-species bosonic Hubbard model with variable interspecies interaction and hopping strength. We analyze the superfluid-insulator (SI) transition for the relevant parameter regimes and compute the ground state phase diagram for odd filling at commensurate densities. We find that in contrast to the even commensurate filling case, the superfluid-insulator transition occurs with (a) simultaneous onset of superfluidity of both species or (b) coexistence of Mott insulating state of one species and superfluidity of the other or, in the case of unit filling, (c) complete depopulation of one species. The superfluid-insulator transition can be first order in a large region of the phase diagram. We develop a variational mean-field method which takes into account the effect of second order quantum fluctuations on the superfluid-insulator transition and corroborate the mean-field phase diagram using a quantum Monte Carlo study.Comment: 12 pages, 11 figure

Fractional charges and quantum phase transitions in imbalanced bilayer quantum Hall systems

We extend the Composite Boson theory to study slightly im-balanced bi-layer Quantum Hall systems. In the global $U(1)$ symmetry breaking excitonic superfluid side, as the imbalance increases, the system supports continuously changing fractional charges. In the translational symmetry breaking pseudo-spin density wave (PSDW) side, there are two quantum phase transitions from the commensurate PSDW to an in-commensurate PSDW and then to the excitonic superfluid state. We compare our theory with experimental data and also the previous microscopic calculations.Comment: 4+ pages, 2 figures. 1 table, Final version to appear in Phys. Rev. Let

Asymmetry gap in the electronic band structure of bilayer graphene.

A tight binding model is used to calculate the band structure of bilayer graphene in the presence of a potential difference between the layers that opens a gap U between the conduction and valence bands. In particular, a self consistent Hartree approximation is used to describe imperfect screening of an external gate, employed primarily to control the density n of electrons on the bilayer, resulting in a potential difference between the layers and a density dependent gap U(n). We discuss the influence of a finite asymmetry gap U(0) at zero excess density, caused by the screening of an additional transverse electric field, on observations of the quantum Hall effect

Multi-flavor bosonic Hubbard models in the first excited Bloch band of an optical lattice

We propose that by exciting ultra cold atoms from the zeroth to the first Bloch band in an optical lattice, novel multi-flavor bosonic Hubbard Hamiltonians can be realized in a new way. In these systems, each flavor hops in a separate direction and on-site exchange terms allow pairwise conversion between different flavors. Using band structure calculations, we determine the parameters entering these Hamiltonians and derive the mean field ground state phase diagram for two effective Hamiltonians (2D, two-flavors and 3D, three flavors). Further, we estimate the stability of atoms in the first band using second order perturbation theory and find lifetimes that can be considerable (10-100 times) longer than the relevant time scale associated with inter-site hopping dynamics, suggesting that quasi-equilibrium can be achieved in these meta-stable states.Comment: 26 pages, 18 figure