scholarly journals Higher-order Floquet topological phases with corner and bulk bound states

2019 ◽  
Vol 100 (8) ◽  
Author(s):  
Martin Rodriguez-Vega ◽  
Abhishek Kumar ◽  
Babak Seradjeh
Keyword(s):  
Bound States ◽  
Higher Order ◽  
Topological Phases

scholarly journals Non-Hermitian route to higher-order topology in an acoustic crystal

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
He Gao ◽  
Haoran Xue ◽  
Zhongming Gu ◽  
Tuo Liu ◽  
Jie Zhu ◽  
...  
Keyword(s):  
Higher Order ◽  
Order Topology ◽  
Topological Phases ◽  
Edge States ◽  
Experimental Realization ◽  
Artificial Materials ◽  
Intrinsic Loss ◽  
Topological Phases Of Matter ◽  
Hierarchical Features ◽  
Nontrivial Topology

AbstractTopological phases of matter are classified based on their Hermitian Hamiltonians, whose real-valued dispersions together with orthogonal eigenstates form nontrivial topology. In the recently discovered higher-order topological insulators (TIs), the bulk topology can even exhibit hierarchical features, leading to topological corner states, as demonstrated in many photonic and acoustic artificial materials. Naturally, the intrinsic loss in these artificial materials has been omitted in the topology definition, due to its non-Hermitian nature; in practice, the presence of loss is generally considered harmful to the topological corner states. Here, we report the experimental realization of a higher-order TI in an acoustic crystal, whose nontrivial topology is induced by deliberately introduced losses. With local acoustic measurements, we identify a topological bulk bandgap that is populated with gapped edge states and in-gap corner states, as the hallmark signatures of hierarchical higher-order topology. Our work establishes the non-Hermitian route to higher-order topology, and paves the way to exploring various exotic non-Hermiticity-induced topological phases.

scholarly journals SCHRÖDINGER EQUATION FOR HEAVY MESONS EXPANDED IN 1/mQ

1996 ◽  
Vol 11 (03) ◽  
pp. 257-266 ◽  
Author(s):  
TAKAYUKI MATSUKI
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound States ◽  
Higher Order ◽  
Wave Functions ◽  
Heavy Mesons ◽  
Higher Order Corrections

Operating just once the naive Foldy-Wouthuysen-Tani transformation on the Schrödinger equation for [Formula: see text] bound states described by a Hamiltonian, we systematically develop a perturbation theory in 1/mQ which enables one to solve the Schrödinger equation to obtain masses and wave functions of the bound states in any order of 1/mQ. There also appear negative components of the wave function in our formulation which contribute also to higher order corrections to masses.

scholarly journals Topological phases for bound states moving in a finite volume

2011 ◽  
Vol 84 (9) ◽  
Author(s):  
Shahin Bour ◽  
Sebastian König ◽  
Dean Lee ◽  
H.-W. Hammer ◽  
Ulf-G. Meißner
Keyword(s):  
Finite Volume ◽  
Bound States ◽  
Topological Phases

scholarly journals Floquet Second-Order Topological Phases in Momentum Space

Nanomaterials ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 1170
Author(s):  
Longwen Zhou
Keyword(s):  
Momentum Space ◽  
Bound States ◽  
Second Order ◽  
Large Integer ◽  
Open Boundary ◽  
Topological Invariants ◽  
Topological Phases ◽  
Open Boundary Conditions ◽  
Kicked Rotor ◽  
Symmetry Protected

Higher-order topological phases (HOTPs) are characterized by symmetry-protected bound states at the corners or hinges of the system. In this work, we reveal a momentum-space counterpart of HOTPs in time-periodic driven systems, which are demonstrated in a two-dimensional extension of the quantum double-kicked rotor. The found Floquet HOTPs are protected by chiral symmetry and characterized by a pair of topological invariants, which could take arbitrarily large integer values with the increase of kicking strengths. These topological numbers are shown to be measurable from the chiral dynamics of wave packets. Under open boundary conditions, multiple quartets Floquet corner modes with zero and π quasienergies emerge in the system and coexist with delocalized bulk states at the same quasienergies, forming second-order Floquet topological bound states in the continuum. The number of these corner modes is further counted by the bulk topological invariants according to the relation of bulk-corner correspondence. Our findings thus extend the study of HOTPs to momentum-space lattices and further uncover the richness of HOTPs and corner-localized bound states in continuum in Floquet systems.

scholarly journals Geometry symmetry-free and higher-order optical bound states in the continuum

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Qingjia Zhou ◽  
Yangyang Fu ◽  
Lujun Huang ◽  
Qiannan Wu ◽  
Andrey Miroshnichenko ◽  
...  
Keyword(s):  
Significant Role ◽  
Bound States ◽  
Higher Order ◽  
Multiple Objects ◽  
Material Parameters ◽  
Geometrical Symmetry ◽  
Geometric Symmetry ◽  
Symmetry Protected ◽  
Zero Index ◽  
The Continuum

AbstractGeometrical symmetry plays a significant role in implementing robust, symmetry-protected, bound states in the continuum (BICs). However, this benefit is only theoretical in many cases since fabricated samples’ unavoidable imperfections may easily break the stringent geometrical requirements. Here we propose an approach by introducing the concept of geometrical-symmetry-free but symmetry-protected BICs, realized using the static-like environment induced by a zero-index metamaterial (ZIM). We find that robust BICs exist and are protected from the disordered distribution of multiple objects inside the ZIM host by its physical symmetries rather than geometrical ones. The geometric-symmetry-free BICs are robust, regardless of the objects’ external shapes and material parameters in the ZIM host. We further show theoretically and numerically that the existence of those higher-order BICs depends only on the number of objects. By practically designing a structural ZIM waveguide, the existence of BICs is numerically confirmed, as well as their independence on the presence of geometrical symmetry. Our findings provide a way of realizing higher-order BICs and link their properties to the disorder of photonic systems.

scholarly journals Geometry symmetry-free and Higher-order Optical Bound States in the Continuum

2021 ◽  
Author(s):  
Qingjia Zhou ◽  
Yangyang Fu ◽  
Lujun Huang ◽  
Qiannan Wu ◽  
Andrey Miroshnichenko ◽  
...  
Keyword(s):  
Significant Role ◽  
Bound States ◽  
Higher Order ◽  
Multiple Objects ◽  
New Approach ◽  
Geometrical Symmetry ◽  
Symmetry Protected ◽  
Zero Index ◽  
The Continuum

Abstract Geometrical symmetry plays a significant role in realizing robust, symmetry-protected, bound states in the continuum (BICs). However, this benefit is only theoretical in many cases since the unavoidable imperfections of fabricated samples may easily break the stringent geometrical requirements. Here we propose an essentially new approach by introducing the concept of geometrical-symmetry-free but symmetry-protected BICs, realized using the static-like environment induced by a zero-index metamaterial (ZIM). We find that robust BICs exist and are protected from the disordered distribution of multiple objects inside ZIM host by its physical symmetries rather than geometrical ones. We further show theoretically and numerically that the existence of those higher-order BICs depends only on the number of objects. By practically designing a structural ZIM waveguide, the existence of BICs is numerically confirmed, as well as their independence on the presence of geometrical symmetry. Our findings provide a new way of realizing higher-order BICs and link their properties to disorder of photonic systems.

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