arXiv subjects

Ling Lu

Publications and source records attributed to Ling Lu.

At least 37 records · Page 2Linked to original sources

arXiv2017

Observation of optical vortices in momentum space

Vortex, the winding of a vector field in two dimensions, has its core the field singularity and its topological charge defined by the quantized winding angle of the vector field. Vortices are one of the most fundamental topological excitations in nature, widely known in hair whorls as the winding of hair strings, in fluid dynamics as the winding of velocities, in angular-momentum beams as the winding of phase angle and in superconductors and superfluids as the winding of order parameters. Nevertheless, vortices have hardly been observed other than those in the real space. Although band degeneracies, such as Dirac cones, can be viewed as momentum-space vortices in their mathematical structures, there lacks a well-defined physical observable whose winding number is an arbitrary signed integer. Here, we experimentally observed momentum-space vortices as the winding of far-field polarization vectors in the Brillouin zone (BZ) of periodic plasmonic structures. Using a home-made polarization-resolved momentum-space imaging spectroscopy, we completely map out the dispersion, lifetime and polarization of all radiative states at the visible wavelengths. The momentum space vortices were experimentally identified by their winding patterns in the polarization-resolved iso-frequency contours and their diverging radiative quality factors. Such polarization vortices can exist robustly on any periodic systems of vectorial fields, while they are not captured by the existing topological band theory developed for scaler fields. This work opens up a promising avenue for exploring topological photonics in the momentum space, studying bound states in continuum (BICs), as well as for rendering and steering vector beams and designing high-Q plasmonic resonances.

physics.optics↗

arXiv2017

Nodal-link semimetals

In topological semimetals, the valence band and conduction band meet at zero-dimensional nodal points or one-dimensional nodal rings, which are protected by band topology and symmetries. In this Rapid Communication, we introduce "nodal-link semimetals", which host linked nodal rings in the Brillouin zone. We put forward a general recipe based on the Hopf map for constructing models of nodal-link semimetal. The consequences of nodal ring linking in the Landau levels and Floquet properties are investigated.

cond-mat.str-el↗

arXiv2017

Experimental discovery of nodal chains

Three-dimensional (3D) topological nodal points, such as Weyl and Dirac nodes have attracted wide-spread interest across multiple disciplines and diverse material systems. Unlike nodal points that contain little structural variations, nodal lines can have numerous topological configurations in the momentum space, forming nodal rings, nodal chains and potentially nodal links and nodal knots. However, nodal lines have much less development for the lack of ideal material platforms. In condensed matter for example, nodal lines are often fragile to spin-orbit-coupling, locating off the Fermi level, coexisting with energy-degenerate trivial bands and dispersing strongly in energy of the line degeneracy. Here, overcoming all above difficulties, we theoretically predict and experimentally observe nodal chains in a metallic-mesh photonic crystal having frequency-isolated linear bandtouching rings chained across the entire Brillouin zone (BZ). These nodal chains are protected by mirror symmetries and have a frequency variation less than 1%. We used angle-resolved transmission (ART) to probe the projected bulk dispersions and performed Fourier-transformed field scan (FTFS) to map out the surface dispersions, which is a quadratic touching between two drumhead surface bands. Our results established an ideal nodal-line material for further studies of topological line-degeneracies with nontrivial connectivities, as well as the consequent wave dynamics richer than 2D Dirac and 3D Weyl materials.

cond-mat.mtrl-sci↗

arXiv2017

Double-Weyl phonons in transition-metal monosilicides

Topological states of electrons and photons have attracted significant interest recently. Topological mechanical states also being actively explored, have been limited to macroscopic systems of kHz frequency. The discovery of topological phonons of atomic vibrations at THz frequency can provide a new venue for studying heat transfer, phonon scattering and electron-phonon interaction. Here, we employed ab initio calculations to identify a class of noncentrosymmetric materials of $M$Si ($M$=Fe,Co,Mn,Re,Ru) having double Weyl points in both their acoustic and optical phonon spectra. They exhibit novel topological points termed "spin-1 Weyl point" at the Brillouin zone~(BZ) center and "charge-2 Dirac point" at the zone corner. The corresponding gapless surface phonon dispersions are double helicoidal sheets whose isofrequency contours form a single non-contractible loop in the surface BZ. In addition, the global structure of the surface bands can be analytically expressed as double-periodic Weierstrass elliptic functions. Our prediction of topological bulk and surface phonons can be experimentally verified by neutron scattering and electron energy loss spectroscopy, opening brand new directions for topological phononics.

cond-mat.mtrl-sci↗

arXiv2017

Electromagnetic Scattering Laws in Weyl Systems

Wavelength determines the length scale of the cross section when electromagnetic waves are scattered by an electrically small object. The cross section diverges for resonant scattering, and diminishes for non-resonant scattering, when wavelength approaches infinity. This scattering law explains the color of the sky as well as the strength of a mobile phone signal. We show that such wavelength scaling comes from free space's conical dispersion at zero frequency. Emerging Weyl systems, offering similar dispersion at non-zero frequencies, lead to new laws of electromagnetic scattering that allow cross sections to be decoupled from the wavelength limit. Diverging and diminishing cross sections can be realized at any target wavelength in a Weyl system, providing unprecedented ability to tailor the strength of wave-matter interactions for radio-frequency and optical applications.

physics.optics↗

arXiv2017

Topological defects in Floquet systems: Anomalous chiral modes and topological invariant

Backscattering-immune chiral modes arise along certain line defects in three-dimensional materials. In this paper, we study Floquet chiral modes along Floquet topological defects, namely, the defects come entirely from spatial modulations of periodic driving. We define a precise topological invariant that counts the number of Floquet chiral modes, which is expressed as an integral on a five-dimensional torus parameterized by $(k_x,k_y,k_z,θ,t)$. This work demonstrates the possibility of creating chiral modes in three-dimensional bulk materials by modulated driving. We hope that it will stimulate further studies of Floquet topological defects.

cond-mat.str-el↗

arXiv2017

Nodal-knot semimetals

Topological nodal-line semimetals are characterized by one-dimensional lines of band crossing in the Brillouin zone. In contrast to nodal points, nodal lines can be in topologically nontrivial configurations. In this paper, we study the simplest topologically nontrivial forms of nodal line, namely, a single nodal line taking the shape of a knot in the Brillouin zone. We introduce a generic construction for various "nodal-knot semimetals", which yields the simplest trefoil nodal knot and other more complicated nodal knots in the Brillouin zone. The knotted-unknotted transitions by nodal-line reconnections are also studied. Our work brings the knot theory to the subject of topological semimetals.

cond-mat.str-el↗

arXiv2017

Infrared Topological Plasmons in Graphene

We propose a two-dimensional plasmonic platform - periodically patterned monolayer graphene - which hosts topological one-way edge states operable up to infrared frequencies. We classify the band topology of this plasmonic system under time-reversal-symmetry breaking induced by a static magnetic field. At finite doping, the system supports topologically nontrivial bandgaps with mid-gap frequencies up to tens of terahertz. By the bulk-edge correspondence, these bandgaps host topologically protected one-way edge plasmons, which are immune to backscattering from structural defects and subject only to intrinsic material and radiation loss. Our findings reveal a promising approach to engineer topologically robust chiral plasmonic devices and demonstrate a realistic example of high-frequency topological edge state.

cond-mat.mes-hall↗

arXiv2016

Topological magnetoplasmon

Classical wave fields are real-valued, ensuring the wave states at opposite frequencies and momenta to be inherently identical. Such a particle-hole symmetry can open up new possibilities for topological phenomena in classical systems. Here we show that the historically studied two-dimensional (2D) magnetoplasmon, which bears gapped bulk states and gapless one-way edge states near zero frequency, is topologically analogous to the 2D topological $p+\Ii p$ superconductor with chiral Majorana edge states and zero modes. We further predict a new type of one-way edge magnetoplasmon at the interface of opposite magnetic domains, and demonstrate the existence of zero-frequency modes bounded at the peripheries of a hollow disk. These findings can be readily verified in experiment, and can greatly enrich the topological phases in bosonic and classical systems.

cond-mat.mes-hall↗

arXiv2016

Topological one-way fiber of second Chern number

Optical fiber is a ubiquitous and indispensable component in communications, sensing, biomedicine and many other lightwave technologies and applications. Here we propose topological one-way fibers to remove two fundamental mechanisms that limit fiber performance: scattering and reflection. We design three-dimensional~(3D) photonic crystal fibers, inside which photons propagate only in one direction, that are completely immune to Rayleigh and Mie scatterings and significantly suppress the nonlinear Brillouin and Raman scatterings. A one-way fiber is also free from Fresnel reflection, naturally eliminating the needs for fiber isolators. Our finding is enabled by the recently discovered Weyl points in a double-gyroid~(DG) photonic crystal. By annihilating two Weyl points by supercell modulation in a magnetic DG, we obtain the photonic analogue of the 3D quantum Hall phase with a non-zero first Chern number~($C_1$). When the modulation becomes helixes, one-way fiber modes develop along the winding axis, with the number of modes determined by the spatial frequency of the helix. These single-polarization single-mode and multi-mode one-way fibers, having nearly identical group and phase velocities, are topologically-protected by the second Chern number~($C_2$) in the 4D parameter space of the 3D wavevectors plus the winding angle of the helixes. This work suggests a unique way to utilize higher-dimensional topological physics without resorting to artificial dimensions.

cond-mat.mes-hall↗

arXiv2016

Probing topological protection using a designer surface plasmon structure

Topological photonic states, inspired by robust chiral edge states in topological insulators, have recently been demonstrated in a few photonic systems, including an array of coupled on-chip ring resonators at communication wavelengths. However, the intrinsic difference between electrons and photons determines that the topological protection in time-reversal-invariant photonic systems does not share the same robustness as its counterpart in electronic topological insulators. Here, in a designer surface plasmon platform consisting of tunable metallic sub-wavelength structures, we construct photonic topological edge states and probe their robustness against a variety of defect classes, including some common time-reversal-invariant photonic defects that can break the topological protection, but do not exist in electronic topological insulators. This is also the first experimental realization of anomalous Floquet topological edge states, whose topological phase cannot be predicted by the usual Chern number topological invariants.

physics.optics↗

arXiv2015

Topological semimetals with Riemann surface states

Riemann surfaces are geometric constructions in complex analysis that may represent multi-valued holomorphic functions using multiple sheets of the complex plane. We show that the energy dispersion of surface states in topological semimetals can be represented by Riemann surfaces generated by holomorphic functions in the two-dimensional momentum space, whose constant height contours correspond to Fermi arcs. This correspondence is demonstrated in the recently discovered Weyl semimetals and leads us to predict new types of topological semimetals, whose surface states are represented by double- and quad-helicoid Riemann surfaces. The intersection of multiple helicoids, or the branch cut of the generating function, appears on high-symmetry lines in the surface Brillouin zone, where surface states are guaranteed to be doubly degenerate by a glide reflection symmetry. We predict the heterostructure superlattice [(SrIrO$_3$)$_2$(CaIrO$_3$)$_2$] to be a topological semimetal with double-helicoid Riemann surface states.

cond-mat.mes-hall↗

arXiv2015

Experimental Observation of Large Chern numbers in Photonic Crystals

Despite great interest in the quantum anomalous Hall phase and its analogs, all experimental studies in electronic and bosonic systems have been limited to a Chern number of one. Here, we perform microwave transmission measurements in the bulk and at the edge of ferrimagnetic photonic crystals. Bandgaps with large Chern numbers of 2, 3, and 4 are present in the experimental results which show excellent agreement with theory. We measure the mode profiles and Fourier transform them to produce dispersion relations of the edge modes, whose number and direction match our Chern number calculations.

physics.optics↗

arXiv2015

An Invisible Metallic Mesh

We introduce a solid material that is itself invisible, possessing identical electromagnetic properties as air (i.e. not a cloak) at a desired frequency. Such a material could provide improved mechanical stability, electrical conduction and heat dissipation to a system, without disturbing incident electromagnetic radiation. One immediate application would be towards perfect antenna radomes. Unlike cloaks, such a transparent and self-invisible material has yet to be demonstrated. Previous research has shown that a single sphere or cylinder coated with plasmonic or dielectric layers can have a dark-state with considerably suppressed scattering cross-section, due to the destructive interference between two resonances in one of its scattering channels. Nevertheless, a massive collection of these objects will have an accumulated and detectable disturbance to the original field distribution. Here we overcome this bottleneck by lining up the dark-state frequencies in different channels. Specifically, we derive analytically, verify numerically and demonstrate experimentally that deliberately designed corrugated metallic wires can have record-low scattering amplitudes, achieved by aligning the nodal frequencies of the first two scattering channels. This enables an arbitrary assembly of these wires to be omnidirectionally invisible and the effective constitutive parameters nearly identical to air. Measured transmission spectra at microwave frequencies reveal indistinguishable results for all the arrangements of the 3D-printed samples studied.

physics.optics↗

arXiv2015

Three-dimensional topological photonic crystal with a single surface Dirac cone

A single Dirac cone on the surface is the hallmark of three-dimensional (3D) topological insulators, where the double degeneracy at the Dirac point is protected by time-reversal symmetry and the spin-splitting away from the point is provided by the spin-orbital coupling. Here we predict a single Dirac-cone surface state in a 3D photonic crystal, where the degeneracy at the Dirac point is protected by a nonsymmorphic glide reflection and the linear splitting away from it is enabled by breaking time-reversal symmetry. Such a gapless surface state is fully robust against random disorder of any type. This bosonic topological band structure is achieved by applying alternating magnetization to gap out the 3D "generalized Dirac points" discovered in the bulk of our crystal. The $Z_2$ bulk invariant is characterized through the evolution of Wannier centers. Our proposal--readily realizable using ferrimagnetic materials at microwave frequencies--can also be regarded as the photonic analog of topological crystalline insulators, providing the first 3D bosonic symmetry-protected topological system.

cond-mat.mes-hall↗

arXiv2015

Topological Phononic Crystals with One-Way Elastic Edge Waves

We report a new type of phononic crystals with topologically non-trivial bandgaps for both longitudinal and transverse polarizations, resulting in protected one-way elastic edge waves. In our design, gyroscopic inertial effects are used to break the time-reversal symmetry and realize the phononic analogue of the electronic quantum Hall effect. We investigate the response of both hexagonal and square gyroscopic lattices and observe bulk Chern number of 1 and 2, indicating that these structures support single and multi-mode edge elastic waves immune to back-scattering. These robust one-way phononic waveguides could potentially lead to the design of a novel class of surface wave devices that are widely used in electronics, telecommunication and acoustic imaging.

cond-mat.mes-hall↗

arXiv2015

Spawning rings of exceptional points out of Dirac cones

The Dirac cone underlies many unique electronic properties of graphene and topological insulators, and its band structure--two conical bands touching at a single point--has also been realized for photons in waveguide arrays, atoms in optical lattices, and through accidental degeneracy. Deformations of the Dirac cone often reveal intriguing properties; an example is the quantum Hall effect, where a constant magnetic field breaks the Dirac cone into isolated Landau levels. A seemingly unrelated phenomenon is the exceptional point, also known as the parity-time symmetry breaking point, where two resonances coincide in both their positions and widths. Exceptional points lead to counter-intuitive phenomena such as loss-induced transparency, unidirectional transmission or reflection, and lasers with reversed pump dependence or single-mode operation. These two fields of research are in fact connected: here we discover the ability of a Dirac cone to evolve into a ring of exceptional points, which we call an "exceptional ring." We experimentally demonstrate this concept in a photonic crystal slab. Angle-resolved reflection measurements of the photonic crystal slab reveal that the peaks of reflectivity follow the conical band structure of a Dirac cone from accidental degeneracy, whereas the complex eigenvalues of the system are deformed into a two-dimensional flat band enclosed by an exceptional ring. This deformation arises from the dissimilar radiation rates of dipole and quadrupole resonances, which play a role analogous to the loss and gain in parity-time symmetric systems. Our results indicate that the radiation that exists in any open system can fundamentally alter its physical properties in ways previously expected only in the presence of material loss and gain.

physics.optics↗

arXiv2015

Experimental observation of Weyl points

In 1929, Hermann Weyl derived the massless solutions from the Dirac equation - the relativistic wave equation for electrons. Neutrinos were thought, for decades, to be Weyl fermions until the discovery of the neutrino mass. Moreover, it has been suggested that low energy excitations in condensed matter can be the solutions to the Weyl Hamiltonian. Recently, photons have also been proposed to emerge as Weyl particles inside photonic crystals. In all cases, two linear dispersion bands in the three-dimensional (3D) momentum space intersect at a single degenerate point - the Weyl point. Remarkably, these Weyl points are monopoles of Berry flux with topological charges defined by the Chern numbers. These topological invariants enable materials containing Weyl points to exhibit a wide variety of novel phenomena including surface Fermi arcs, chiral anomaly, negative magnetoresistance, nonlocal transport, quantum anomalous Hall effect, unconventional superconductivity[15] and others [16, 17]. Nevertheless, Weyl points are yet to be experimentally observed in nature. In this work, we report on precisely such an observation in an inversion-breaking 3D double-gyroid photonic crystal without breaking time-reversal symmetry.

cond-mat.mtrl-sci↗