Experimental realization of the topological Haldane model with ultracold fermions

By G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, Tilman Esslinger. Nature, 2014

1,877 citations recorded by the source corpus.

The Haldane model on a honeycomb lattice is a paradigmatic example of a Hamiltonian featuring topologically distinct phases of matter. It describes a mechanism through which a quantum Hall effect can appear as an intrinsic property of a band structure, rather than being caused by an external magnetic field. Although physical implementation has been considered unlikely, the Haldane model has provided the conceptual basis for theoretical and experimental research exploring topological insulators and superconductors. Here we report the experimental realization of the Haldane model and the characterization of its topological band structure, using ultracold fermionic atoms in a periodically modulated optical honeycomb lattice. The Haldane model is based on breaking both time-reversal symmetry and inversion symmetry. To break time-reversal symmetry, we introduce complex next-nearest-neighbour tunnelling terms, which we induce through circular modulation of the lattice position. To break inversion symmetry, we create an energy offset between neighbouring sites. Breaking either of these symmetries opens a gap in the band structure, which we probe using momentum-resolved interband transitions. We explore the resulting Berry curvatures, which characterize the topology of the lowest band, by applying a constant force to the atoms and find orthogonal drifts analogous to a Hall current. The competition between the two broken symmetries gives rise to a transition between topologically distinct regimes. By identifying the vanishing gap at a single Dirac point, we map out this transition line experimentally and quantitatively compare it to calculations using Floquet theory without free parameters. We verify that our approach, which allows us to tune the topological properties dynamically, is suitable even for interacting fermionic systems. Furthermore, we propose a direct extension to realize spin-dependent topological Hamiltonians.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/c4dda81b952f3c3e77c8c1803ed028474289ae45

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Citations in the corpus

Floquet topological transitions in a driven one-dimensional topological insulator (2015, background): “…much interest in driven topological phases from the theoretical point of view [46–48] and where recent experimental progress has allowed the realization of the SSH model [49], the Haldane model [20], the Hofstadter model [50], and even the measurement of the relevant topological invariants [49,50].”
Inhomogeneous Weyl and Dirac Semimetals: Transport in Axial Magnetic Fields and Fermi Arc Surface States from Pseudo-Landau Levels (2016, background): “[79] Gregor Jotzu, Michael Messer, Remi Desbuquois, Martin Lebrat, Thomas Uehlinger, Daniel Greif, and Tilman Esslinger, “Experimental realization of the topological haldane model with ultracold fermions,” Nature 515, 237–240 (2014).”
Realization of an anomalous Floquet topological system with ultracold atoms (2020, methodology): “Nonetheless, if the spread is not too large and if we can perform the measurement close enough at the phase transition point, we can identify the topological charge of the singularity by determining the sign of the local Hall drifts across the phase transition [14, 18]:”
Symmetry and Topology in Non-Hermitian Physics (2018, background): “[197] G.”
New perspectives for Rashba spin-orbit coupling. (2015, background): “7) [154], as well as the realization of the Haldane model [155].”
Band geometry, Berry curvature and superfluid weight (2016, methodology): “Our results could also be of immediate experimental interest, as the Haldane-Hubbard model has recently been realized in cold atomic gases experiments [27,28], and a realization of the Kane-Mele-Hubbard model has also been proposed [27].”
Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport (2016, background): “electronic systems; rather, it is universal: it was recently demonstrated for photons [9–11], cold atoms [12,13], mechanical systems [14,15], and was also predicted for”
Topological Phases of Non-Hermitian Systems (2018, background): “[15] Gregor Jotzu, Michael Messer, Rémi Desbuquois, Martin Lebrat, Thomas Uehlinger, Daniel Greif, and Tilman Esslinger, “Experimental realization of the topological haldane model with ultracold fermions,” Nature 515, 237 (2014).”