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- 摘要
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- 实验方案
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Experimental Observation of Bound States of 2D Dirac Electrons at Surface Steps of the Topological Insulator Bi <sub/>2</sub> Se <sub/>3</sub>
摘要： Topologically protected surface states of three-dimensional topological insulators provide a model framework for studying massless Dirac electrons in two dimensions. Usually a step on the surface of a topological insulator is treated as a scatterer for the Dirac electrons, and the study of its effect is focused on the interference of the incident and scattered electrons. Then a major role plays the warping of the Dirac cone far from the Dirac point. The existence of another significant effect near the Dirac point brought about by the presence of steps is experimentally demonstrated here. Namely the band bending in the vicinity of steps leads to formation of 1D bound states in the corresponding potential wells. The observation of bound states in such potential wells in our scanning tunneling microscopy and spectroscopy investigation of the surface of the topological insulator Bi2Se3 is reported. Numerical simulations support our conclusion and provide a recipe for the identification of such states.
关键词： density of states,Dirac electrons,surface states,edge states,bound states,scanning tunneling microscopy,Bi2Se3,topological insulators,scanning tunneling spectroscopy
更新于2025-09-23 15:23:52
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Experimental Realization of Multiple Topological Edge States in a 1D Photonic Lattice
摘要： Topological photonic systems offer light transport that is robust against defects and disorder, promising a new generation of chip-scale photonic devices and facilitating energy-efficient on-chip information routing and processing. However, present quasi one dimensional (1D) designs, such as the Su–Schrieffer–Heeger and Rice–Mele models, support only a limited number of nontrivial phases due to restrictions on dispersion band engineering. Here, a flexible topological photonic lattice on a silicon photonic platform is experimentally demonstrated that realizes multiple topologically nontrivial dispersion bands. By suitably setting the couplings between the 1D waveguides, different lattices can exhibit the transition between multiple different topological phases and allow the independent realization of the corresponding edge states. Heterodyne measurements clearly reveal the ultrafast transport dynamics of the edge states in different phases at a femtosecond scale, validating the designed topological features. The study equips topological models with enriched edge dynamics and considerably expands the scope to engineer unique topological features into photonic, acoustic, and atomic systems.
关键词： multi-topological numbers,topological photonics,topological edge states,ultra-fast heterodyne imaging
更新于2025-09-23 15:23:52
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Edge-dependent reflection and inherited fine structure of higher-order plasmons in graphene nanoribbons
摘要： We investigate higher-order plasmons in graphene nanoribbons, and we present how electronic edge states and wave-function fine structure influence the graphene plasmons. Based on nearest-neighbor tight-binding calculations, we find that a standing-wave model based on nonlocal bulk plasmon dispersion is surprisingly accurate for armchair ribbons of widths even down to a few nanometers, and we determine the corresponding phase shift upon edge reflection and an effective ribbon width. Wider zigzag ribbons exhibit a similar phase shift, whereas the standing-wave model describes few-nanometer zigzag ribbons less satisfactorily, to a large extent because of their edge states. We directly confirm that also the larger broadening of plasmons for zigzag ribbons is due to their edge states. Furthermore, we report a prominent fine structure in the induced charges of the ribbon plasmons, which for armchair ribbons follows the electronic wave-function oscillations induced by intervalley coupling. Interestingly, the wave-function fine structure is also found in our analogous density-functional theory calculations, and both these and tight-binding numerical calculations are explained quite well with analytical Dirac theory for graphene ribbons.
关键词： plasmons,edge states,tight-binding,density-functional theory,Dirac theory,graphene nanoribbons
更新于2025-09-23 15:23:52
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Two dimensional topological insulators in bilayer BiB
摘要： With the help of ?rst-principles calculations, we propose a new type of two dimensional (2D) topological insulator BiB with bilayer hexagonal lattice. Its dynamic stability was con?rmed by the phonon spectrum. When spin-orbit coupling (SOC) e?ect is not considered, the low energy electronic states around the Fermi level show metallic characteristics. However, the SOC will induce a global band gap and turn this 2D material into topological insulators with nontrivial edge states. Surprisingly, two mechanisms, including crystal ?eld and strong SOC, induce two band inversions and manipulate the low energy electronic states simultaneously. The BiB provides a fertile platform for studying the interactions between the two di?erent mechanisms in the same topological insulator. Moreover, the sizable global nontrivial band gap indicates its high working temperature.
关键词： Topological insulator,Edge states,Z2,Spin-orbit coupling (SOC)
更新于2025-09-23 15:22:29
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Recipe for Dirac Phonon States with a Quantized Valley Berry Phase in Two-Dimensional Hexagonal Lattices
摘要： The topological quantum states in two-dimensional (2D) materials are fascinating subjects of research, which usually highlight electron-related systems. In this work, we present a recipe that leads to Dirac phonon states with quantized valley Berry phase in 2D hexagonal lattices by first-principles calculations. We show that candidates possessing the three-fold rotational symmetry at the corners of the hexagonal Brillouin zone host valley Dirac phonons, which are guaranteed to remain intact with respect to perturbations. We identify that such special topological features populated by Dirac phonons can be realized in various 2D materials. In particular, the monolayer CrI3, an attractive 2D magnetic semiconductor with exotic applications in spintronics, is an ideal platform to investigate nontrivial phonons in experiments. We further confirm that the phonon Berry phase is quantized to ±π at two inequivalent valleys. The phonon edge states terminated at the projection of phonon Dirac cones are clearly visible. This work demonstrates that 2D hexagonal lattices with attractive valley Dirac phonons will extend the knowledge of valley physics, providing wide applications of topological phonons.
关键词： Dirac phonons,first-principles calculations,valley Berry phase,phonon edge states,2D hexagonal lattices
更新于2025-09-23 15:21:21
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Numerical analysis of surface and edge states in slabs, stripes, rods and surface steps of topological insulators
摘要： By numerically solving the e?ective continuous model of a topological insulator with parameters corresponding to the band structure of the topological insulator Bi2Se3, we analyze possible appearance of one-dimensional states in various geometries. Massless Dirac fermions are found at the edges of thin ribbons with surface oriented not only along the van der Waals gap but also in the perpendicular direction. Thick rods and slabs with surface steps host massive modes localized on surface faces. We argue that the modes are massive and their origin is due to the di?erence in the Dirac point energy of adjacent faces. The absence of one-dimensional states near edges of a large rectangular rod and surface steps is demonstrated.
关键词： bound state,topological insulator,edge states,surface step
更新于2025-09-23 15:21:21
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Quantum Hall phase and chiral edge states simulated by a coupled dipole method
摘要： We present theoretical modeling of the quantum Hall phase and chiral edge states in a gyroelectric photonic crystal. The theoretical framework represented here is based on a coupled dipole method, which is a direct counterpart of the tight-binding approximation. We con?rm that gyrotropic coupling produces a band gap characterized by a nonzero Chern number. Gapless edge states appear at an interface between a gyroeletric photonic crystal and a vacuum. At a domain wall between media of positive and negative gyrotropy, topological edge states that are analogous to the Jackiw-Rebbi states are observed. Propagation of the chiral edge states is also simulated in real space under excitation of an external dipole source. This analysis provides a toy model to describe the quantum Hall phase in a purely optical manner, without using a mapping or an analogy of the electron wave function in the quantum Hall effect.
关键词： quantum Hall phase,chiral edge states,coupled dipole method,topological edge states,gyroelectric photonic crystal
更新于2025-09-23 15:21:01
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Photonic Topological Insulating Phase Induced Solely by Gain and Loss
摘要： We reveal a one-dimensional topological insulating phase induced solely by gain and loss control in non-Hermitian optical lattices. The system comprises units of four uniformly coupled cavities, where the successive two have loss; the others experience gain, and they are balanced under two magnitudes. The gain and loss parts are effectively dimerized, and a bulk band gap, topological transition, midgap topological edge, and interface states in finite systems can all be achieved by controlled pumping. We also clarify non-Hermitian topological invariants and edge states in gapless conditions.
关键词： Topological Transition,Photonic Topological Insulating Phase,Non-Hermitian Optical Lattices,Midgap Topological Edge States,Gain and Loss Control
更新于2025-09-23 15:21:01
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Dynamics and transport properties of Floquet topological edge modes in coupled photonic waveguides
摘要： We study theoretically the Floquet edge states in a photonic analog of the driven Su-Schrieffer-Heeger model implemented by an array of identical single-mode dielectric waveguides, where the time-dependent driving is modeled by periodically bended waveguides. We combine the coupled-mode theory with the Floquet-Bloch analysis and within this framework determine a band structure of the periodic system. We develop a theoretical approach for calculation of the edge states in semi-infinite systems and investigate their topological properties. In particular, we explore the dynamics of the 0- and π-edge states which reveal profound differences depending on their topological phase. To verify our observations, we simulate the power transport along the end of such a waveguide array and show that its spectra can be assigned to the excitation of the edge modes. The results obtained indicate that driving-induced topological properties of the edge modes can be exploited in controlling flow of light in periodically driven photonic structures and may provide insight into Floquet engineering of the realistic photonic systems.
关键词： photonic analog,coupled-mode theory,dielectric waveguides,Floquet edge states,power transport,Floquet engineering,topological properties,Su-Schrieffer-Heeger model,Floquet-Bloch analysis
更新于2025-09-19 17:13:59
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Electrically pumped topological laser with valley edge modes
摘要： Quantum cascade lasers are compact, electrically pumped light sources in the technologically important mid-infrared and terahertz region of the electromagnetic spectrum1,2. Recently, the concept of topology3 has been expanded from condensed matter physics into photonics4, giving rise to a new type of lasing5–8 using topologically protected photonic modes that can efficiently bypass corners and defects4. Previous demonstrations of topological lasers have required an external laser source for optical pumping and have operated in the conventional optical frequency regime5–8. Here we demonstrate an electrically pumped terahertz quantum cascade laser based on topologically protected valley edge states9–11. Unlike topological lasers that rely on large-scale features to impart topological protection, our compact design makes use of the valley degree of freedom in photonic crystals10,11, analogous to two-dimensional gapped valleytronic materials12. Lasing with regularly spaced emission peaks occurs in a sharp-cornered triangular cavity, even if perturbations are introduced into the underlying structure, owing to the existence of topologically protected valley edge states that circulate around the cavity without experiencing localization. We probe the properties of the topological lasing modes by adding different outcouplers to the topological cavity. The laser based on valley edge states may open routes to the practical use of topological protection in electrically driven laser sources.
关键词： terahertz,topological photonics,valley edge states,Quantum cascade lasers,electrically pumped lasers
更新于2025-09-19 17:13:59