Topological semimetal in a fermionic optical lattice

Abstract

Optical lattices have an important role in advancing our understandingof correlated quantum matter. The recent implementation of orbital degrees of freedom in chequerboard1,2 and hexagonal3 optical lattices opens up a new avenue towards discovering novel quantum states of matter that have no prior analogues in solid-state electronic materials. Here, we predict that an exotic topological semimetal emerges as a parity-protected gapless state in the orbital bands of a two-dimensional fermionic optical lattice. This new quantum state is characterized by a parabolic band-degeneracy point with Berry flux 2π, in sharp contrast to the π flux of Dirac points as in graphene. We show that the appearance of this topological liquid is universal for all lattices with D4 point-group symmetry, as long as orbitals with opposite parities hybridize strongly with each other and the band degeneracy is protected by odd parity. Turning on inter-particle repulsive interactions, the system undergoes a phase transition to a topological insulator whose experimental signature includes chiral gapless domain-wall modes, reminiscent of quantum Hall edge states.

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Figure 1: The optical lattice potential and its experimental implementation.
Figure 2: The single-particle energy spectrum (measured in units of ER) for the lowest four bands and the topological structure near band-degeneracy points.
Figure 3: Topologically protected edge states and domain-wall modes.

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Acknowledgements

We appreciate the very helpful discussions with L. Fu, C. L. Kane and X-L. Qi. The work of K.S. and S.D.S. is supported by JQI-NSF-PFC, AFOSR-MURI, ARO-DARPA-OLE, and ARO-MURI. W.V.L. is supported by ARO (W911NF-07-1-0293 and 11-1-0230), ARO-DARPA-OLE (W911NF-07-1-0464) and the National Basic Research Program of China (Grant No 2012CB922101). A.H. acknlowledges support by DFG-SFB925. We thank the Kavli Institute for Theoretical Physics at UCSB for its hospitality where this research is supported in part by National Science Foundation Grant No. PHY05-51164.

Author information

W.V.L., K.S., and S.D.S. planned the work. K.S. and W.V.L. carried out most of the calculations with input from S.D.S. A.H. provided the experimental protocol. All authors contributed to the writing of the manuscript.

Correspondence to W. Vincent Liu.

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Sun, K., Liu, W., Hemmerich, A. et al. Topological semimetal in a fermionic optical lattice. Nature Phys 8, 67–70 (2012). https://doi.org/10.1038/nphys2134

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