Localized vibrational,edges and breathing modes of graphene nanoribbons with topological line defects

Peculiar vibrational modes of graphene nanoribbons (GNRs) with topological line defects were presented. We find that phonon dispersion relations of the topological defective GNRs are more similar to those of perfect armchair-edge GNR than to zigzag-edge GNR in spite of their zigzag edge. All vibrational modes at Γ point are assigned in detail by analyzing their eigenvectors and are presented by video. Three types of characteristic vibrational modes, namely, localized vibrational modes in defect sites, edges, and breathing modes, are observed. Five localized vibrational modes near the defect sites are found to be robust against the width of the topological line-defective GNR. The Raman D’ band just originates from one localized mode, 1622 cm^-1. The vibrational mode is sensitive to symmetry. The edge modes are related with structural symmetry but not with widths. Two edge modes are asymmetrical and only one is symmetrical. The breathing modes are inversely proportional to the width for wide-defect GNRs, and inversely proportional to the square root of the width for narrow-defect GNRs. The breathing mode frequencies of defective GNRs are slightly higher than those of perfect GNRs. These vibrational modes may be useful in the manipulation of thermal conductance and implementation of single phonon storage.     

Realizing Majorana fermion modes in the Kitaev model

We study the possibility to realize a Majorana zero mode that is robust and may be easily manipulated for braiding in quantum computing in the ground state of the Kitaev model in this work. To achieve this we first apply a uniform [111] magnetic field to the gapless Kitaev model and turn the Kitaev model to an effective p+ip topological superconductor of spinons. We then study possible vortex binding in such system to a topologically trivial spot in the ground state. We consider two cases in the system: one is a vacancy and the other is a fully polarized spin. We show that in both cases, the system binds a vortex with the defect and a robust Majorana zero mode in the ground state at a weak uniform [111] magnetic field. The distribution and asymptotic behavior of these Majorana zero modes are studied. The Majorana zero modes in both cases decay exponentially in space, and are robust against local perturbations and other Majorana zero modes far away, which makes them promising candidates for braiding in topological quantum computing.     

Formation of topological domain walls and quantum transport properties of zero-line modes in commensurate bilayer graphene systems

We study theoretically the construction of topological conducting domain walls with a finite width between AB/BA stacking regions via finite element method in bilayer graphene systems with tunable commensurate twisting angles. We find that the smaller is the twisting angle, the more significant the lattice reconstruction would be, so that sharper domain boundaries declare their existence. We subsequently study the quantum transport properties of topological zero-line modes which can exist because of the said domain boundaries via Green’s function method and Landauer−Büttiker formalism, and find that in scattering regions with tri-intersectional conducting channels, topological zero-line modes both exhibit robust behavior exemplified as the saturated total transmissionG_tot ≈ 2e²/h and obey a specific pseudospin-conserving current partition law among the branch transport channels. The former property is unaffected by Aharonov−Bohm effect due to a weak perpendicular magnetic field, but the latter is not. Results from our genuine bilayer hexagonal system suggest a twisting angle aroundθ ≈ 0.1° for those properties to be expected, consistent with the existing experimental reports.     

Topology of a <Superscript>3</Superscript>He-A Film on a Corrugated Graphene Substrate

A thin film of superfluid ³He on a corrugated graphene substrate represents topological matter with a smooth disorder. It is possible that the atomically smooth disorder produced by the corrugated graphene does not destroy the superfluidity even in a very thin film, where the system can be considered as quasi two-dimensional topological material. This will allow us to study the effect of disorder on different classes of the 2 + 1 topological materials: the chiral ³He-A with intrinsic quantum Hall effect and the time reversal invariant planar phase with intrinsic spin quantum Hall effect. In the limit of smooth disorder, the system can be considered as a Chern mosaic, i.e., a collection of domains with different values of Chern numbers. In this limit, the quantization of the Hall conductance is determined by the percolated domain, while the density of the fermionic states is determined by the edge modes on the boundaries of the finite domains. This system can be useful for the general consideration of disorder in the topological matter.     

Two-dimensional topological insulator state and topological phase transition in bilayer graphene

We show that gated bilayer graphene hosts a strong topological insulator (TI) phase in the presence of Rashba spin-orbit (SO) coupling. We find that gated bilayer graphene under preserved time-reversal symmetry is a quantum valley Hall insulator for small Rashba SO coupling λ(R), and transitions to a strong TI when λ(R)>√[U(2)+t(⊥)(2)], where U and t(⊥) are, respectively, the interlayer potential and tunneling energy. Different from a conventional quantum spin Hall state, the edge modes of our strong TI phase exhibit both spin and valley filtering, and thus share the properties of both quantum spin Hall and quantum valley Hall insulators. The strong TI phase remains robust in the presence of weak graphene intrinsic SO coupling.     

Guided modes in asymmetric graphene waveguides

An asymmetric quantum well in graphene can act as a slab waveguide for electron waves in a manner analogous to the electromagnetic waves in dielectrics. Guided modes and the probability current density are analyzed in the graphene electron waveguide induced by asymmetric electrostatic potential. The modes in an asymmetric graphene waveguide include guided modes, “cover modes”, “substrate modes” and “radiation modes”. The conditions for a guided mode are quantified. It is found that the fundamental mode is absent when both the Klein tunneling and classical motion are present. The confinement of electrons for lower order mode is stronger than for higher order mode. We hope that these characteristics in asymmetric graphene waveguide can provide potential applications in graphene-based waveguide devices.     

Vibrational properties and Raman spectra of different edge graphene nanoribbons,studied by first-principles calculations

The vibrational properties and Raman spectra of graphene nanoribbons with six different edges have been studied by using the first-principles calculations. It is found that edge reconstruction leads to the emergence of localized vibrational modes and new topological defect modes, making the different edges identified by polarized Raman spectra. The radial breathing-like modes are found to be independent of the edge structures, while the G-band-related modes are affected by different edge structures. Our results suggest that the polarized Raman spectrum could be a powerful experimental tool for distinguishing the GNRs with different edge structures due to their different vibrational properties.     

Topological confinement in bilayer graphene

We study a new type of one-dimensional chiral states that can be created in bilayer graphene (BLG) by electrostatic lateral confinement. These states appear on the domain walls separating insulating regions experiencing the opposite gating polarity. While the states are similar to conventional solitonic zero modes, their properties are defined by the unusual chiral BLG quasiparticles, from which they derive. The number of zero mode branches is fixed by the topological vacuum charge of the insulating BLG state. We discuss how these chiral states can manifest experimentally and emphasize their relevance for valleytronics.     

Logic of Quench Protection Assembly for BEPC-ⅡInteraction Region Superconducting Magnet

Two superconducting magnet complexes are used in BEPCⅡ interaction region. The corresponding quench protection system divides all related faults into two classes and takes different protection actions according to the urgency degree. Since BEPCⅡ has two operating modes and the superconducting magnets use different power supplies in different operating modes, the quench protection system must take the mode switching into consideration.     

Topological insight into the non-arrhenius mode hopping of semiconductor ring lasers

We investigate both theoretically and experimentally the stochastic switching between two counterpropagating lasing modes of a semiconductor ring laser. Experimentally, the residence time distribution cannot be described by a simple one-parameter Arrhenius exponential law and reveals the presence of two different mode-hop scenarios with distinct time scales. In order to elucidate the origin of these two time scales, we propose a topological approach based on a two-dimensional dynamical system.     

Dual-channel tunable near-infrared absorption enhancement with graphene induced by coupled modes of topological interface states

The dual-channel nearly perfect absorption is realized by the coupled modes of topological interface states (TIS) in the near-infrared range. An all-dielectric layered heterostructure composed of photonic crystals (PhC)/graphene/PhC/graphene/PhC on GaAs substrate is proposed to excite the TIS at the interface of adjacent PhC with opposite topological properties. Based on finite element method (FEM) and transfer matrix method (TMM), the dual-channel absorption can be modulated by the periodic number of middle PhC, Fermi level of graphene, and angle of incident light (TE and TM polarizations). Especially, by fine-tuning the Fermi level of graphene around 0.4 eV, the absorption of both channels can be switched rapidly and synchronously. This design is hopefully integrated into silicon-based chips to control light.     

涂覆石墨烯的非对称并行电介质纳米线波导的模式特性分析

采用多级展开方法,对涂覆石墨烯的非对称并行电介质纳米线波导的模式特性进行了分析.首先对这种波导中的表面等离子模式进行分类,然后对七种低阶模式的有效折射率和传播长度随工作频率、几何结构参数和石墨烯费米能的依赖关系进行详细的分析.结果表明,通过改变工作频率、几何结构参数和石墨烯的费米能,可以在较大范围内调节模式的特性.与有限元法进行的对比表明,基于多级方法的半解析结果与有限元法的数值结果非常符合.研究结果可为涂覆石墨烯的非对称并行电介质纳米线的设计和制作提供一定的理论基础.     

Thermoplasma polariton within scaling theory of single-layer graphene

The electrodynamics of single-layer graphene is studied in the scaling regime. At any finite temperature, there is a weakly damped collective thermoplasma polariton mode whose dispersion and wavelength-dependent damping is determined analytically. The electric and magnetic fields associated with this mode decay exponentially in the direction perpendicular to the graphene layer, but, unlike the surface plasma polariton modes of metals, the decay length and the mode frequency are strongly temperature-dependent. This may lead to new ways of generation and manipulation of these modes.     

时间反演对称性破缺系统中的拓扑零能模

Su-Schreiffer-Heeger模型预测了在一维周期晶格的边缘处可能出现零维的拓扑零能模,其能量本征值总是出现在能隙的正中间.本文以半导体微腔阵列中光子和激子在强耦合情况下形成的准粒子为例,通过准粒子的自旋轨道耦合与Zeeman效应,研究了时间反演对称性破缺对拓扑零能模的影响.发现拓扑零能模的能量本征值可以随着自旋轨道耦合强度的变化在整个带隙内移动,自旋相反的模式移动方向相反;在二维微腔阵列中发现了沿着晶格边缘移动的拓扑零能模,提出了一维零能模的概念.由于时间反演对称性的破缺,这种一维拓扑零能模解除了在相反传输方向上的能级的简并,从而在传输过程中出现极强的绕过障碍物的能力.     

A6相对论磁控管模式切换射频信号馈入方法

目前国际上提出了采用短脉冲射频（RF）信号实现相对论磁控管的模式切换,数值模拟经证实了可以采用几十kW到几百kW的RF信号实现相对论磁控管采用轴向提取功率的相邻模式以及同一模式的不同纵向模式之间的切换,这里假设所需的RF信号的能量已经馈入到相对论磁控管腔体内。提出了实验系统中采用扇形波导和探针天线来馈入前级微波源来提供模式切换所需的RF信号的能量的方法。该方法分为两个步骤,首先采用扇形波导来将前级微波源提供的能量馈入到相对论磁控管的阳极体中;然后利用探针天线将馈入的RF信号辐射至相对论磁控管腔体内,提供模式切换所需的能量。数值模拟证实了该方法在实际应用中具有可行性以及实用性。     

Band topology and the quantum spin Hall effect in bilayer graphene

We consider bilayer graphene in the presence of spin-orbit coupling, in order to assess its behavior as a topological insulator. The first Chern number n for the energy bands of single-layer graphene and that for the energy bands of bilayer graphene are computed and compared. It is shown that for a given valley and spin, n for a Bernal-stacked bilayer is doubled with respect to that for the monolayer. This implies that this form of bilayer graphene will have twice as many edge states as single-layer graphene, which we confirm with numerical calculations and analytically in the case of an armchair terminated surface. Bernal-stacked bilayer graphene is a weak topological insulator, whose surface spectrum is susceptible to gap opening under spin-mixing perturbations. We assess the stability of the associated topological bulk state of bilayer graphene under various perturbations. In contrast, we show that AA-stacked bilayer graphene is not a topological insulator unless the spin-orbit coupling is bigger than the interlayer hopping. Finally, we consider an intermediate situation in which only one of the two layers has spin-orbit coupling, and find that although individual valleys have non-trivial Chern numbers for the case of Bernal stacking, the spectrum as a whole is not gapped, so the system is not a topological insulator.     

Non-Hermitian anomalous skin effect

A non-Hermitian topological insulator is fundamentally different from conventional topological insulators. The non-Hermitian skin effect arises in a nonreciprocal tight binding lattice with open edges. In this case, not only topological states but also bulk states are localized around the edges of the nonreciprocal system. We discuss that controllable switching from topological edge states into topological extended states in a chiral symmetric non-Hermitian system is possible. We show that the skin depth decreases with non-reciprocity for bulk states but increases with it for topological zero energy states.     

缺陷单层和双层石墨烯的拉曼光谱及其激发光能量色散关系

拉曼光谱作为一种无破坏性、快速且敏锐的测试技术已经成 为表征石墨烯样品和研究其缺陷的最重要的实验手段之一. 本论文用离子注入在单层和双层石墨烯中产生缺陷, 并利用拉曼光谱研究了存在缺陷时单层和双层石墨烯的一阶和二阶拉曼模, 单层石墨烯的D模为双峰结构, 而双层石墨烯的D模具有四峰结构. 同时, 利用四条激光线系统地研究了本征和缺陷单层和双层石墨烯的拉曼峰频率的激发光能量依赖关系, 并基于石墨材料的双共振拉曼散射机理指认了离子注入后样品各拉曼峰的物理根源. 关键词： 石墨烯 缺陷 拉曼光谱 能量色散关系     

Investigation on thermal conductivity of graphene/Si heterostructure with different defect ratios and sizes

The thermal conductivity (TC) of graphene/Si heterostructures with different defect ratios and sizes was investigated using the molecular dynamics method. As the defect ratio of heterostructure increased, the TC decreased first sharply and then slowly under a high temperature stage. The TC of heterostructure also showed a significant size effect. This phenomenon was explained by phonon dispersion and flip competition. The phonon density of states for the graphene heterostructure with different defect ratios and sizes was obtained to understand the thermal transport mechanism. Analysis showed that with the increase in the defect ratio and when the flexural modes of the heterostructure became weak, the longitudinal and transverse modes gradually dominated the phonon transport. This phenomenon can be explained that the Si atom vibration was harder in the vertical plane than that of graphene. The vibration mode hindered the heat carrier of graphene and affected heat transport to the heterostructure.     

Surface plasmon resonance and field confinement in graphene nanoribbons in a nanocavity

In this work, we demonstrate surface plasmon resonance properties and field confinement under a strong interaction between a waveguide and graphene nanoribbons (GNRs), obtained by coupling with a nanocavity. The optical transmission of a waveguide–cavity–graphene structure is investigated by finite-difference time-domain simulations and coupled-mode theory. The resonant frequency and intensity of the GNR resonant modes can be precisely controlled by tuning the Fermi energy and carrier mobility of the graphene, respectively. Moreover, the refractive index of the cavity core, the susceptibility χ⁽³⁾ and the intensity of incident light have little effect on the GNR resonant modes, but have good tunability to the cavity resonant mode. The cavity length also has good tunability to the resonant mode of cavity. A strong interaction between the GNR resonant modes and the cavity resonant mode appears at a cavity length of L₁ = 350 nm. We also demonstrate the slow-light effect of this waveguide–cavity–graphene structure and an optical bistability effect in the plasmonic cavity mode by changing the intensity of the incident light. This waveguide–cavity–graphene structure can potentially be utilised to enhance optical confinement in graphene nano-integrated circuits for optical processing applications.