Topological materials are often characterized by unique edge states which are in turn used to detect different topological phases in experiments.Recently,with the discovery of various higher-order topological insulato...Topological materials are often characterized by unique edge states which are in turn used to detect different topological phases in experiments.Recently,with the discovery of various higher-order topological insulators,such spectral topological characteristics are extended from edge states to corner states.However,the chiral symmetry protecting the corner states is often broken in genuine materials,leading to vulnerable corner states even when the higher-order topological numbers remain quantized and invariant.Here,we show that a local artificial gauge flux can serve as a robust probe of the Wannier type higher-order topological insulators,which is effective even when the chiral symmetry is broken.The resultant observable signature is the emergence of the cyclic spectral flows traversing one or multiple band gaps.These spectral flows are associated with the local modes bound to the artificial gauge flux.This phenomenon is essentially due to the cyclic transformation of the Wannier orbitals when the local gauge flux acts on them.We extend topological Wannier cycles to systems with C_(2)and C_(3)symmetries and show that they can probe both the bulk and the edge Wannier centers,yielding rich topological phenomena.展开更多
We theoretically propose a reconfigurable two-dimensional(2 D)hexagonal sonic crystal with higher-order topology protected by the six-fold,C6,rotation symmetry.The acoustic band gap and band topology can be controlled...We theoretically propose a reconfigurable two-dimensional(2 D)hexagonal sonic crystal with higher-order topology protected by the six-fold,C6,rotation symmetry.The acoustic band gap and band topology can be controlled by rotating the triangular scatterers in each unit cell.In the nontrivial phase,the sonic crystal realizes the topological spin Hall effect in a higher-order fashion:(i)the edge states emerging in the bulk band gap exhibit partial spin-momentum correlation and are gapped due to the reduced spatial symmetry at the edges.(ii)The gapped edge states,on the other hand,stabilize the topological corner states emerging in the edge band gap.The partial spin-momentum correlation is manifested as pseudo-spin-polarization of edge states away from the time-reversal invariant momenta,where the pseudospin is emulated by the acoustic orbital angular momentum.We reveal the underlying topological mechanism using a corner topological index based on the symmetry representation of the acoustic Bloch bands.展开更多
Topological band theory has conventionally been concerned with the topology of bands around a single gap. Only recently non-Abelian topologies that thrive on involving multiple gaps were studied, unveiling a new horiz...Topological band theory has conventionally been concerned with the topology of bands around a single gap. Only recently non-Abelian topologies that thrive on involving multiple gaps were studied, unveiling a new horizon in topological physics beyond the conventional paradigm. Here, we report on the first experimental realization of a topological Euler insulator phase with unique meronic characterization in an acoustic metamaterial. We demonstrate that this topological phase has several nontrivial features:First, the system cannot be described by conventional topological band theory, but has a nontrivial Euler class that captures the unconventional geometry of the Bloch bands in the Brillouin zone.Second, we uncover in theory and probe in experiments a meronic configuration of the bulk Bloch states for the first time. Third, using a detailed symmetry analysis, we show that the topological Euler insulator evolves from a non-Abelian topological semimetal phase via. the annihilation of Dirac points in pairs in one of the band gaps. With these nontrivial properties, we establish concretely an unconventional bulk-edge correspondence which is confirmed by directly measuring the edge states via. pump-probe techniques. Our work thus unveils a nontrivial topological Euler insulator phase with a unique meronic pattern and paves the way as a platform for non-Abelian topological phenomena.展开更多
Metamaterials with higher-order topological band gaps that exhibit topological physics beyond the bulkedge correspondence provide unique application values due to their ability of integrating topological boundary stat...Metamaterials with higher-order topological band gaps that exhibit topological physics beyond the bulkedge correspondence provide unique application values due to their ability of integrating topological boundary states at multiple dimensions in a single chip.On the other hand,in the past decade,micromechanical metamaterials are developing rapidly for various applications such as micro-piezoelectricgenerators,intelligent micro-systems,on-chip sensing and self-powered micro-systems.To empower these cutting-edge applications with topological manipulations of elastic waves,higher-order topological mechanical systems working at high frequencies(MHz)with high quality-factors are demanded.The current realizations of higher-order topological mechanical systems,however,are still limited to systems with large scales(centimetres)and low frequencies(k Hz).Here,we report the first experimental realization of an on-chip micromechanical metamaterial as the higher-order topological insulator for elastic waves at MHz.The higher-order topological phononic band gap is induced by the band inversion at the Brillouin zone corner which is achieved by configuring the orientations of the elliptic pillars etched on the silicon chip.With consistent experiments,theory and simulations,we demonstrate the emergence of coexisting topological edge and corner states in a single silicon chip as induced by the higher-order band topology.The experimental realization of on-chip micromechanical metamaterials with higherorder topology opens a new regime for materials and applications based on topological elastic waves.展开更多
Topological phases of matter have been extensively investigated in solid-state materials and classical wave systems with integer dimensions. However, topological states in non-integer dimensions remain almost unexplor...Topological phases of matter have been extensively investigated in solid-state materials and classical wave systems with integer dimensions. However, topological states in non-integer dimensions remain almost unexplored. Fractals, being self-similar on different scales, are one of the intriguing complex geometries with non-integer dimensions. Here, we demonstrate fractal higher-order topological states with unprecedented emergent phenomena in a Sierpin? ski acoustic metamaterial. We uncover abundant topological edge and corner states in the acoustic metamaterial due to the fractal geometry. Interestingly,the numbers of the edge and corner states depend exponentially on the system size, and the leading exponent is the Hausdorff fractal dimension of the Sierpin? ski carpet. Furthermore, the results reveal the unconventional spectrum and rich wave patterns of the corner states with consistent simulations and experiments. This study thus unveils unconventional topological states in fractal geometry and may inspire future studies of topological phenomena in non-Euclidean geometries.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12125504 and 12074281)。
文摘Topological materials are often characterized by unique edge states which are in turn used to detect different topological phases in experiments.Recently,with the discovery of various higher-order topological insulators,such spectral topological characteristics are extended from edge states to corner states.However,the chiral symmetry protecting the corner states is often broken in genuine materials,leading to vulnerable corner states even when the higher-order topological numbers remain quantized and invariant.Here,we show that a local artificial gauge flux can serve as a robust probe of the Wannier type higher-order topological insulators,which is effective even when the chiral symmetry is broken.The resultant observable signature is the emergence of the cyclic spectral flows traversing one or multiple band gaps.These spectral flows are associated with the local modes bound to the artificial gauge flux.This phenomenon is essentially due to the cyclic transformation of the Wannier orbitals when the local gauge flux acts on them.We extend topological Wannier cycles to systems with C_(2)and C_(3)symmetries and show that they can probe both the bulk and the edge Wannier centers,yielding rich topological phenomena.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11675116 and 11904060)the Jiangsu Distinguished Professor Fundthe Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)。
文摘We theoretically propose a reconfigurable two-dimensional(2 D)hexagonal sonic crystal with higher-order topology protected by the six-fold,C6,rotation symmetry.The acoustic band gap and band topology can be controlled by rotating the triangular scatterers in each unit cell.In the nontrivial phase,the sonic crystal realizes the topological spin Hall effect in a higher-order fashion:(i)the edge states emerging in the bulk band gap exhibit partial spin-momentum correlation and are gapped due to the reduced spatial symmetry at the edges.(ii)The gapped edge states,on the other hand,stabilize the topological corner states emerging in the edge band gap.The partial spin-momentum correlation is manifested as pseudo-spin-polarization of edge states away from the time-reversal invariant momenta,where the pseudospin is emulated by the acoustic orbital angular momentum.We reveal the underlying topological mechanism using a corner topological index based on the symmetry representation of the acoustic Bloch bands.
基金the National Key R&D Program of China (2022YFA1404400)the National Natural Science Foundation of China (12125504 and 12074281)+7 种基金the “Hundred Talents Program” of the Chinese Academy of Sciencesthe Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutionspartially funded by a Marie-Curie fellowship (101025315)financial support from the Swedish Research Council (Vetenskapsradet) (2021-04681)funding from a New Investigator Award,EPSRC grant EP/W00187X/1EPSRC ERC underwrite grant EP/X025829/1a Royal Society exchange grant IES/ R1/221060Trinity College,Cambridge。
文摘Topological band theory has conventionally been concerned with the topology of bands around a single gap. Only recently non-Abelian topologies that thrive on involving multiple gaps were studied, unveiling a new horizon in topological physics beyond the conventional paradigm. Here, we report on the first experimental realization of a topological Euler insulator phase with unique meronic characterization in an acoustic metamaterial. We demonstrate that this topological phase has several nontrivial features:First, the system cannot be described by conventional topological band theory, but has a nontrivial Euler class that captures the unconventional geometry of the Bloch bands in the Brillouin zone.Second, we uncover in theory and probe in experiments a meronic configuration of the bulk Bloch states for the first time. Third, using a detailed symmetry analysis, we show that the topological Euler insulator evolves from a non-Abelian topological semimetal phase via. the annihilation of Dirac points in pairs in one of the band gaps. With these nontrivial properties, we establish concretely an unconventional bulk-edge correspondence which is confirmed by directly measuring the edge states via. pump-probe techniques. Our work thus unveils a nontrivial topological Euler insulator phase with a unique meronic pattern and paves the way as a platform for non-Abelian topological phenomena.
基金supported by the Natural Science Foundation of Guangdong Province(2020A1515010549)China Postdoctoral Science Foundation(2020M672615 and 2019M662885)+1 种基金National Postdoctoral Program for Innovative Talents(BX20190122)the Jiangsu specially-appointed professor funding。
文摘Metamaterials with higher-order topological band gaps that exhibit topological physics beyond the bulkedge correspondence provide unique application values due to their ability of integrating topological boundary states at multiple dimensions in a single chip.On the other hand,in the past decade,micromechanical metamaterials are developing rapidly for various applications such as micro-piezoelectricgenerators,intelligent micro-systems,on-chip sensing and self-powered micro-systems.To empower these cutting-edge applications with topological manipulations of elastic waves,higher-order topological mechanical systems working at high frequencies(MHz)with high quality-factors are demanded.The current realizations of higher-order topological mechanical systems,however,are still limited to systems with large scales(centimetres)and low frequencies(k Hz).Here,we report the first experimental realization of an on-chip micromechanical metamaterial as the higher-order topological insulator for elastic waves at MHz.The higher-order topological phononic band gap is induced by the band inversion at the Brillouin zone corner which is achieved by configuring the orientations of the elliptic pillars etched on the silicon chip.With consistent experiments,theory and simulations,we demonstrate the emergence of coexisting topological edge and corner states in a single silicon chip as induced by the higher-order band topology.The experimental realization of on-chip micromechanical metamaterials with higherorder topology opens a new regime for materials and applications based on topological elastic waves.
基金supported by the National Natural Science Foundation of China(12125504,12072108,51621004,and 51905162)the Priority Academic Program Development(PAPD)of Jiangsu Higher Education Institutions+1 种基金the Hunan Provincial Natural Science Foundation of China(2021JJ40626)。
文摘Topological phases of matter have been extensively investigated in solid-state materials and classical wave systems with integer dimensions. However, topological states in non-integer dimensions remain almost unexplored. Fractals, being self-similar on different scales, are one of the intriguing complex geometries with non-integer dimensions. Here, we demonstrate fractal higher-order topological states with unprecedented emergent phenomena in a Sierpin? ski acoustic metamaterial. We uncover abundant topological edge and corner states in the acoustic metamaterial due to the fractal geometry. Interestingly,the numbers of the edge and corner states depend exponentially on the system size, and the leading exponent is the Hausdorff fractal dimension of the Sierpin? ski carpet. Furthermore, the results reveal the unconventional spectrum and rich wave patterns of the corner states with consistent simulations and experiments. This study thus unveils unconventional topological states in fractal geometry and may inspire future studies of topological phenomena in non-Euclidean geometries.
