The conventional bulk-boundary correspondence directly connects the number of topological edge states in a finite system with invariant bulk band structure periodic boundary condition (PBC). However, recent studies show that this principle fails certain non-Hermitian systems broken reciprocity, which stems from skin effect (NHSE) where most eigenstates decay exponentially boundary. In work, we experimentally demonstrate 1D circuit reciprocity by utilizing unidirectional coupling feature...

Abstract Exceptional points (EPs), at which two or more eigenvalues and eigenstates of a resonant system coalesce, are associated with non-Hermitian Hamiltonians gain and/or loss elements. Dynamic encircling EPs has received significant interest in recent years, as it been shown to lead highly nontrivial phenomena, such chiral transmission the final state depends on handedness. Previously, for pair eigenmodes realized by establishing closed dynamical trajectory parity-time- (PT-)...

In crystals, two bands may cross each other and form degeneracies along a closed loop in the three-dimensional momentum space, which is called nodal line. Nodal line degeneracy can be designed to exhibit various configurations such as rings, chains, links knots. Very recently, non-Abelian band topology was proposed link systems, where lines formed by consecutive pairs of interesting braiding structures underlying topological charges are described quaternions. Here, we experimentally...

Higher-order topological insulators (HOTIs) represent a new family of materials featuring quantized bulk polarizations and zero-dimensional corner states. In recent years, states have been demonstrated in two-dimensional systems the form quadrupole modes or dipole modes. Due to challenges designing constructing three-dimensional systems, octupole 3D not observed. this work, we experimentally investigate phases electrical circuit, which can be viewed as cubic lattice version Hofstadter model...

Thouless pump provides robust ways to realize quantized transport of waves and particles, it casts the static 2D quantum Hall effect onto 1D dynamic systems where one momentum dimensions is replaced by evolution time or path parameter. In past few decades, various types Abelian have been achieved theoretically experimentally. However, study non-Abelian scarce, which tells us that order two loops with same base point cannot be changed, there has no experimental observation pump. Here we...

Tellegen medium has long been a topic of debate, with its existence being contested over several decades. It was first proposed by in 1948 and is characterized real-valued cross coupling between electric magnetic responses, distinguishing it from the well-known chiral that imaginary coefficients. Significantly, responses are closely linked to axion dynamics, an extensively studied subject condensed matter physics. Here, we report realization metamaterials microwave region through judicious...

Topological singularities, such as Weyl points (WPs) and Dirac points, can give rise to unidirectional propagation channels known chiral zero modes (CZMs) when subject a magnetic field. CZMs, distinct zeroth Landau levels (bulk modes) with high degeneracy, are responsible for intriguing phenomena like the anomaly in quantum systems. The direction of each CZM is determined by both applied field topological charge singularity point. While counterpropagating CZMs have been observed 2D 3D...

Non-Abelian braiding describes the exchange behavior of anyons, useful for encoding qubits quantum computing. Recently, this concept has been realized in classical photonic and acoustic systems. However, these implementations are constrained by adiabatic conditions, necessitating long operation distances hindering practical applications. Here, we conceive demonstrate shortcut to (STA) light three-dimensional silicon chips. Our device comprises trilayer waveguides embedded SU-8 polymer, using...

Topological phases arise from the elegant mathematical structures imposed by interplay between symmetry and topology1-5. From gapped topological insulators to gapless semimetals, materials in both quantum classical systems, have grown rapidly last decade. Among them, three-dimensional Dirac semimetal lies at phase transition point various phases. It shares multiple exotic features with other materials, such as Fermi arcs chiral anomaly Weyl semimetals30, spin-dependent surface states...

Generalization of the concept band topology from lower-dimensional to higher-dimensional (n > 3) physical systems is expected introduce new bulk and boundary topological effects. However, theoretically predicted singularities in five-dimensional systems-Weyl surfaces Yang monopoles-have either not been demonstrated realistic or are limited purely synthetic dimensions. We constructed a system possessing monopoles Weyl based on metamaterials with engineered electromagnetic properties, leading...

Scatterings and transport in Weyl semimetals have caught growing attention condensed matter physics, with observables including chiral zero modes the associated magnetoresistance magnetic effects. Measurement of electrical conductance is usually performed these studies, which, however, cannot resolve momentum electrons, preventing direct observation phase singularities scattering matrix point. Here we experimentally demonstrate a helical distribution angle (momentum) resolved electromagnetic...

Topological pump describes the quantized transport of charges (or particles) in absence a net external electric or magnetic field. Here authors show that topological pumps can happen between disclination states with different chiralities distorted lattice. By constructing structures one and two cores, they achieve pumping both within single core cores.

Abstract Berry curvature, the counterpart of magnetic field in momentum space, plays a vital role transport electrons condensed matter physics. It also lays foundation for emerging topological In three-dimensional systems, much attention has been paid to Weyl points, which serve as sources and drains curvature. Here, we demonstrate toroidal moment curvature with flux approaching π judiciously engineered metamaterials. The exhibits vortex-like configuration without any source drain space....

Topological pumps have garnered substantial attention in physics. However, the requirement for slow evolution speed to satisfy adiabaticity greatly restricts their application on-chip devices. Here, we discover a direct link between and quantum metric, real part of geometry that has been relatively less explored compared its imaginary counterpart, Berry curvature. We demonstrate topological nontrivial edge states can be increased by reducing metric via introduction long-range coupling...

Tellegen medium has long been a topic of debate, with its existence being contested over several decades. It was first proposed by in 1948 and is characterized real-valued cross coupling between electric magnetic responses, distinguishing it from the well-known chiral that imaginary coefficients. Significantly, responses are closely linked to axion dynamics, an extensively studied subject condensed matter physics. Here, we report realization metamaterials microwave region through judicious...

Nonreciprocal transmission, resulting from the breaking of Lorentz reciprocity, plays a pivotal role in nonreciprocal communication systems by enabling asymmetric forward and backward propagations. Metasurfaces endowed with nonreciprocity represent compact facile platform for manipulating electromagnetic waves an unprecedented manner. However, most passive metasurfaces that achieve transmissions are polarization dependent. While incorporation active elements or nonlinear materials can...

Abstract Non-trivial linking invariant encodes robust information of topological matter. It has been recently shown that the and winding complex eigenenergy strings can classify one-dimensional non-Hermitian However, in higher dimensions, bundles linked emerge such every string is mutually with all other strings. To best our knowledge, a Hopf bundle not experimentally clarified. Here, we attempt to explore by visualizing global structure spinor momentum space two-dimensional electric...

Non-Hermitian physics has received great attention recently. In particular, band structures in non-Hermitian systems can be engineered to exhibit various topological effects. Among them, one of the most intriguing phenomena is skin effect (NHSE). Here, we investigate NHSE featuring directed chains or graphs, where arrows denote directions non-reciprocal hopping between neighbouring nodes. We show that pure modes with non-oscillatory wavefunctions, contrast previously studied NHSE....

Topological singularities, such as Weyl points and Dirac points, can give rise to unidirectional propagation channels known chiral zero modes (CZMs) when subject a magnetic field. These CZMs are responsible for intriguing phenomena like the anomaly in quantum systems. The direction of each CZM is determined by both applied field topological charge singularity point. While counter-propagating have been observed 2D 3D systems, realization co-propagating has remained elusive. Here we present...

The non-Abelian braiding describes the exchange behavior of anyons, which can be leveraged to encode qubits for quantum computing. Recently, this concept has been realized in classical photonic and acoustic systems. However, these implementations are constrained by adiabatic conditions, necessitating long operation distances impeding practical applications. Here, we conceive demonstrate a shortcut (STA) telecommunication light three-dimensional silicon chips. Our device comprises tri-layer...

Abstract Line excitations in topological phases are a subject of particular interest because their mutual linking structures encode robust information matter. It has been recently shown that the and winding complex eigenenergy strings can classify one-dimensional non-Hermitian However, higher dimensions, bundles linked emerge such every string is mutually with all other strings. Interestingly, despite being an unconventional structure, Hopf bundle not experimentally clarified. Here, we make...

A topological pump enables robust transport of quantized particles when the system parameters are varied in a cyclic process. In previous studies, was achieved inhomogeneous systems guaranteed by invariant bulk band structure time is included as an additional synthetic dimension. Recently, bulk-boundary correspondence has been generalized to bulk-disclination correspondence, describing emergence bounded states crystallographic defects protected topology. Here we show pumping can happen...

Scatterings and transport in Weyl semimetals have caught growing attention condensed matter physics, with observables including chiral zero modes the associated magnetoresistance magnetic effects. Measurement of electrical conductance is usually performed these studies, which, however, cannot resolve momentum electrons, preventing direct observation phase singularities scattering matrix point. Here we experimentally demonstrate a helical distribution angle (momentum) resolved electromagnetic...

Line excitations in topological phases are a subject of particular interest because their mutual linking structures encode robust information matter. It has been recently shown that the and winding complex eigenenergy strings can classify one-dimensional non-Hermitian However, higher dimensions, bundles linked emerge such every string is mutually with all other strings. Interestingly, despite being an unconventional structure, Hopf bundle not experimentally clarified. Here, we make first...

Abstract The Thouless pump refers to the quantized transport of a one-dimensional system under cyclic motion parameters without external forces. This phenomenon has first Chern class topological invariant and typically requires slow evolution meet adiabatic condition, which imposes constraint on system's compactness. In this study, we propose method accelerate in an optical that consists bilayer integrated silicon waveguides operating at telecommunication wavelengths. effective long-range...