Topological insulators represent a new phase of matter,characterized by conductive surfaces,while their bulk remains insulating.When the dimension of the system exceeds that of the topological state by at least two,th...Topological insulators represent a new phase of matter,characterized by conductive surfaces,while their bulk remains insulating.When the dimension of the system exceeds that of the topological state by at least two,the insulators are classified as higher-order topological insulators(HOTI).The appearance of higher-order topological states,such as corner states,can be explained by the filling anomaly,which leads to the fractional spectral charges in the unit cell.Previously reported fractional charges have been quite limited in number and size.In this work,based on the two-dimensional(2D)Su-Schrieffer-Heeger model lattice,we demonstrated a new class of HOTIs with adjustable fractional charges that can take any value ranging from 0 to 1,achieved by utilizing the Lorentz transformation.Furthermore,this transformation generates novel bound-state-in-continuum-like corner states,even when the lattice is in a topological trivial phase,offering a new approach to light beam localization.This work paves the way for fabricating HOTIs with diverse corner states that offer promising applicative potential.展开更多
Introduction of controllable deformations into periodic materials that lead to disclinations in their structure opens novel routes for construction of higher-order topological insulators hosting topological states at ...Introduction of controllable deformations into periodic materials that lead to disclinations in their structure opens novel routes for construction of higher-order topological insulators hosting topological states at disclinations.Appearance of these topological states is consistent with the bulk-disclination correspondence principle,and is due to the filling anomaly that results in fractional charges to the boundary unit cells.So far,topological disclination states were observed only in the linear regime,while the interplay between nonlinearity and topology in the systems with disclinations has been never studied experimentally.We report here on the experimental observation of the nonlinear photonic disclination states in waveguide arrays with pentagonal or heptagonal disclination cores inscribed in transparent optical medium using the fs-laser writing technique.The transition between nontopological and topological phases in such structures is controlled by the Kekulédistortion coefficient r with topological phase hosting simultaneously disclination states at the inner disclination core and spatially separated from them corner-I,corner-II,and extended edge states at the outer edge of the structure.We show that the robust nonlinear disclination states bifurcate from their linear counterparts and that location of their propagation constants in the gap and,hence,their spatial localization can be controlled by their power.Nonlinear disclination states can be efficiently excited by Gaussian input beams,but only if they are focused into the waveguides belonging to the disclination core,where such topological states reside.Our results open new prospects for investigation of nonlinear effects in topological systems with disclinations and are relevant for different areas of science,including Bose-Einstein and polariton condensates,where potentials with the disclinations can be created.展开更多
基金supported by the Natural Science Basic Research Program of Shaanxi Province(No.2024JC-JCQN-06)the National Natural Science Foundation of China(Nos.12474337,12304370)Fundamental Research Funds for the Central Universities(No.xzy012024135).
文摘Topological insulators represent a new phase of matter,characterized by conductive surfaces,while their bulk remains insulating.When the dimension of the system exceeds that of the topological state by at least two,the insulators are classified as higher-order topological insulators(HOTI).The appearance of higher-order topological states,such as corner states,can be explained by the filling anomaly,which leads to the fractional spectral charges in the unit cell.Previously reported fractional charges have been quite limited in number and size.In this work,based on the two-dimensional(2D)Su-Schrieffer-Heeger model lattice,we demonstrated a new class of HOTIs with adjustable fractional charges that can take any value ranging from 0 to 1,achieved by utilizing the Lorentz transformation.Furthermore,this transformation generates novel bound-state-in-continuum-like corner states,even when the lattice is in a topological trivial phase,offering a new approach to light beam localization.This work paves the way for fabricating HOTIs with diverse corner states that offer promising applicative potential.
基金B.R.,H.W.and Y.Z.acknowledge funding by the National Natural Science Foundation of China(Grant No.:12074308)the Fundamental Research Funds for the Central Universities(Grant No.:xzy022022058)+2 种基金A.A.A.,Y.V.K.,S.A.Z.,N.N.S.,A.A.K.,V.O.K.,S.V.C.,and V.N.Z.acknowledge funding by the Russian Science Foundation grant 21-12-00096the research project FFUU2021-0003 of the Institute of Spectroscopy of the Russian Academy of Sciences.A.A.KS.P.K.are supported by the Ministry of Science and Higher Education of the Russian Federation on the basis of the FSAEIHE SUSU(NRU)(Agreement No.:075-15-2022-1116).
文摘Introduction of controllable deformations into periodic materials that lead to disclinations in their structure opens novel routes for construction of higher-order topological insulators hosting topological states at disclinations.Appearance of these topological states is consistent with the bulk-disclination correspondence principle,and is due to the filling anomaly that results in fractional charges to the boundary unit cells.So far,topological disclination states were observed only in the linear regime,while the interplay between nonlinearity and topology in the systems with disclinations has been never studied experimentally.We report here on the experimental observation of the nonlinear photonic disclination states in waveguide arrays with pentagonal or heptagonal disclination cores inscribed in transparent optical medium using the fs-laser writing technique.The transition between nontopological and topological phases in such structures is controlled by the Kekulédistortion coefficient r with topological phase hosting simultaneously disclination states at the inner disclination core and spatially separated from them corner-I,corner-II,and extended edge states at the outer edge of the structure.We show that the robust nonlinear disclination states bifurcate from their linear counterparts and that location of their propagation constants in the gap and,hence,their spatial localization can be controlled by their power.Nonlinear disclination states can be efficiently excited by Gaussian input beams,but only if they are focused into the waveguides belonging to the disclination core,where such topological states reside.Our results open new prospects for investigation of nonlinear effects in topological systems with disclinations and are relevant for different areas of science,including Bose-Einstein and polariton condensates,where potentials with the disclinations can be created.
