Topological aspects in the photonic crystal analog of single-particle transport in quantum Hall systems

Abstract

We present a perturbative approach to derive the semiclassical equations of motion for the two-dimensional electron dynamics under the simultaneous presence of static electric and magnetic fields, where the quantized Hall conductance is known to be directly related to the topological properties of translationally invariant magnetic Bloch bands. In close analogy to this approach, we develop a perturbative theory of two-dimensional photonic transport in gyrotropic photonic crystals to mimic the physics of quantum Hall systems. We show that a suitable permittivity grading of a gyrotropic photonic crystal is able to simulate the simultaneous presence of analog electric and magnetic field forces for photons, and we rigorously derive the topology-related term in the equation for the electromagnetic energy velocity that is formally equivalent to the electronic case. A possible experimental configuration is proposed to observe a bulk photonic analog to the quantum Hall physics in graded gyromagnetic photonic crystals.

to be published in Phys Rev A

References in corpus (6)

• Photonic Floquet Topological Insulators
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
• Analogs of quantum Hall effect edge states in photonic crystals
• Time-reversal symmetry breaking in circuit-QED based photon lattices
• Geometrical Aspects in Optical Wavepacket Dynamics

Cited by in corpus (3)

• On the Role of Symmetries in the Theory of Photonic Crystals
• Effective Light Dynamics in Perturbed Photonic Crystals
• The Perturbed Maxwell Operator as Pseudodifferential Operator