Topological materials and metamaterials opened new paradigms to create and manipulate phases of matter with unconventional properties.Topological D-class phases(TDPs)are archetypes of the ten-fold classification of to...Topological materials and metamaterials opened new paradigms to create and manipulate phases of matter with unconventional properties.Topological D-class phases(TDPs)are archetypes of the ten-fold classification of topological phases with particle-hole symmetry.In two dimensions,TDPs support propagating topological edge modes that simulate the elusive Majorana elementary particles.Furthermore,a piercing ofπ-flux Dirac-solenoids in TDPs stabilizes localized Majorana excitations that can be braided for the purpose of topological quantum computation.Such two-dimensional(2D)TDPs have been a focus in the research frontier,but their experimental realizations are still under debate.Here,with a novel design scheme,we realize 2D TDPs in an acoustic crystal by synthesizing both the particle-hole and fermion-like time reversal symmetries for a wide range of frequencies.The design scheme leverages an enriched unit cell structure with real-valued couplings that emulate the targeted Hamiltonian of TDPs with complex hoppings:A technique that could unlock the realization of all topological classes with passive metamaterials.In our experiments,we realize a pair of TDPs with opposite Chern numbers in two independent sectors that are connected by an intrinsic fermion-like timereversal symmetry built in the system.We measure the acoustic Majorana-like helical edge modes and visualize their robust topological transport,thus revealing the unprecedented D and DIII class topologies with direct evidence.Our study opens up a new pathway for the experimental realization of two fundamental classes of topological phases and may offer new insights in fundamental physics,materials science,and phononic information processing.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
基金the support from the National Key R&D Program of China(2022YFA1404400)the National Natural Science Foundation of China(12125504 and 12074281)+5 种基金the support from the National Natural Science Foundation of China(12047541)the Gusu Leading Innovation Scientists Program of Suzhou City,and the Priority Academic Program Development(PAPD)of Jiangsu Higher Education Institutionsthe Research Fund of Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology(2020B1212030010)support from the US National Science Foundation(CMMI2131759)support from the US National Science Foundation(DMR-1823800 and CMMI-2131760)the U.S.Army Research Office through contract W911NF-23-1-0127。
文摘Topological materials and metamaterials opened new paradigms to create and manipulate phases of matter with unconventional properties.Topological D-class phases(TDPs)are archetypes of the ten-fold classification of topological phases with particle-hole symmetry.In two dimensions,TDPs support propagating topological edge modes that simulate the elusive Majorana elementary particles.Furthermore,a piercing ofπ-flux Dirac-solenoids in TDPs stabilizes localized Majorana excitations that can be braided for the purpose of topological quantum computation.Such two-dimensional(2D)TDPs have been a focus in the research frontier,but their experimental realizations are still under debate.Here,with a novel design scheme,we realize 2D TDPs in an acoustic crystal by synthesizing both the particle-hole and fermion-like time reversal symmetries for a wide range of frequencies.The design scheme leverages an enriched unit cell structure with real-valued couplings that emulate the targeted Hamiltonian of TDPs with complex hoppings:A technique that could unlock the realization of all topological classes with passive metamaterials.In our experiments,we realize a pair of TDPs with opposite Chern numbers in two independent sectors that are connected by an intrinsic fermion-like timereversal symmetry built in the system.We measure the acoustic Majorana-like helical edge modes and visualize their robust topological transport,thus revealing the unprecedented D and DIII class topologies with direct evidence.Our study opens up a new pathway for the experimental realization of two fundamental classes of topological phases and may offer new insights in fundamental physics,materials science,and phononic information processing.
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.
