Topological phases for fermionic cold atoms on the Lieb lattice

N. Goldman, D. F. Urban, and D. Bercioux
Phys. Rev. A 83, 063601 – Published 2 June 2011

Abstract

We investigate the properties of the Lieb lattice, that is, 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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  • Received 24 January 2011

DOI:https://doi.org/10.1103/PhysRevA.83.063601

©2011 American Physical Society

Authors & Affiliations

N. Goldman*

  • Center for Nonlinear Phenomena and Complex Systems - Université Libre de Bruxelles (U.L.B.), Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium

D. F. Urban

  • Physikalisches Institut, Albert-Ludwigs-Universität, D-79104 Freiburg, Germany

D. Bercioux

  • Freiburg Institute for Advanced Studies, Albert-Ludwigs-Universität, D-79104 Freiburg, Germany and Physikalisches Institut, Albert-Ludwigs-Universität, D-79104 Freiburg, Germany

  • *ngoldman@ulb.ac.be

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Vol. 83, Iss. 6 — June 2011

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