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Photonic topological insulators and self-induced nonreciprocity based on nonlinear effects in asymmetric structures have garnered increased attention due to their potential applications in quantum information technologies and advanced…
In non-relativistic physics, the concepts of geometry and topology are usually applied to characterize spatial structures or structures in momentum space. We introduce the concept of temporal geometry, which encompasses the geometric and…
Beyond the well-known topological band theory for single-particle systems, it is a great challenge to characterize the topological nature of interacting multi-particle quantum systems. Here, we uncover the relation between topological…
Topological properties lie at the heart of many fascinating phenomena in solid state systems such as quantum Hall systems or Chern insulators. The topology can be captured by the distribution of Berry curvature, which describes the geometry…
Berry curvature that describes local geometrical properties of energy bands can elucidate many fascinating phenomena in solid-state, photonic, and phononic systems, given its connection to global topological invariants such as the Chern…
The topological structure of the wavefunctions of particles in periodic potentials is characterized by the Berry curvature $\Omega_{kn}$ whose integral on the Brillouin zone is a topological invariant known as the Chern number. The…
Topology is central to phenomena that arise in a variety of fields, ranging from quantum field theory to quantum information science to condensed matter physics. Recently, the study of topology has been extended to open systems, leading to…
Exploring topological phases in non-Hermitian systems has attracted significant recent attention. One intriguing question is how topological edge states compete with the non-Hermitian skin effect. Here, we report the experimental…
Recently the possibility of achieving one-way backscatter immune transportation of light by mimicking the topological order present within certain solid state systems, such as topological insulators, has received much attention. Thus far…
Berry curvature is a fundamental element to characterize topological quantum physics, while a full measurement of Berry curvature in momentum space was not reported for topological states. Here we achieve two-dimensional Berry curvature…
Non-reciprocal interactions, where the influence of agent $i$ on $j$ differs from that of $j$ on $i$, are fundamental in active and living matter. Yet, most models implement such asymmetry phenomenologically. Here we show that…
The properties that quantify photonic topological insulators (PTIs), Berry phase, Berry connection, and Chern number, are typically obtained by making analogies between classical Maxwell's equations and the quantum mechanical…
We compute the intrinsic contributions to the Berry-phase mediated anomalous Hall and Nernst effects in electron- and hole-doped semiconductors in the presence of an in-plane magnetic field as well as Rashba and Dresselhaus spin orbit…
Topological properties of materials, as manifested in the intriguing phenomena of quantum Hall effect and topological insulators, have attracted overwhelming transdisciplinary interest in recent years. Topological edge states, for instance,…
The topology of the non-adiabatic parameter space bundle is discussed for evolution of exact cyclic state vectors in Berry's original example of split angular momentum eigenstates. It turns out that the change in topology occurs at a…
We study and present the results of Berry connection for the topological states in quantum matter. The Berry connection plays a central role in the geometric phase and topological phenomenon in quantum many-body system. We present the…
In these notes, we review the role of Berry phases and topology in noninteracting electron systems. Topics including the adiabatic theorem, parallel transport, and Wannier functions are reviewed, with a focus on the connection to…
There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. They are realized by the strong light irradiation to materials that results in nonlinear…
Through understanding Maxwell's equations as an effective Dirac equation (the `optical Dirac equation'), we re--examine the relationship between electromagnetic interface states and topology. We illustrate a simple case where…
The Chern index characterizes the topological phases of nonreciprocal photonic systems. Unlike in electronic systems, the photonic Chern number has no clear physical meaning, except that it determines the net number of unidirectional edge…