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Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice

Nature volume 483, pages 302–305 (2012)Cite this article

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Abstract

Dirac points are central to many phenomena in condensed-matter physics, from massless electrons in graphene to the emergence of conducting edge states in topological insulators1,2. At a Dirac point, two energy bands intersect linearly and the electrons behave as relativistic Dirac fermions. In solids, the rigid structure of the material determines the mass and velocity of the electrons, as well as their interactions. A different, highly flexible means of studying condensed-matter phenomena is to create model systems using ultracold atoms trapped in the periodic potential of interfering laser beams3,4. Here we report the creation of Dirac points with adjustable properties in a tunable honeycomb optical lattice. Using momentum-resolved interband transitions, we observe a minimum bandgap inside the Brillouin zone at the positions of the two Dirac points. We exploit the unique tunability of our lattice potential to adjust the effective mass of the Dirac fermions by breaking inversion symmetry. Moreover, changing the lattice anisotropy allows us to change the positions of the Dirac points inside the Brillouin zone. When the anisotropy exceeds a critical limit, the two Dirac points merge and annihilate each other—a situation that has recently attracted considerable theoretical interest5,6,7,8,9 but that is extremely challenging to observe in solids10. We map out this topological transition in lattice parameter space and find excellent agreement with ab initio calculations. Our results not only pave the way to model materials in which the topology of the band structure is crucial, but also provide an avenue to exploring many-body phases resulting from the interplay of complex lattice geometries with interactions11,12,13.

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Figure 1: Optical lattice with adjustable geometry.
Figure 2: Probing the Dirac points.
Figure 3: Movement of the Dirac points.
Figure 4: Topological transition.

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Acknowledgements

We would like to thank D. Poletti for bringing our attention to honeycomb lattices without six-fold symmetry, and N. Cooper and F. Hassler for discussions. We acknowledge SNF, NCCR-MaNEP, NCCR-QSIT, NAME-QUAM (EU, FET open), SQMS (ERC advanced grant) and ESF (POLATOM) for funding.

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Authors and Affiliations

  1. Institute for Quantum Electronics, ETH Zurich, Zurich, 8093, Switzerland

    Leticia Tarruell, Daniel Greif, Thomas Uehlinger, Gregor Jotzu & Tilman Esslinger

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  1. Leticia Tarruell
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  2. Daniel Greif
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  3. Thomas Uehlinger
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  4. Gregor Jotzu
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Contributions

The data were measured and analysed by L.T., D.G., T.U. and G.J. The tunable optical lattice was built by D.G. The experimental concept was developed by T.E. All authors contributed extensively to the discussion of the results, as well as to the preparation of the manuscript.

Corresponding author

Correspondence to Tilman Esslinger.

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The authors declare no competing financial interests.

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Tarruell, L., Greif, D., Uehlinger, T. et al. Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice. Nature 483, 302–305 (2012). https://doi.org/10.1038/nature10871

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