Together with the researchers from Institute for Basic Science (IBS), South Korea, Nankai University’s School of Physics has made important progress in the field of Flat-band Photonics. For the first time, they directly observed a new ring-shaped flat-band pattern similar to a three-dimensional torus on a specially designed flat-band photonic lattice, revealing the real-space topological properties of the flat-band lattice system.

The classic subject of the jumping of electrons in the periodic lattice has been long been the target of vigorous research topic in the field of solid state physics and its intersectional fields. Generally, the energy of electron jumping is closely related to its momentum, showing a colorful band dispersion curve. In some lattice systems with translation invariance, one or more completely flat energy dispersion bands can be achieved by intelligently controlling the internal symmetry or coupling of the lattice, which theoretically does not depend on momentum, so it is called “flat-band”. The introduction of the concept was just a convenient theoretical tool for studying the properties of ferromagnetic substances in solid physics. Today, the flat-band system has involved many fields of physics, from electronic systems to ultra-cold atomic gases, from artificial superconstructive material to photonic device design. Especially in the field of photonics, there are many possible applications of using flat-band systems to realize optical field control, including photonic sensors, optical signal processing and image transmission, nonlinear optical components and micro lasers. Thus, the study of flat-band physics is becoming an exciting subject.

Flat-band and topology are two leading concepts in quantum mechanics and condensed matter physics. Flat-band systems have always been the perfect platform for studying complex multi-body quantum states and strongly correlated multi-body physics that are not related to magnetic fields. In flat-band systems, the electron kinetic energy is completely quenched, and its jump is considered immovable or local. In photonics, the combination of the two concepts of flat-band photonics and topological photonics has ushered in rapid development. The tunable and controllable photonic system has become an experimental platform for studying the physical problems of flat-band and topological frontiers, which provides a new way to realize novel photon states and light field control.

[The figure on the left] A torus showing two NLSs mimicking an infinite lattice. 

[The figure in the middle] A Corbino-shaped KL, where the orange loop illustrates an NLS.

[The figure on the right] Experimentally established Corbino-Kagome lattice.

Usually, the topological properties of materials come from the topological protection of momentum space. In this work, the Nankai research group and collaborators studied unconventional loop states, namely, the noncontractible loop states (NLSs) and robust boundary modes, mediated by nontrivial topology in real space from both theoretical and experimental aspects. In most of the so-called geometric “hampered” lattice structures, the flat band of momentum space intersects the dispersion band at some discrete points. The energy band at the intersection point is simplified and shows that the local mode of the flat-band in this system is incomplete. In other words, there are some “lost states” to form a complete set of flat-band local patterns. The study has shown that these “lost states” exist in an infinite lattice system, or are characterized by an incompressible ring morphology along the torus that meets the periodic boundary conditions (see figure on the left), which are caused by the real-space topological properties of the system. Although these unconventional ring flat-band modes are theoretically predicted and play a key role in understanding the basic physics of flat-band systems, they are difficult to achieve in traditional materials due to the harsh requirements on periodic boundary conditions. This work took the two-dimensional Kagome lattice as a starting point, ingeniously designed a circular Corbino finite photon lattice structure (see figure in the middle), and used a low-power continuous laser direct writing method to induce such a photon lattice in a nonlinear crystal (see right-hand figure above), thus for the first time directly observed the incompressible ring morphology related to the topological characteristics of real space, and experimentally proved the robustness of the boundary mode related to the non-trivial flat-band ring morphology. Direct observation and rigorous analysis of the incompressible ring morphology show that the ring-shaped Kagome photonic lattice has flat-band energy contacts in the momentum space, and that these unconventional flat-band ring morphologies are related to the existence of singularities in Bloch functions and are determined by the topological characteristics of the real space of the lattice. Their results could be of great importance for people’s understanding of the singular flat-bands and the intriguing physics phenomenon applicable for strongly interacting systems.

The research paper entitled with “Direct Observation of Flat-band Loop States Arising from Nontrivial Real-Space Topology” has been published in “Physical Review Letters”. Nankai University is the first corresponding unit, Nankai University’s Ph.D. student Jina Ma and IBS’s postdoctoral researcher Jun-Won Rhim are first authors. Nankai University’s Prof. Zhigang Chen and Associate Prof. Liqin Tang are corresponding authors. The research is supported by National Key R&D Project and National Natural Science Foundation of China.

The research group has recently made a series of important advances in the study of basic physical phenomena in different flat-band photonic lattices. Related work has been published in “Physical Review Letters”, “Advanced Optics Materials”, “APL Photonics” and so on. At present, the research group has been invited to write two review articles on flat-band photonics, which will be published in Nanophotonics and “Acta Physica Sinica”.

Link to paper: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.183901

（Reported by Liqin Tang and Renming Qiao, Translated by Yuchen Shi, Edited by A.J.Strong and JianjingYun)