A square-root topological insulator with non-quantized indices realized with photonic Aharonov-Bohm cages
Mark Kremer, Ioannis Petrides, Eric Meyer, Matthias Heinrich, Oded Zilberberg, Alexander Szameit
Abstract
Topological Insulators are a novel state of matter where spectral bands are characterized by quantized topological invariants. This unique quantized nonlocal property commonly manifests through exotic bulk phenomena and corresponding robust boundary effects. In our work we study a system where the spectral bands are associated with non-quantized indices, but nevertheless possess robust boundary states. We present a theoretical analysis, where we show that the square of the Hamiltonian exhibits quantized indices. The findings are experimentally demonstrated by using photonic Aharonov-Bohm cages.
Topics & Concepts
Topological insulatorHamiltonian (control theory)PhysicsPhotonicsSquare rootAharonov–Bohm effectTopology (electrical circuits)Periodic boundary conditionsState of matterBoundary (topology)Quantization (signal processing)Quantum mechanicsBoundary value problemCondensed matter physicsMathematicsElectromagnetic fieldMathematical analysisCombinatoricsGeometryMathematical optimizationAlgorithmTopological Materials and PhenomenaQuantum many-body systemsQuantum Mechanics and Non-Hermitian Physics