Topological Phases for Fermionic Cold Atoms on the Lieb Lattice

Details Topological Phases for Fermionic Cold Atoms on the Lieb Lattice Topological Phases for Fermionic Cold Atoms on the Lieb Lattice

2011-01-24

arxiv.org/abs/1101.4500v1

Phys. Rev. A 83, 063601 (2011)

Physics

Condensed Matter

Quantum Gases

12 pages, 9 figures

Scientific paper

10.1103/PhysRevA.83.063601

We investigate the properties of the Lieb lattice, i.e a face-centered square lattice, subjected to external gauge fields. We show that an Abelian gauge field leads to a peculiar quantum Hall effect, which is a consequence of the single Dirac cone and the flat band characterizing the energy spectrum. Then we explore the effects of an intrinsic spin-orbit term - a non-Abelian gauge field - and demonstrate the occurrence of the quantum spin Hall effect in this model. Besides, we obtain the relativistic Hamiltonian describing the Lieb lattice at low energy and derive the Landau levels in the presence of external Abelian and non-Abelian gauge fields. Finally, we describe concrete schemes for realizing these gauge fields with cold fermionic atoms trapped in an optical Lieb lattice. In particular, we provide a very efficient method to reproduce the intrinsic (Kane-Mele) spin-orbit term with assisted-tunneling schemes. Consequently, our model could be implemented in order to produce a variety of topological states with cold-atoms.

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