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Register a new userNon-Abelian optical lattices: Anomalous quantum Hall effect and Dirac Fermions
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We study the properties of an ultracold Fermi gas loaded in an optical square lattice and subjected to an external and classical non-Abelian gauge field. We show that this system can be exploited as an optical analogue of relativistic quantum electrodynamics, offering a remarkable route to access the exotic properties of massless Dirac fermions with cold atoms experiments. In particular we show that the underlying Minkowski space-time can also be modified, reaching anisotropic regimes where a remarkable anomalous quantum Hall effect and a squeezed Landau vacuum could be observed.
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In this work we present an optical lattice setup to realize a full Dirac Hamiltonian in 2+1 dimensions. We show how all possible external potentials coupled to the Dirac field can arise from perturbations of the existing couplings of the honeycomb lattice model, without the need of additional laser fields. This greatly simplifies the proposed implementations, requiring only spatial modulations of the intensity of the laser beams. We finally suggest several experiments to observe the properties of the Dirac field in the setup.
Two fundamental aspects of so-called non-abelian quantum Hall states (the q-pfaffian states and more general) are a (generalized) pairing of the participating electrons and the non-abelian statistics of the quasi-hole excitations. In this paper, we show that these two aspects are linked by a duality relation, which can be made manifest by considering the K-matrices that describe the exclusion statistics of the fundamental excitations in these systems.
We study excitations in edge theories for non-abelian quantum Hall states, focussing on the spin polarized states proposed by Read and Rezayi and on the spin singlet states proposed by two of the authors. By studying the exclusion statistics properties of edge-electrons and edge-quasiholes, we arrive at a novel K-matrix structure. Interestingly, the duality between the electron and quasihole sectors links the pseudoparticles that are characteristic for non-abelian statistics with composite particles that are associated to the `pairing physics of the non-abelian quantum Hall states.
Dirac fermions are actively investigated, and the discovery of the quantized anomalous Hall effect of massive Dirac fermions has spurred the promise of low-energy electronics. Some materials hosting Dirac fermions are natural platforms for interlayer coherence effects such as Coulomb drag and exciton condensation. Here we determine the role played by the anomalous Hall effect in Coulomb drag in massive Dirac fermion systems. We focus on topological insulator films with out-of plane magnetizations in both the active and passive layers. The transverse response of the active layer is dominated by a topological term arising from the Berry curvature. We show that the topological mechanism does not contribute to Coulomb drag, yet the longitudinal drag force in the passive layer gives rise to a transverse drag current. This anomalous Hall drag current is independent of the active-layer magnetization, a fact that can be verified experimentally. It depends non-monotonically on the passive-layer magnetization, exhibiting a peak that becomes more pronounced at low densities. These findings should stimulate new experiments and quantitative studies of anomalous Hall drag.
We numerically study the interplay of band structure, topological invariant and disorder effect in two-dimensional electron system of graphene in a magnetic field. Two emph{distinct} quantum Hall effect (QHE) regimes exist in the energy band with the unconventional half-integer QHE appearing near the band center, consistent with the experimental observation. The latter is more robust against disorder scattering than the conventional QHE states near the band edges. The phase diagram for the unconventional QHE is obtained where the destruction of the Hall plateaus at strong disorder is through the float-up of extended levels toward band center and higher plateaus always disappear first. We further predict a new insulating phase between $ u =pm 2$ QHE states at the band center, which may explain the experimentally observed resistance discontinuity near zero gate voltage.
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