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Topology has returned to prominence in physics thanks to the discovery of topological insulators — a class of materials that are characterized by topological properties. This Focus showcases the recent advances in realizing and exploiting topological phases in condensed matter and beyond.
Topological matter can host low-energy quasiparticles, which, in a superconductor, are Majorana fermions described by a real wavefunction. The absence of complex phases provides protection for quantum computations based on topological superconductivity.
The topological state of matter depends on its dimension. Remarkably, topological properties of quasiperiodic systems are found to emerge from higher dimensions.
Optics played a key role in the discovery of geometric phase. It now joins the journey of exploring topological physics, bringing bosonic topological states that equip us with the ability to make perfect photonic devices using imperfect interfaces.
Using optical lattices to trap ultracold atoms provides a powerful platform for probing topological phases, analogues to those found in condensed matter. But as these systems are highly tunable, they could be used to engineer even more exotic phases.