Topological states realized in metamaterials have provided a versatile platform for exploring topological physics and enabling novel applications,with topolectrical circuits emerging as a prominent example.However,pre...Topological states realized in metamaterials have provided a versatile platform for exploring topological physics and enabling novel applications,with topolectrical circuits emerging as a prominent example.However,previous research in this feld has primarily focused on lumped-element implementations,while non-lumped microwave circuits remain relatively underexplored.In this work,we design and investigate a one-dimensional non-lumped Su–Schriefer–Heeger topolectrical circuit composed of copper parallel-plate transmission lines and inductors,ofering compatibility with integrated microwave applications.Full-wave microwave simulations in the 0–10 GHz range show excellent agreement with theoretical predictions.The impedance spectrum of a fveunit-cell system displays periodic resonant passbands and stopbands corresponding to bulk states,while distinct high-Q(on the order of 10^(2))topological boundary resonances(TBRs)emerge within the stopbands,indicating the presence of localized edge states.Furthermore,the TBRs vanish when the system is reconfgured into the trivial phase,providing direct evidence of its topological nature.These response characteristics make the proposed resonator a promising candidate for future microwave devices and topological circuit applications.展开更多
We study topological phases of a non-Hermitian coupled Su-Schrieffer-Heeger(SSH) ladder. The model originates from the brick-wall lattices in the two-row limit. The Hamiltonian can be brought into block off-diagonal f...We study topological phases of a non-Hermitian coupled Su-Schrieffer-Heeger(SSH) ladder. The model originates from the brick-wall lattices in the two-row limit. The Hamiltonian can be brought into block off-diagonal form and the winding number can be defined with the determine of the block off-diagonal matrix. We find the determine of the offdiagonal matrix has nothing to do with the interleg hopping of the ladder. So the topological phases of the model are the same as those of the chains. Further numerical simulations verify the analysis.展开更多
The non-Hermitian skin effect breaks the conventional bulk–boundary correspondence and leads to non-Bloch topological invariants.Inspired by the fact that the topological protected zero modes are immune to perturbati...The non-Hermitian skin effect breaks the conventional bulk–boundary correspondence and leads to non-Bloch topological invariants.Inspired by the fact that the topological protected zero modes are immune to perturbations,we construct a partner of a non-Hermitian system by getting rid of the non-Hermitian skin effect.Through adjusting the imbalance hopping,we find that the existence of zero-energy boundary states still dictate the bulk topological invariants based on the band-theory framework.Two non-Hermitian Su–Schrieffer–Heeger(SSH)models are used to illuminate the ideas.Specially,we obtain the winding numbers in analytical form without the introduction of the generalized Brillouin zone.The work gives an alternative method to calculate the topological invariants of non-Hermitian systems.展开更多
Non-orthogonality in non-Hermitian quantum systems gives rise to tremendous exotic quantum phenomena,which can be fundamentally traced back to non-unitarity.In this paper,we introduce an interesting quantity(denoted a...Non-orthogonality in non-Hermitian quantum systems gives rise to tremendous exotic quantum phenomena,which can be fundamentally traced back to non-unitarity.In this paper,we introduce an interesting quantity(denoted asη)as a new variant of the Petermann factor to directly and efficiently measure non-unitarity and the associated non-Hermitian physics.By tuning the model parameters of underlying non-Hermitian systems,we find that the discontinuity of bothηand its first-order derivative(denoted as■η)pronouncedly captures rich physics that is fundamentally caused by non-unitarity.More concretely,in the 1D non-Hermitian topological systems,two mutually orthogonal edge states that are respectively localized on two boundaries become non-orthogonal in the vicinity of discontinuity ofηas a function of the model parameter,which is dubbed"edge state transition".Through theoretical analysis,we identify that the appearance of edge state transition indicates the existence of exceptional points(EPs)in topological edge states.Regarding the discontinuity of■η,we investigate a two-level non-Hermitian model and establish a connection between the points of discontinuity of■ηand EPs of bulk states.By studying this connection in more general lattice models,we find that some models have discontinuity of■η,implying the existence of EPs in bulk states.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11874431)the National Key R&D Program of China(Grant No.2018YFA0306800)。
文摘Topological states realized in metamaterials have provided a versatile platform for exploring topological physics and enabling novel applications,with topolectrical circuits emerging as a prominent example.However,previous research in this feld has primarily focused on lumped-element implementations,while non-lumped microwave circuits remain relatively underexplored.In this work,we design and investigate a one-dimensional non-lumped Su–Schriefer–Heeger topolectrical circuit composed of copper parallel-plate transmission lines and inductors,ofering compatibility with integrated microwave applications.Full-wave microwave simulations in the 0–10 GHz range show excellent agreement with theoretical predictions.The impedance spectrum of a fveunit-cell system displays periodic resonant passbands and stopbands corresponding to bulk states,while distinct high-Q(on the order of 10^(2))topological boundary resonances(TBRs)emerge within the stopbands,indicating the presence of localized edge states.Furthermore,the TBRs vanish when the system is reconfgured into the trivial phase,providing direct evidence of its topological nature.These response characteristics make the proposed resonator a promising candidate for future microwave devices and topological circuit applications.
基金Project supported by Hebei Provincial Natural Science Foundation of China(Grant Nos.A2012203174 and A2015203387)the National Natural Science Foundation of China(Grant Nos.10974169 and 11304270)
文摘We study topological phases of a non-Hermitian coupled Su-Schrieffer-Heeger(SSH) ladder. The model originates from the brick-wall lattices in the two-row limit. The Hamiltonian can be brought into block off-diagonal form and the winding number can be defined with the determine of the block off-diagonal matrix. We find the determine of the offdiagonal matrix has nothing to do with the interleg hopping of the ladder. So the topological phases of the model are the same as those of the chains. Further numerical simulations verify the analysis.
基金Project supported by Hebei Provincial Natural Science Foundation of China(Grant Nos.A2012203174 and A2015203387)the National Natural Science Foundation of China(Grant Nos.10974169 and 11304270)
文摘The non-Hermitian skin effect breaks the conventional bulk–boundary correspondence and leads to non-Bloch topological invariants.Inspired by the fact that the topological protected zero modes are immune to perturbations,we construct a partner of a non-Hermitian system by getting rid of the non-Hermitian skin effect.Through adjusting the imbalance hopping,we find that the existence of zero-energy boundary states still dictate the bulk topological invariants based on the band-theory framework.Two non-Hermitian Su–Schrieffer–Heeger(SSH)models are used to illuminate the ideas.Specially,we obtain the winding numbers in analytical form without the introduction of the generalized Brillouin zone.The work gives an alternative method to calculate the topological invariants of non-Hermitian systems.
基金supported by the National Natural Science Foundation of China(NSFC)Grant No.12074438the Guangdong Basic and Applied Basic Research Foundation under Grant No.2020B1515120100+1 种基金the Open Project of Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices under Grant No.2022B1212010008the Fundamental Research Funds for the Central Universities,Sun Yat-sen University(No.23ptpy05).
文摘Non-orthogonality in non-Hermitian quantum systems gives rise to tremendous exotic quantum phenomena,which can be fundamentally traced back to non-unitarity.In this paper,we introduce an interesting quantity(denoted asη)as a new variant of the Petermann factor to directly and efficiently measure non-unitarity and the associated non-Hermitian physics.By tuning the model parameters of underlying non-Hermitian systems,we find that the discontinuity of bothηand its first-order derivative(denoted as■η)pronouncedly captures rich physics that is fundamentally caused by non-unitarity.More concretely,in the 1D non-Hermitian topological systems,two mutually orthogonal edge states that are respectively localized on two boundaries become non-orthogonal in the vicinity of discontinuity ofηas a function of the model parameter,which is dubbed"edge state transition".Through theoretical analysis,we identify that the appearance of edge state transition indicates the existence of exceptional points(EPs)in topological edge states.Regarding the discontinuity of■η,we investigate a two-level non-Hermitian model and establish a connection between the points of discontinuity of■ηand EPs of bulk states.By studying this connection in more general lattice models,we find that some models have discontinuity of■η,implying the existence of EPs in bulk states.
