7 papers
Mathematical Theory for Photonic Hall Effect in Honeycomb Photonic Crystals
Wei Li, Junshan Lin, Jiayu Qiu +1
In this work, we develop a mathematical theory for the photonic Hall effect and prove the existence of guided electromagnetic waves at the interface of two honeycomb photonic cryst…
Generalized bulk-interface correspondence for non-quantized spin transport
Jiayu Qiu, Hai Zhang
This paper establishes a rigorous mathematical framework for a generalized bulk-interface correspondence (BIC) in electronic systems with possibly nonconserved spin charge, where t…
Bulk-edge correspondence in finite photonic structure
Jiayu Qiu, Hai Zhang
In this work, we establish the bulk-edge correspondence principle for finite two-dimensional photonic structures. Specifically, we focus on the divergence-form operator with period…
Interface Modes in Honeycomb Topological Photonic Structures with Broken Reflection Symmetry
Wei Li, Junshan Lin, Jiayu Qiu +1
In this work, we present a mathematical theory for Dirac points and interface modes in honeycomb topological photonic structures consisting of impenetrable obstacles. Starting from…
A Mathematical Theory of Integer Quantum Hall Effect in Photonics
Jiayu Qiu, Hai Zhang
This paper investigates interface modes in a square lattice of photonic crystal composed of gyromagnetic particles with point group symmetry. The study shows that Dirac or…
On the bifurcation of a Dirac point in a photonic waveguide without band gap openning
Jiayu Qiu, Hai Zhang
Recent progress in topological insulators and topological phases of matter has motivated new methods for the localization of waves in photonic structures. Especially, it is establi…
Hall algebras associated to complexes of fixed size
Haicheng Zhang
Let $\A$ be a finitary hereditary abelian category with enough projectives. We study the Hall algebra of complexes of fixed size over projectives. Explicitly, we first give a relat…