High Chern Numbers in Photonic Crystals

Abstract

The romance with topological physics is now more than thirty years old and remains as fiery as ever [1]. Some see the primary importance of the class of materials called topological insulators as enabling revolutionary technologies such as quantum computers and spintronic devices, others as the realization of a new type of order that goes beyond conventional phases of matter, or as a real-world manifestation of the most abstract mathematical theories of topology. But in my view, the most enticing feature of topological behavior is its universality, the fact that the physical properties of a system are characterized by a single topological number, rather than by specific systemdependent details. This implies that systems made of entirely different microscopic elements, but whose topological numbers are the same, are fundamentally equivalent. Now, Marin Soljacic at the Massachusetts Institute of Technology, Cambridge, and colleagues report a striking example of this universality [2]. The authors investigate the propagation of photons in twodimensional photonic crystals known to exhibit an optical version of the electronic “quantum anomalous Hall effect” [3]—a prototypical topological phenomenon. Their experiments demonstrate that the universal number that captures the properties of such crystals—the “Chern number,” which characterizes the number of topologically protected states—takes on unprecedentedly large values. The availability of multiple topological channels might enable novel photonic devices and effects that would be impossible with Chern numbers limited to 1. The use of abstract topological concepts to describe condensed-matter systems was first put forward in the description of the integer quantum Hall effect by David Thouless, Mahito Kohmoto, Peter Nightingale, and Marcel den Nijs [4]. They showed that the Hall conductance of a two-dimensional electron system under a large magnetic field can be quantized, that is, fixed to be an integer times a fundamental constant, e2/h. That integer, known as the Chern number, corresponds to the number of edge states that carry current, without scattering, across the system. The Chern number indicates topological behavior in the sense that small deformations of the system (such as disorder, strain, and localized defects) have little effect on its properties. This makes the system’s physics independent of its minute details (such as hopping parameters, number of dopants, or atomic constituents) and only dependent on this global quantity, which must be an integer. In other words, it depends on the system’s topology rather than on its geometry. Although the initial interest in topological phenomena focused on electrons, topological behavior can be generalized to any type of wave, including light, as first predicted in Ref. [5]. A magnetic photonic crystal—a photonic crystal made of materials that break Lorentz reciprocity due to their response to an external magnetic field—can have a nonzero Chern number (and associated nonscattering edge states) for electromagnetic modes, that is, photons, rather than electrons. Soljacic’s group demonstrated this in 2009, showing that a topological protection of microwave photons could be observed in photonic crystals [6]. The finding launched a search for the realization of topological insulators for photons at optical wavelengths [7], motivated by the prospect of engineering robust optical devices, immune to disorder. Using similar mechanisms as in Ref. [6] proved challenging because of the weakness of magnetic effects in the optical regime. But alternative mechanisms later enabled robust topological edge states for light in a photonic lattice [8] and silicon ring resonator arrays [9]. Employing a microwave photonic crystal similar to the one they used previously [6], Soljacic’s team now reports another important discovery, that of high-Chern number (> 1) bands in a photonic quantum anomalous Hall system. The authors utilized a scheme (see Fig. 1) based on two-dimensional photonic crystals made of ferromagnetic garnet rods sandwiched between two copper plates. Sim-