Cold-atom lattice bends the topological rules

At the heart of topological physics is the bulk–edge correspondence, the principle that characteristics of a system’s bulk relate to and determine unusual behavior at its boundaries. An otherwise insulating material, for example, may support charge-carrying states confined to its surface. Those edge modes arise because of the properties of the bulk; in many systems, the relevant bulk properties are quantified by topological invariants called Chern numbers. Now Monika Aidelsburger and colleagues, at Ludwig-Maximilians University Munich, have used a lattice of ultracold potassium atoms to engineer a system that exhibits edge modes despite having no nonzero Chern numbers.

An ordinary crystalline solid couldn’t have those properties. An edge mode in a solid corresponds to a connection between two electron-energy bands; each band’s Chern number is equal to the number of connections it makes to higher-energy bands minus the number it makes to lower-energy bands. So if a material has any edge modes at all, its Chern numbers must be nonzero for at least the lowest- and highest-energy bands that participate in the edge modes.

Aidelsburger and colleagues get around that restriction by studying a system that’s permanently out of equilibrium due to a periodically time-varying Hamiltonian. (The same technique is used to create time crystals; see the article by Norman Yao and Chetan Nayak, Physics Today, September 2018, page 40 .) In a periodically driven system, absolute energy no longer exists; states have only a quasi-energy that’s defined modulo ℏω, where ω is the driving frequency. Because there’s no longer a lowest-energy band, it’s possible for every band to connect via an edge mode to one band below it and one band above it. The system has plenty of edge modes, and every Chern number is zero.

The theory of those unusual phases, called anomalous Floquet insulators, has been around for about a decade, but Aidelsburger and colleagues are the first to realize one in a cold-atom system. In a honeycomb optical lattice created with three lasers, they modulate the laser intensity to periodically lower the energy barriers along each set of parallel edges in turn, as shown by the red line segments in the figure. The system’s band structure depends on the amplitude and frequency of the laser modulations, so by tuning those parameters, the experimenters can bring the system into and out of the anomalous Floquet regime.

So far, the researchers have focused on the anomalous Floquet insulator in its simplest form: The potassium atoms in the lattice are noninteracting, and apart from the laser modulations, the lattice is perfectly uniform. Future work may include introducing interactions, disorder, or both, to see how the phase is affected by Fermi or Bose statistics or many-body localization. (K. Wintersperger et al., Nat. Phys., 2020, doi:10.1038/s41567-020-0949-y .)