arXiv subjects

C. T. Chan

Publications and source records attributed to C. T. Chan.

At least 55 records · Page 3Linked to original sources

arXiv2022

Edge and corner states in 2D non-Abelian topological insulators from an eigenvector frame rotation perspective

We propose the concept of 2D non-Abelian topological insulator which can explain the energy distributions of the edge states and corner states in systems with parity-time symmetry. From the viewpoint of non-Abelian band topology, we establish the constraints on the 2D Zak phase and polarization. We demonstrate that the corner states in some 2D systems can be explained as the boundary mode of the 1D edge states arising from the multi-band non-Abelian topology of the system. We also propose the use of off-diagonal Berry phase as complementary information to assist the prediction of edge states in non-Abelian topological insulators. Our work provides an alternative approach to study edge and corner modes and this idea can be extended to 3D systems.

cond-mat.mes-hall↗

arXiv2022

Topological classification for intersection singularities of exceptional surfaces in pseudo-Hermitian systems

Exceptional points play a pivotal role in the topology of non-Hermitian systems, and significant advances have been made in classifying exceptional points and exploring the associated phenomena. Exceptional surfaces, which are hypersurfaces of exceptional degeneracies in parameter space, can support hypersurface singularities, such as cusps, intersections and swallowtail catastrophes. Here we topologically classify the intersection singularity of exceptional surfaces for a generic pseudo-Hermitian system with parity-time symmetry. By constructing the quotient space under equivalence relations of eigenstates, we reveal that the topology of such gapless structures can be described by a non-Abelian free group on three generators. Importantly, the classification predicts a new kind of non-Hermitian gapless topological phase and can systematically explain how the exceptional surfaces and their intersections evolve under perturbations with symmetries preserved. Our work opens a new pathway for designing systems with robust topological phases, and provides inspiration for applications such as sensing and lasing which can utilize the special properties inherent in exceptional surfaces and intersections.

cond-mat.mtrl-sci↗

arXiv2022

Photonic $\mathbb{Z}_2$ topological Anderson insulators

That disorder can induce nontrivial topology is a surprising discovery in topological physics. As a typical example, Chern topological Anderson insulators (TAIs) have been realized in photonic systems, where the topological phases exist without symmetry protection. In this work, by taking TM and TE polarizations as pseudo-spin degrees of freedom, we theoretically propose a scheme to realize disorder-induced symmetry-protected topological (SPT) phase transitions in two-dimensional photonic crystals (PCs) with a combined time-reversal, mirror and duality symmetry $\mathcal{T}_f=\mathcal{T}M_z\mathcal{D}$. In particular, we demonstrate that the disorder-induced SPT phase persists even without pseudo-spin conservation, thereby realizing a photonic $\mathbb{Z}_2$ TAI, in contrast to a $\mathbb{Z}$-classified quantum spin Hall (QSH) TAI with decoupled spins. By formulating a new scattering approach, we show that the topology of both the QSH and $\mathbb{Z}_2$ TAIs can be manifested by the accumulated spin rotations of the reflected waves from the PCs. Using a transmission structure, we also illustrate the trivialization of a disordered QSH phase with an even integer topological index caused by spin coupling.

physics.optics↗

arXiv2022

Observation of boundary induced chiral anomaly bulk states and their transport properties

The robust transport of edge modes is perhaps the most useful property of topological materials. The existence of edge modes is guaranteed by the bulk-edge correspondence, which states that the number of topological edge modes is determined by the bulk topological invariants. To obtain robust transport on the edge, we need to make volumetric changes to many bulk atoms to control the properties of a few edge atoms in a lower dimension. We suggest here that we can do the reverse in some cases: the properties of the edge can guarantee chiral transport phenomena in some bulk modes, achieving phenomena that are essentially the same as those observed in topological valley-Hall systems. Specifically, we show that a topologically trivial 2D hexagonal phononic crystal slab (waveguide) bounded by hardwall boundaries guarantees the existence of bulk modes with chiral anomaly inside a pseudogap. We experimentally observed robust valley-selected transport, complete valley state conversion, and valley focusing of the chiral anomaly bulk states (CABSs) in such phononic crystal waveguides.

cond-mat.mes-hall↗

arXiv2022

Topology in non-Hermitian Chern insulators with skin effect

The non-Hermitian skin effect can arise in materials that have asymmetric hoppings between atoms or resonating units, which makes the bulk eigenspectrum sensitive to boundary conditions. When skin effect emerges, eigenstates in the bulk continuum can become localized on the edges, making the distinction between edge and bulk states challenging. We establish the bulk-boundary correspondence for a Chern insulator model with non-Hermitian skin effect by combining two approaches ("non-Bloch" approach and "biorthogonal" approach). Both approaches can suppress the skin effect but they are based on different mathematical tools. A biorthogonal inverse participation ratio is used as a measure to distinguish between bulk states and edge states, and a non-Bloch Chern number is used to characterize the topology and predict the number of topological edge bands. In addition to tangential degeneracies, crossing degeneracies are found to occur between the bulk and edge bands. Their presence enriches the (de)localization behavior of the edge states but does not affect the Chern number. The phase diagram of the system has interesting features that are not found in Hermitian systems. For example, one topological transition and two non-Hermitian phase transitions can be induced by tuning a single parameter. The gapless phase is topologically protected due to the stable existence of the non-Hermitian band degeneracies guaranteed by nonzero discriminant numbers.

cond-mat.mes-hall↗

arXiv2021

Disordered transmission-line networks with and without parity symmetry

Topological states are useful because they are robust against disorder and imperfection. In this study, we consider the effect of disorder and the breaking of parity symmetry on a topological network system in which the edge states are protected by Chern numbers. In the absence of periodicity, the local Chern number is adopted to characterize the topological features of the network. Our numerical results show that the local Chern number and the edge states are very robust against onsite disorder as long as the gap of the bulk state continuum remains open and survives even when the bulk band gap is closed. Breaking the parity symmetry can destroy the quantization of local Chern numbers, compromising the existence of edge modes. We observed non-integer local Chern number peaks that are non-zero inside the bulk bands but these non-zero non-integral local Chern numbers are not associated with the existence of robust edge states.

cond-mat.dis-nn↗

arXiv2021

Near-field energy transfer between graphene and magneto-optic media

We consider the near-field radiative energy transfer between two separated parallel plates: graphene supported by a substrate and a magneto-optic medium. We first study the scenario in which the two plates have the same temperature. An electric current through the graphene gives rise to nonequilibrium fluctuations and induces energy transfer. Both the magnitude and direction of the energy flux can be controlled by the electric current and an in-plane magnetic field in the magneto-optic medium. This is due to the interplay between the nonreciprocal photon occupation number in the graphene and nonreciprocal surface modes in the magneto-optic plate. Furthermore, we report that a tunable thermoelectric current can be generated in the graphene in the presence of a temperature difference between the two plates.

physics.optics↗

arXiv2021

Four-band non-Abelian topological insulator and its experimental realization

Very recently, increasing attention has been focused on non-Abelian topological charges, e.g. the quaternion group Q8. Different from Abelian topological band insulators, these systems involve multiple tangled bulk bandgaps and support non-trivial edge states that manifest the non-Abelian topological features. Furthermore, a system with even or odd number of bands will exhibit significant difference in non-Abelian topological classifications. Up to now, there is scant research investigating the even-band non-Abelian topological insulators. Here, we both theoretically explored and experimentally realized a four-band PT (inversion and time-reversal) symmetric system, where two new classes of topological charges as well as edge states are comprehensively studied. We illustrate their difference from four-dimensional rotation senses on the stereographically projected Clifford tori. We show the evolution of bulk topology by extending the 1D Hamiltonian onto a 2D plane and provide the accompanying edge state distributions following an analytical method. Our work presents an exhaustive study of four-band non-Abelian topological insulators and paves the way to other even band systems.

cond-mat.mes-hall↗

arXiv2021

Experimental observation of non-Abelian earring nodal links in phononic crystals

Nodal lines are symmetry-protected one-dimensional band degeneracies in momentum space, which can appear in numerous topological configurations such as nodal rings, chains, links, and knots. Very recently, non-Abelian topological physics has been proposed in space-time inversion (PT) symmetric systems, and attract widespread attention. One of the most special configurations in non-Abelian system is the earring nodal link, composing of a nodal chain linking with an isolated nodal line, is signature of non-Abelian topology and cannot be elucidated using Abelian topological classifications. However, the earring nodal links have not been yet observed in real system. Here we design the phononic crystals with earring nodal links, and verify its non-Abelian topologicial charge in full-wave simulations. Moreover, we experimentally observed two different kinds of earring nodal links by measuring the band structures for two phononic crystals. Specifically, we found that the order of the nodal chain and line can switch after band inversion but their link cannot be severed. Our work provides experimental evidence for phenomena unique to non-Abelian band topology and our simple acoustic system provides a convenient platform for studying non-Abelian charges.

cond-mat.mes-hall↗

arXiv2021

Photonic nodal lines with quadrupole Berry curvature distribution

In periodic systems, nodal lines are loops in the three-dimensional momentum space where two bands are degenerate with each other. Nodal lines exhibit rich topological features as they can take various configurations such as rings, links, chains and knots. These line nodes are usually protected by mirror or PT symmetry. Here we propose and demonstrate a novel type of photonic straight nodal lines in a D2d meta-crystal which are protected by roto-inversion time (roto-PT) symmetry. The nodal lines are located at the central axis and hinges of the Brillouin zone. They appear as quadrupole sources of Berry curvature flux and allow for the precise control of the quadrupole strength. Interestingly, there exist topological surface states at all three cutting surfaces, as guaranteed by the pi-quantized Zak phases along all three directions. As frequency changes, the surface state equi-frequency contours evolve from closed to open contours, and become straight lines at a critical transition frequency, at which diffraction-less surface wave propagation are demonstrated, paving way towards development of super-imaging photonic devices.

cond-mat.mes-hall↗

arXiv2021

Chiral transport of pseudo-spinors induced by synthetic gravitational field in photonic Weyl metamaterials

Weyl particles exhibit chiral transport property under external curved space-time geometry. This effect is called chiral gravitational effect, which plays an important role in quantum field theory. However, the absence of real Weyl particles in nature hinders the observation of such interesting phenomena. In this paper, we show that chiral gravitational effect can be manifested in Weyl metamaterials with spatially controlled nonlocality. This inhomogeneous modulation results in a spatially dependent group velocity in the Weyl cone dispersion, which is equivalent to introducing a curved background space-time (or gravitational field) for Weyl pseudo-spinors. The synthetic gravitational field leads to the quantization of energy levels, including chiral zeroth order energy modes (or simply chiral zero modes) that determine the chiral transport property of pseudo-spinors. The inhomogeneous Weyl metamaterial provides an experimentally realizable platform for investigating the interaction between Weyl particles and gravitational field, allowing for observation of chiral gravitational effect in table-top experiments.

physics.app-ph↗

arXiv2021

Strong geometry dependence of the Casimir force between interpenetrated rectangular gratings

Quantum fluctuations give rise to Casimir forces between two parallel conducting plates, the magnitude of which increases monotonically as the separation decreases. By introducing nanoscale gratings to the surfaces, recent advances have opened opportunities for controlling the Casimir force in complex geometries. Here, we measure the Casimir force between two rectangular gratings in regimes not accessible before. Using an on-chip detection platform, we achieve accurate alignment between the two gratings so that they interpenetrate as the separation is reduced. Just before interpenetration occurs, the measured Casimir force is found to have a geometry dependence that is much stronger than previous experiments, with deviations from the proximity force approximation reaching a factor of ~500. After the gratings interpenetrate each other, the Casimir force becomes non-zero and independent of displacement. This work shows that the presence of gratings can strongly modify the Casimir force to control the interaction between nanomechanical components.

quant-ph↗

arXiv2020

Exceptional points make an astroid in non-Hermitian Lieb lattice: evolution and topological protection

An astroid-shaped loop of exceptional points (EPs), comprising four cusps, is found to spawn from the triple degeneracy point in the Brillouin zone (BZ) of a Lieb lattice with nearest-neighbor hoppings when non-Hermiticity is introduced. The occurrence of the EP loop is due to the realness of the discriminant which is guaranteed by the non-Hermitian chiral symmetry. The EPs at the four cusps involve the coalescence of three eigenstates, which is the combined result of the non-Hermitian chiral symmetry and mirror-T symmetry. The EP loop is exactly an astroid in the limit of an infinitesimal non-Hermiticity. The EP loop expands from the $M$ point with increasing non-Hermiticity and splits into two EP loops at a critical non-Hermiticity. The further increase of non-Hermiticity contracts the two EP loops towards and finally to two EPs at the $X$ and $Y$ points in the BZ, accompanied by the emergence of Dirac-like cones. The two EPs vanish at a larger non-Hermiticity. The EP loop disappears and several discrete EPs are found to survive when next-nearest hoppings are introduced to break the non-Hermitian chiral symmetry. A topological invariant called the discriminant number is used to characterize their robustness against perturbations. Both discrete EPs and those on the EP loop(s) are found to show anisotropic asymptotic behaviors. Finally, the experimental realization of the Lieb lattice using a coupled waveguide array is discussed.

cond-mat.mes-hall↗

arXiv2020

Hidden-symmetry-enforced nexus points of nodal lines in layer-stacked dielectric photonic crystals

It was recently demonstrated that the connectivities of bands emerging from zero frequency in dielectric photonic crystals are distinct from their electronic counterparts with the same space groups. We discover that, in an AB-layer-stacked photonic crystal composed of anisotropic dielectrics, the unique photonic band connectivity leads to a new kind of symmetry-enforced triply degenerate points at the nexuses of two nodal rings and a Kramers-like nodal line. The emergence and intersection of the line nodes are guaranteed by a generalized 1/4-period screw rotation symmetry of Maxwell's equations. The bands with a constant $k_z$ and iso-frequency surfaces near a nexus point both disperse as a spin-1 Dirac-like cone, giving rise to exotic transport features of light at the nexus point. We show that the spin-1 conical diffraction occurs at the nexus point which can be used to manipulate the charges of optical vortices. Our work reveals that Maxwell's equations can have hidden symmetries induced by the fractional periodicity of the material tensor components and hence paves the way to finding novel topological nodal structures unique to photonic systems.

physics.optics↗

arXiv2020

Topological one-way large-area waveguide states in magnetic photonic crystals

We have theoretically and experimentally achieved large-area one-way transport by using heterostructures consisting of a domain of an ordinary photonic crystal (PC) sandwiched between two domains of magnetic PCs. The non-magnetized domain carries two orthogonal one-way waveguide states which have amplitude uniformly distributed over a large-area. These two waveguide states support unidirectional transport even though the medium of propagation is not magnetized. We show both experimentally and numerically that such one-way waveguide states can be utilized to abruptly narrow the beam width of an extended state to concentrate energy. Such extended waveguide modes are robust to different kinds of defects, such as voids and PEC barriers. They are also immune to the Anderson type localization when large randomness is introduced.

physics.optics↗

arXiv2020

Optical pulling using topologically protected one-way-transport surface-arc waves

This paper proposes a new method to achieve robust optical pulling of particles by using an air waveguide sandwiched between two chiral hyperbolic metamaterials. The pulling force is induced by mode conversion between a pair of one-way-transport surface-arc waves supported on the two metamaterial surfaces of the waveguide. The surface arcs bridge the momentum gaps between isolated bulk equifrequency surfaces (EFSs) and are topologically protected by the nontrivial Chern numbers of the EFSs. When an incident surface-arc wave with a relatively small wavenumber $k_{x1}$ is scattered by the particle, a part of its energy is transferred to the other surface-arc mode with $k_{x2}(>k_{x1}). Because the electromagnetic wave acquires an additional forward momentum from the particle proportional to $k_{x2}-k_{x1}$ during this process, the particle will always be subjected to an optical pulling force irrespective of its material, shape and size. Since the chiral surface-arc waves are immune to backscattering from local disorders and the metamaterials are isotropic in the xy plane, robust optical pulling can be achieved in a curved air waveguide and can go beyond standard optical pulling mechanisms which are limited to pull in a straight-line.

physics.optics↗

arXiv2020

Robust acoustic pulling using chiral surface waves

We show that long-range and robust acoustic pulling can be achieved by using a pair of one-way chiral surface waves supported on the interface between two phononic crystals composed of spinning cylinders with equal but opposite spinning velocities embedded in water. When the chiral surface mode with a relative small Bloch wave vector is excited, the particle located in the interface waveguide will scatter the excited surface mode to another chiral surface mode with a greater Bloch wave vector, resulting in an acoustic pulling force, irrespective of the size and material of the particle. Thanks to the backscattering immunity of the chiral surface waves against local disorders, the particle can be pulled following a flexible trajectory as determined by the shape of the interface. As such, this new acoustic pulling scheme overcomes some of the limitations of the traditional acoustic pulling using structured beams, such as short pulling distances, straight-line type pulling and strong dependence on the scattering properties of the particle. Our work may also inspire the application of topological acoustics to acoustic manipulations.

physics.class-ph↗

arXiv2020

Experimental observation of non-Abelian topological charges and bulk-edge correspondence

In the past decades, topological concepts have emerged to classify matter states beyond the Ginzburg-Landau symmetry breaking paradigm. The underlying global invariants are usually characterized by integers, such as Chern or winding numbers. Very recently, band topology characterized by non-Abelian topological charges has been proposed, which possess non-commutative and fruitful braiding structures with multiple (>1) bandgaps entangled together. Despite many potential exquisite applications including quantum computations, no experimental observation of non-Abelian topological charges has been reported. Here, we experimentally observe the non-Abelian topological charges in a PT (parity and time-reversal) symmetric system. More importantly, we propose non-Abelian bulk-edge correspondence, where edge states are found to be described by non-Abelian charges. Our work opens the door towards non-Abelian topological phase characterization and manipulation.

cond-mat.mes-hall↗