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We discuss the possible topological order/topological quantum field theory of different quantum Hall systems. Given the value of the Hall conductivity, we constrain the global symmetry of the low-energy theory and its anomaly. Specifically,…
Abundant in nature, colloids also find increasingly important applications in science and technology, ranging from direct probing of kinetics in crystals and glasses to fabrication of third-generation quantum-dot solar cells. Because…
Topology is a powerful framework for controlling and manipulating light, minimizing detrimental perturbations on the photonic properties. Combining nanophotonics with topological concepts presents opportunities for both fundamental physics…
Much of the richness in nature emerges because the same simple constituents can form an endless variety of ordered states. While many such states are fully characterized by their symmetries, interacting quantum systems can also exhibit…
Topological photonics started out as a pursuit to engineer systems that mimic fermionic single-particle Hamiltonians with symmetry-protected modes, whose number can only change in spectral phase transitions such as band inversions. The…
Topological photonics sheds light on some of the surprising phenomena seen in condensed matter physics that arise with the appearance of topological invariants. Optical waveguides provide a well-controlled platform to investigate effects…
Topological photonics provides a new degree of freedom to robustly control electromagnetic fields. To date, most of established topological states in photonics have been employed in Euclidean space. Motivated by unique properties of…
Topological photonics revolutionizes some of the traditional approaches to light propagation and manipulation, and it provides unprecedented means for developing novel photonic devices. Recently discovered higher-order topological phases go…
The modern conception of phases of matter has undergone tremendous developments since the first observation of topologically ordered states in fractional quantum Hall systems in the 1980s. In this paper, we explore the question: How much…
The recent synthesis of two-dimensional staggered materials opens up burgeoning opportunities to study optical spin-orbit interactions in semiconducting Dirac-like systems. We unveil topological phase transitions in the photonic spin Hall…
Topological photonics is an emerging research area that focuses on the topological states of classical light. Here we reveal the topological phases that are intrinsic to the particle nature of light, i.e., solely related to the quantized…
Topological insulators are materials that conduct on the surface and insulate in their interior due to non-trivial topological order. The edge states on the interface between topological (non-trivial) and conventional (trivial) insulators…
Topological states in photonics offer novel prospects for guiding and manipulating photons and facilitate the development of modern optical components for a variety of applications. Over the past few years, photonic topology physics has…
Systems displaying quantum topological order feature robust characteristics that are very attractive to quantum computing schemes. Topological quantum field theories have proven to be powerful in capturing the quintessential attributes of…
The study of dissipative systems has attracted great attention, as dissipation engineering has become an important candidate towards manipulating light in classical and quantum ways. Here,we investigate the behavior of a topological system…
Topology-driven nonlinear light-matter effects open up new paradigms for both topological photonics and nonlinear optics. Here, we propose to achieve high-efficiency second-harmonic generation in a second-order photonic topological…
The three-dimensional topological insulator (originally called "topological insulators") is the first example in nature of a topologically ordered electronic phase existing in three dimensions that cannot be reduced to multiple copies of…
Topological orders emerge in both microscopic quantum dynamics and macroscopic materials as a fundamental principle to characterize intricate properties in nature with vital significance, for instance, the Landau levels of electron systems…
Topological photonics seeks to control the behaviour of the light through the design of protected topological modes in photonic structures. While this approach originated from studying the behaviour of electrons in solid-state materials, it…
Two-dimensional electron gases in strong magnetic fields provide a canonical platform for realizing a variety of electronic ordering phenomena. Here we review the physics of one intriguing class of interaction-driven quantum Hall states:…