We investigate ultracold fermionic atoms in the trilayer honeycomb lattice.In the low energy approximation,we derive an effective Hamiltonian for pseudospins.The energy spectrum shows a cubic form of the wavevector an...We investigate ultracold fermionic atoms in the trilayer honeycomb lattice.In the low energy approximation,we derive an effective Hamiltonian for pseudospins.The energy spectrum shows a cubic form of the wavevector andis gapless.The quasiparticles and quasiholes are chiral and show Berry's phase π when the wavevector adiabaticallyevolves along a closed circle.Furthermore,the experimental detection of the energy spectrum is proposed with Braggscattering techniques.展开更多
Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewe...Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewed here, along with different applications to lattice potentials with two minima per unit cell, in one and two spatial dimensions. Two independent methods for computing the tight-binding coefficients—one ab initio, based on the maximally localized Wannier functions, the other through analytic expressions in terms of the energy spectrum—are considered. In the one dimensional case, where the tight-binding coefficients can be obtained by designing a specific gauge transformation, we consider both the case of quasi resonance between the two lowest bands, and that between s and p orbitals. In the latter case, the role of the Wannier functions in the derivation of an effective Dirac equation is also reviewed. Then, we consider the case of a two dimensional honeycomb potential, with particular emphasis on the Haldane model, its phase diagram, and the breakdown of the Peierls substitution. Tunable honeycomb lattices, characterized by movable Dirac points, are also considered. Finally, general considerations for dealing with the interaction terms are presented.展开更多
We investigate the unconventional Landau levels of ultracold fermionic atoms on the two-dimensionalhoneycomb optical lattice subjected to an effective magnetic field,which is created with optical means.In the presence...We investigate the unconventional Landau levels of ultracold fermionic atoms on the two-dimensionalhoneycomb optical lattice subjected to an effective magnetic field,which is created with optical means.In the presenceof the effective magnetic field,the energy spectrum of the unconventional Landau levels is calculated.Furthermore,wepropose to detect the unconventional Landau levels with Bragg scattering techniques.展开更多
基金Supported by the Teaching and Research Foundation for the Outstanding Young Faculty of Southeast University
文摘We investigate ultracold fermionic atoms in the trilayer honeycomb lattice.In the low energy approximation,we derive an effective Hamiltonian for pseudospins.The energy spectrum shows a cubic form of the wavevector andis gapless.The quasiparticles and quasiholes are chiral and show Berry's phase π when the wavevector adiabaticallyevolves along a closed circle.Furthermore,the experimental detection of the energy spectrum is proposed with Braggscattering techniques.
基金supported by the Universidad del Pais Vasco/Euskal Herriko Unibertsitatea (Grant No. UFI 11/55)the Ministerio de Economia y Competitividad (Grant No. FIS2012-36673-C03-03)+2 种基金the Basque Government (Grant No. IT472-10)the Helmholtz Gemeinschaft Deutscher-Young Investigators Group (Grant No. VH-NG-717, Functional Nanoscale Structure and Probe Simulation Laboratory)the Impuls und Vernetzungsfonds der HelmholtzGemeinschaft Postdoc Programme
文摘Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewed here, along with different applications to lattice potentials with two minima per unit cell, in one and two spatial dimensions. Two independent methods for computing the tight-binding coefficients—one ab initio, based on the maximally localized Wannier functions, the other through analytic expressions in terms of the energy spectrum—are considered. In the one dimensional case, where the tight-binding coefficients can be obtained by designing a specific gauge transformation, we consider both the case of quasi resonance between the two lowest bands, and that between s and p orbitals. In the latter case, the role of the Wannier functions in the derivation of an effective Dirac equation is also reviewed. Then, we consider the case of a two dimensional honeycomb potential, with particular emphasis on the Haldane model, its phase diagram, and the breakdown of the Peierls substitution. Tunable honeycomb lattices, characterized by movable Dirac points, are also considered. Finally, general considerations for dealing with the interaction terms are presented.
基金Supported by the Teaching and Research Foundation for the Outstanding Young Faculty of Southeast University
文摘We investigate the unconventional Landau levels of ultracold fermionic atoms on the two-dimensionalhoneycomb optical lattice subjected to an effective magnetic field,which is created with optical means.In the presenceof the effective magnetic field,the energy spectrum of the unconventional Landau levels is calculated.Furthermore,wepropose to detect the unconventional Landau levels with Bragg scattering techniques.
