Strain induced topological transitions in twisted double bilayer graphene

We theoretically study the band structures and the valley Chern numbers of the AB–AB and AB–BA stacked twisted double bilayer graphene under heterostrain effect. In the absence of heterostrain, due to the constrains by the spatial symmetries, the central two flat bands of the AB–AB are topological trivial bands, while in the AB–BA they have a finite Chern number. The heterostrain breaks all the point group symmetries and the constrains are lifted, hence the topological properties of the two arrangements can be tuned by different strain magnitudes ϵ and directions ϕ. The heterostrain has dissimilar impacts on the Chern numbers of the AB–AB and AB–BA, owing to their different band gaps, and these gaps can be modified by a vertical electric field. Our results show that the topological transitions for both arrangements occur in the ϵ range of 0.1%–0.4%, which can be realized in the graphene-based sample.     

Topological Fulde–Ferrell and Larkin–Ovchinnikov states in spin-orbit-coupled lattice system

The spin-orbit coupled lattice system under Zeeman fields provides an ideal platform to realize exotic pairing states. Notable examples range from the topological superfluid/superconducting (tSC) state, which is gapped in the bulk but metallic at the edge, to the Fulde–Ferrell (FF) state (having a phase-modulated order parameter with a uniform amplitude) and the Larkin–Ovchinnikov (LO) state (having a spatially varying order parameter amplitude). Here, we show that the topological FF state with Chern number (C=−1) (tFF₁) and topological LO state with C= 2 (tLO₂) can be stabilized in Rashba spin-orbit coupled lattice systems in the presence of both in-plane and out-of-plane Zeeman fields. Besides the inhomogeneous tSC states, in the presence of a weak in-plane Zeeman field, two topological BCS phases may emerge with C=−1 (tBCS₁) far from half filling and C= 2 (tBCS₂) near half filling. We show intriguing effects such as different spatial profiles of order parameters for FF and LO states, the topological evolution among inhomogeneous tSC states, and different non-trivial Chern numbers for the tFF₁ and tLO_1,2 states, which are peculiar to the lattice system. Global phase diagrams for various topological phases are presented for both half-filling and doped cases. The edge states as well as local density of states spectra are calculated for tSC states in a 2D strip.     

二维三角格点系统中的拓扑陈数

利用紧束缚模型对二维三角周期格点中各能带的陈数分布进行研究.通过严格对角化方法得到体系能量本征值和对应的本征态，再利用Kubo公式计算出量子化的霍尔电导、态密度及各扩展态对应的陈数.在傅里叶变换下将哈密顿量转换到k空间从而得到体系的能谱分布.研究表明：次近邻格点之间的跳跃积分t'的不同取值影响体系各能带对应的陈数分布，计算得到当t'=1/2时体系三个能带从低到高对应的陈数分布为{-4，5，-1}，t'=-1/2时其对应陈数分布变化为{2，-4，2}，而t'=±1/4时对应的陈数分布都为{2，-1，-1}.同时发现：能谱帯隙的宽度和对应霍尔平台的宽度一致，并且k空间的能带越平坦，其对应的在霍尔电导跳跃处的态密度峰就越高越尖锐，而该处霍尔电导跳跃就越陡峭.     

Atomic-Ordering-Induced Quantum Phase Transition between Topological Crystalline Insulator and Z_2 Topological Insulator

Topological phase transition in a single material usually refers to transitions between a trivial band insulator and a topological Dirac phase, and the transition may also occur between different classes of topological Dirac phases.It is a fundamental challenge to realize quantum transition between Z_2 nontrivial topological insulator(TI) and topological crystalline insulator(TCI) in one material because Z_2 TI and TCI have different requirements on the number of band inversions. The Z_2 TIs must have an odd number of band inversions over all the time-reversal invariant momenta, whereas the newly discovered TCIs, as a distinct class of the topological Dirac materials protected by the underlying crystalline symmetry, owns an even number of band inversions. Taking PbSnTe_2 alloy as an example, here we demonstrate that the atomic-ordering is an effective way to tune the symmetry of the alloy so that we can electrically switch between TCI phase and Z_2 TI phase in a single material. Our results suggest that the atomic-ordering provides a new platform towards the realization of reversibly switching between different topological phases to explore novel applications.     

Anisotropic plasmon dispersion and damping in multilayer 8-Pmmn borophene structures

We investigate the collective plasma oscillations theoretically in multilayer 8-Pmmn borophene structures, where the tilted Dirac electrons in spatially separated layers are coupled via the Coulomb interaction. We calculate the energy dispersions and Landau dampings of the multilayer plasmon excitations as a function of the total number of layers, the interlayer separation, and the different orientations. Like multilayer graphene, the plasmon spectrum in multilayer borophene consists of one in-phase optical mode and N - 1 out-of-phase acoustical modes. We show that the plasmon modes possess kinks at the boundary of the interband single-particle continuum and the apparent anisotropic behavior. All the plasmon modes approach the same dispersion at a sufficiently large interlayer spacing in the short-wavelength limit. Especially along specific orientations, the optical mode could touch an energy maximum in the nondamping region, which shows non-monotonous behavior. Our work provides an understanding of the multilayer borophene plasmon and may pave the way for multilayer borophene-based plasmonic devices.     

Equivariant PT-symmetric real Chern insulators

It was understood that Chern insulators cannot be realized in the presence of PT symmetry.In this paper,we reveal a new class of PT-symmetric Chern insulators,which has internal degrees of freedom forming real representations of a symmetry group with a complex endomorphism field.As a generalization to the conventional 2n-dimensional Chern insulators with integer n≥1,these PT-symmetric Chern insulators have the n-th complex Chern number as their topological invariant,and have a Z classification given by the equivariant orthogonal K theory.Thus,in a fairly different sense,there exist ubiquitously Chern insulators with PT.symmetry.By generalizing the Thouless charge pump argument,we find that,for a PT-symmetric Chern insulator with Chern number v.there are equally many v flavors of coexisting left-and right-handed chiral modes.Chiral modes with opposite chirality are complex conjugates to each other as complex representations of the internal symmetry group,but are not isomorphic.For the physical dimensionality d=2,the PT-symmetric Chern insulators may be realized in artificial systems including photonic crystals and periodic mechanical systems.     

Structural study and magnetoresistance effect of epitaxial La0.67Sr0.33MnO3–δ and Pr0.7Ca0.3MnO3−δ multilayer films

La_0.67Sr_0.33MnO_3−δ (LSMO) and Pr_0.7Ca_0.3MnO_3−δ (PCMO) multilayer epitaxial films, which were fabricated with different LSMO and PCMO layer thickness on LaAlO₃ single crystal substrates of (0 0 1) orientation by a direct current magnetron sputtering technique, were studied further, after the structure, magnetoresistance effect and magnetic properties of LSMO/PCMO/LSMO (LPL) trilayer epitaxial films were systemically studied. The superlattice structures of multilayer films were observed according to the diffraction peaks of X-ray diffraction patterns at small angles. The metal–insulator transition temperature (T_P) and peak resistivity (ρ_max) obviously changed when we altered the thickness of PCMO middle layer and the intra-field related with the thickness of those layers and their interaction. Considering the effect of the distribution of electrical field and current, and the interaction among the layers of LSMO and PCMO, an effective fact n* was introduced to replace n (the number of layer). All the calculated values of ρ (the resistivity of multilayer films) accorded with the experimental values.     

空间盘绕型声学超材料的亚波长拓扑谷自旋态

声子晶体的Dirac线性色散关系,使其具有奇特的声拓扑特性,在声波控制领域具有良好的应用前景.目前,声子晶体的拓扑边缘态主要基于Bragg散射所产生的能带结构,难以实现低频声波的受拓扑保护单向边缘传输.本文引入空间盘绕结构,设计了具有C_(3v)对称性的空间盘绕型声学超材料,并研究其布里渊区高对称点(K/K'点)的亚波长Dirac锥形线性色散.接着,通过旋转打破空间盘绕型声学超材料的镜像对称性,使其Dirac简并锥裂开而产生亚波长拓扑相变和亚波长拓扑谷自旋态.最后,采用拓扑相位互逆的声学超材料构造拓扑界面,实现声拓扑谷自旋传输.空间盘绕型声学超材料的亚波长Dirac线性色散与亚波长拓扑谷自旋态突破了声子拓扑绝缘体的几何尺寸限制,为声拓扑稳健传输在低频段的应用提供理论基础.     

Signatures of bulk topology in the non-linear optical spectra of Dirac-Weyl materials

Graphene, topological insulators (TI) and the Weyl semimetal are shown to be well-characterized using the phenomenon of anomalous Rabi oscillation (ARO). These oscillations occur far from conventional resonance and Floquet theory shows them to be unique to these systems. Of particular interest is the bulk topological insulator (TI) where the wave-vector dependent frequency of the ARO is seen to be gapped in topologically trivial situations and gapless when there is a non-vanishing Chern number. It is shown that the Chern number may be directly inferred by performing a pump-probe experiment in the bulk without referring to surface states. A simpler alternative to the Lindblad method is invoked in order to incorporate dephasing effects that despite leading to a non-unitary time evolution of the wave-function, is nevertheless, probability conserving. The differential transmission coefficient versus the pump pulse duration (when all else is held fixed) has the form of a sinusoidal function with an amplitude that decays as a power law in the pump duration (alternatively, the “area” of the pump pulse). The exponent of this power law decay is indicative of the Chern number of the bulk in case of TI and more generally indicative of the particular member of the family of materials that may be collectively referred to as – Dirac-Weyl materials.     

Enhancement of subgap conductance in a graphene superconductor junction by valley polarization

We theoretically study the differential conductance of a graphene/graphene superconductor junction, where the valley polarization of Dirac electrons is considered in the nonsuperconducting region. It is shown that the subgap conductance will increase monotonically with the valley-polarization strength when the chemical potential μ is near the Dirac point μ≤ 3?(? is the superconducting gap), whereas it will decrease monotonically when μ is far away from the Dirac point, μ≥ 5?.The former case is induced by the specular Andreev reflection while the retro-reflection accounts for the later result. Our findings may shed light on the control of conductance of a graphene superconductor junction by valley polarization.     

Introduction to Topological Phases and Electronic Interactions in (2+1) Dimensions

A brief introduction to topological phases is provided, considering several two-band Hamiltonians in one and two dimensions. Relevant concepts of the topological insulator theory, such as: Berry phase, Chern number, and the quantum adiabatic theorem, are reviewed in a basic framework, which is meant to be accessible to non-specialists. We discuss the Kitaev chain, SSH, and BHZ models. The role of the electromagnetic interaction in the topological insulator theory is addressed in the light of the pseudo-quantum electrodynamics (PQED). The well-known parity anomaly for massless Dirac particle is reviewed in terms of the Chern number. Within the continuum limit, a half-quantized Hall conductivity is obtained. Thereafter, by considering the lattice regularization of the Dirac theory, we show how one may obtain the well-known quantum Hall conductivity for a single Dirac cone. The renormalization of the electron energy spectrum, for both small and large coupling regime, is derived. In particular, it is shown that massless Dirac particles may, only in the strong correlated limit, break either chiral or parity symmetries. For graphene, this implies the generation of Landau-like energy levels and the quantum valley Hall effect.     

Topological Lifshitz transition and novel edge states induced by non-Abelian SU(2) gauge field on bilayer honeycomb lattice

We investigate the SU(2) gauge effects on bilayer honeycomb lattice thoroughly. We discover a topological Lifshitz transition induced by the non-Abelian gauge potential. Topological Lifshitz transitions are determined by topologies of Fermi surfaces in the momentum space. Fermi surface consists of N = 8 Dirac points at π-flux point instead of N = 4 in the trivial Abelian regimes. A local winding number is defined to classify the universality class of the gapless excitations. We also obtain the phase diagram of gauge fluxes by solving the secular equation. Furthermore, the novel edge states of biased bilayer nanoribbon with gauge fluxes are also investigated.     

Rashba自旋轨道耦合下square-octagon晶格的拓扑相变

本文研究了各向同性square-octagon晶格在内禀自旋轨道耦合、Rashba自旋轨道耦合和交换场作用下的拓扑相变,同时引入陈数和自旋陈数对系统进行拓扑分类.系统在自旋轨道耦合和交换场的影响下会出现许多拓扑非平庸态,包括时间反演对称破缺的量子自旋霍尔态和量子反常霍尔态.特别的是,在时间反演对称破缺的量子自旋霍尔效应中,无能隙螺旋边缘态依然能够完好存在.调节交换场或者填充因子的大小会导致系统发生从时间反演对称破缺的量子自旋霍尔态到自旋过滤的量子反常霍尔态的拓扑相变.边缘态能谱和自旋谱的性质与陈数和自旋陈数的拓扑刻画完全一致.这些研究成果为自旋量子操控提供了一个有趣的途径.     

Relativistic symmetries with the trigonometric Pschl-Teller potential plus Coulomb-like tensor interaction

The Dirac equation is solved to obtain its approximate bound states for a spin-1/2 particle in the presence of trigonometric Pschl-Teller(tPT) potential including a Coulomb-like tensor interaction with arbitrary spin-orbit quantum number κ using an approximation scheme to substitute the centrifugal terms κ(κ± 1)r-2.In view of spin and pseudo-spin(p-spin) symmetries,the relativistic energy eigenvalues and the corresponding two-component wave functions of a particle moving in the field of attractive and repulsive tPT potentials are obtained using the asymptotic iteration method(AIM).We present numerical results in the absence and presence of tensor coupling A and for various values of spin and p-spin constants and quantum numbers n and κ.The non-relativistic limit is also obtained.     

Moiré flat bands of twisted few-layer graphite

We report that the twisted few layer graphite (tFL-graphite) is a new family of moiré heterostructures (MHSs), which has richer and highly tunable moiré flat band structures entirely distinct from all the known MHSs. A tFL-graphite is composed of two few-layer graphite (Bernal stacked multilayer graphene), which are stacked on each other with a small twisted angle. The moiré band structure of the tFL-graphite strongly depends on the layer number of its composed two van der Waals layers. Near the magic angle, a tFL-graphite always has two nearly flat bands coexisting with a few pairs of narrowed dispersive (parabolic or linear) bands at the Fermi level, thus, enhances the DOS at E_F . This coexistence property may also enhance the possible superconductivity as been demonstrated in other multiband superconductivity systems. Therefore, we expect strong multiband correlation effects in tFL-graphite. Meanwhile, a proper perpendicular electric field can induce several isolated nearly flat bands with nonzero valley Chern number in some simple tFL-graphites, indicating that tFL-graphite is also a novel topological flat band system.     

Zero-modes and thermodynamics of disordered spin-1/2 ladders

The influence of non-magnetic doping on the thermodynamic properties of two-leg S = 1/2 spin ladders is studied in this paper. It is shown that, for a weak interchain coupling, the problem can be mapped onto a model of random mass Dirac (Majorana) fermions. We investigate in detail the structure of the fermionic states localized at an individual mass kink (zero-modes) in the framework of a generalized Dirac model. The low-temperature thermodynamic properties are dominated by these zero-modes. We use the single-fermion density of states, known to exhibit the Dyson singularity in the zero-energy limit, to construct the thermodynamics of the spin ladder. In particular, we find that the magnetic susceptibility χ diverges at T → 0 as 1/T ln²(1/T), and the specific heat behaves as C 1/ln³(1/T). The predictions on magnetic susceptibility are consistent with the most recent results of quantum Monte Carlo simulations on doped ladders with randomly distributed impurities. We also calculate the average staggered magnetic susceptibility induced in the system by such defects.     

Physical characterization of OMVPE-grown AlxGa1-xAs multi-layer films by means of non-destructive optical reflectometry

A novel Fourier transform technique which was developed by us previously, is applied in this work for non-destructive determination of thickness and refractive index steps of experimental multilayer heteroepitaxial structures. No time consuming least-squares curve-fits are required and theoretically there is no limit on the number of layers which can be analyzed. In order to demonstrate the above method experimentally, multilayer structures of Al_xGa_1-xAs containing up to five layers on GaAs substrates, were grown by organometallic vapour phase epitaxy (OMVPE). For calibration purposes, initial experiments involved the growth of Al_xGa_1-xAs single epilayers on GaAs substrates by the same technique. Layers were grown at five different compositions from x = 0.1 to x = 0.5. Both photoluminescence (at 12 K) and double-crystal X-ray diffraction measurements were undertaken on the single layers in order to establish the composition of the material. The results show excellent correspondence with each other. These results were also compared to secondary ion mass spectrometry data. The agreement between the optical technique developed by us and the other analytical methods was excellent.     

声子晶体中的多重拓扑相

研究了圆环型波导依照蜂窝结构排列的声子晶体系统中的拓扑相变.利用晶格结构的点群对称性实现赝自旋,并在圆环中引入旋转气流来打破时间反演对称性.通过紧束缚近似模型计算的解析结果表明,没有引入气流时,调节几何参数,系统存在普通绝缘体和量子自旋霍尔效应绝缘体两个相;引入气流后,可以实现新的时间反演对称性破缺的量子自旋霍尔效应相,而增大气流强度,则可以实现量子反常霍尔效应相.这三个拓扑相可以通过自旋陈数来分类.通过有限元软件模拟了多个系统中边界态的传播,发现不同于量子自旋霍尔效应相,量子反常霍尔相系统的表面只支持一种自旋的边界态,并且它无需时间反演对称性保护.     

Quantum anomalous Hall effect and related topological electronic states

Over a long period of exploration, the successful observation of quantized version of anomalous Hall effect (AHE) in thin film of magnetically doped topological insulator (TI) completed a quantum Hall trio—quantum Hall effect (QHE), quantum spin Hall effect (QSHE), and quantum anomalous Hall effect (QAHE). On the theoretical front, it was understood that the intrinsic AHE is related to Berry curvature and U(1) gauge field in momentum space. This understanding established connection between the QAHE and the topological properties of electronic structures characterized by the Chern number. With the time-reversal symmetry (TRS) broken by magnetization, a QAHE system carries dissipationless charge current at edges, similar to the QHE where an external magnetic field is necessary. The QAHE and corresponding Chern insulators are also closely related to other topological electronic states, such as TIs and topological semimetals, which have been extensively studied recently and have been known to exist in various compounds. First-principles electronic structure calculations play important roles not only for the understanding of fundamental physics in this field, but also towards the prediction and realization of realistic compounds. In this article, a theoretical review on the Berry phase mechanism and related topological electronic states in terms of various topological invariants will be given with focus on the QAHE and Chern insulators. We will introduce the Wilson loop method and the band inversion mechanism for the selection and design of topological materials, and discuss the predictive power of first-principles calculations. Finally, remaining issues, challenges and possible applications for future investigations in the field will be addressed.     

The spectral density of the QCD Dirac operator and patterns of chiral symmetry breaking

We study the spectrum of the QCD Dirac operator for two colors with fermions in the fundamental representation and for two or more colors with adjoint fermions. For N_f flavors, the chiral flavor symmetry of these theories is spontaneously broken according to SU (2N_f → Sp (2N_f) and SU (N_f → O (N_f), respectively, rather than the symmetry breaking pattern SU (N_f) × SU (N_f) → SU (N_f) for QCD with three or more colors and fundamental fermions. In this paper we study the Dirac spectrum for the first two symmetry breaking patterns. Following previous work for the third case we find the Dirac spectrum in the domain λ Λ_QCD by means of partially quenched chiral perturbation theory. In particular, this result allows us to calculate the slope of the Dirac spectrum at λ = 0. We also show that for λ 1/L₂ Λ_QCD (wing L the linear size fo the system) the Dirac spectrum is given by a chiral Random Matrix Theory with the symmetries of the Dirac operator.