Measurement of the bulk and surface bands in Dirac line-node semimetal ZrSiS

Dirac semimetals are materials in which the conduction and the valence bands have robust crossing points protected by topology or symmetry. Recently, a new type of Dirac semimetals, so called the Dirac line-node semimetals(DLNSs), have attracted a lot of attention, as they host robust Dirac points along the one-dimensional(1D) lines in the Brillouin zone(BZ).In this work, using angle-resolved photoemission spectroscopy(ARPES) and first-principles calculations, we systematically investigated the electronic structures of non-symmorphic ZrSiS crystal where we clearly distinguished the surface states from the bulk states. The photon-energy-dependent measurements further prove the existence of Dirac line node along the X-R direction. Remarkably, by in situ surface potassium doping, we clearly observed the different evolutions of the bulk and surface electronic states while proving the robustness of the Dirac line node. Our studies not only reveal the complete electronic structures of ZrSiS, but also demonstrate the method manipulating the electronic structure of the compound.     

Exact solution of the Dirac–Weyl equation in graphene under electric and magnetic fields

In this paper, we have obtained exact analytical solutions for the bound states of a graphene Dirac electron in magnetic fields with various q-parameters under an electrostatic potential. In order to solve the time-independent Dirac–Weyl equation, the Nikoforov–Uvarov (NU) and Frobenius methods have been used. We have also investigated the thermodynamic properties by using the Hurwitz zeta function method for one of the states. Finally, some of the numerical results are also shown.     

Non-Monotonic Evolution of Carrier Density and Mobility under Thermal Cycling Treatments in Dirac Semimetal Cd_3As_2 Microbelts

Tunable carrier density plays a key role in the investigation of novel transport properties in three-dimensional topological semimetals.We demonstrate that the carrier density,as well as the mobility,of Dirac semimetal Cd_3As_2 nanoplates can be effectively tuned via in situ thermal treatment at 350 K for one hour,resulting in non-monotonic evolution by virtue of the thermal cycling treatments.The upward shift of Fermi level relative to the Dirac nodes blurs the surface Fermi-arc states,accompanied by an anomalous phase shift in the oscillations of bulk states,due to a change in the topology of the electrons.Meanwhile,the oscillation peaks of bulk longitudinal magnetoresistivity shift at high fields,due to their coupling to the oscillations of the surface Fermi-arc states.Our work provides a thermal control mechanism for the manipulation of quantum states in Dirac semimetal Cd_3As_2 at high temperatures,via their carrier density.     

Non-locally correlated disorder and delocalization in one dimension (II). Localization length

We study the delocalization transition in a one-dimensional Dirac fermion system with randomly varying mass by using supersymmetric (SUSY) methods. In a previous paper, we calculated density of states and found that (quasi-) extended states near the band center are enhanced by non-local correlation of the random Dirac mass. Numerical studies support this conclusion. In this paper, we calculate the localization length as a function of the correlation length of the disorder. The result shows that the localization length is an increasing function of the correlation of the random mass.     

Electronic properties of SnTe-class topological crystalline insulator materials

The rise of topological insulators in recent years has broken new ground both in the conceptual cognition of condensed matter physics and the promising revolution of the electronic devices.It also stimulates the explorations of more topological states of matter.Topological crystalline insulator is a new topological phase,which combines the electronic topology and crystal symmetry together.In this article,we review the recent progress in the studies of SnTe-class topological crystalline insulator materials.Starting from the topological identifications in the aspects of the bulk topology,surface states calculations,and experimental observations,we present the electronic properties of topological crystalline insulators under various perturbations,including native defect,chemical doping,strain,and thickness-dependent confinement effects,and then discuss their unique quantum transport properties,such as valley-selective filtering and helicity-resolved functionalities for Dirac fermions.The rich properties and high tunability make SnTe-class materials promising candidates for novel quantum devices.     

Dirac光子晶体

Dirac费米子作为粒子物理中的基本粒子之一,其理论在近年来蓬勃发展的拓扑电子理论领域中被广泛提及并用来刻画具有Dirac费米子性质的电子态.这种特殊的能态通常被称为Dirac点,在能谱上表现为两条不同能带之间的线性交叉点.由于Dirac点往往是发生拓扑相变的转变点,因而也被视为实现各种拓扑态的重要母态.作为可与拓扑电子体系类比的拓扑光子晶体因其独特的潜在应用价值也受到人们的广泛关注,实现包含Dirac点的光子能带已成为研究拓扑光子晶体的核心课题.本文基于电子的拓扑理论,简要地回顾了Dirac点在光子系统中的研究进展,特别介绍了如何在光子晶体中利用不同晶格对称性实现在高对称点/线上的Dirac点,以及由Dirac点衍生的Weyl点.     

Rotating effects on the Dirac oscillator in the cosmic string spacetime

In this contribution, we study the Dirac oscillator under the influence of noninertial effects of a rotating frame in the cosmic string spacetime. We show that both noninertial effects and the topology of the cosmic string spacetime restrict the physical region of the spacetime where the quantum particle can be placed, and discuss two different cases of bound states solutions of the Dirac equation by analysing the behaviour of the Dirac oscillator frequency.     

Both electron and hole Dirac cone states in Ba(FeAs)2 confirmed by magnetoresistance

Quantum transport of Dirac cone states in the iron pnictide Ba(FeAs)(2) with a d-multiband system is studied by using single crystal samples. Transverse magnetoresistance develops linearly against the magnetic field at low temperatures. The transport phenomena are interpreted in terms of the zeroth Landau level by applying the theory predicted by Abrikosov. The results of the semiclassical analyses of a two carrier system in a low magnetic field limit show that both the electron and hole reside as the high mobility states. Our results show that pairs of electron and hole Dirac cone states must be taken into account for an accurate interpretation in iron pnictides, which is in contrast with previous studies.     

基于手性声子晶体的谷拓扑声输运

研究手性风车形散射体构建的谷拓扑声波导。具有右手与左手手性风车形散射体的声子晶体具有截然不同的声谷拓扑特性。当两种手性风车形散射体从-60°旋转到60°时,其所构建的声子晶体均出现2次偶然简并的狄拉克点与谷霍尔相变。基于两种具有相反谷霍尔相的手性声子晶体构建的谷拓扑声波导,在其重叠体带隙内存在一对局域在波导分界面处的谷态边缘态。实验研究表明,该边缘态可以很好的支持谷拓扑声输运,且对弯曲与无序两种缺陷具有一定的鲁棒性.      

Pressure-induced Lifshitz transition in the type Ⅱ Dirac semimetal PtTe_2

Numerous exotic properties have been discovered in Dirac Semimetals(DSMs) and Weyl Semimetals(WSMs). In a given DSM/WSM, the Dirac/Weyl nodes usually coexist with other bulk states, making their respective contribution elusive. In this work, we distinguish the role of bulk states from the tilted Dirac nodes on the transport properties in DSMs. Specifically, we applied pressure to a type-II DSM material, PtTe2, and studied its pressure modified electronic and lattice structure systematically by using in situ transport measurements and X-ray diffraction(XRD). A pressure-induced transition at about 20 GPa is revealed in the transport properties, while the layered lattice structure is robust against pressure as illustrated in XRD measurement results.Density functional theory(DFT) calculations suggest that this is originated from the Lifshitz transition in the bulk states. Our findings provide evidence to identify the bulk states' influence on transport from the topologically-protected DSM states in the DSM material.     

Electron fractionalization in two-dimensional graphenelike structures

Electron fractionalization is intimately related to topology. In one-dimensional systems, fractionally charged states exist at domain walls between degenerate vacua. In two-dimensional systems, fractionalization exists in quantum Hall fluids, where time-reversal symmetry is broken by a large external magnetic field. Recently, there has been a tremendous effort in the search for examples of fractionalization in two-dimensional systems with time-reversal symmetry. In this Letter, we show that fractionally charged topological excitations exist on graphenelike structures, where quasiparticles are described by two flavors of Dirac fermions and time-reversal symmetry is respected. The topological zero modes are mathematically similar to fractional vortices in p-wave superconductors. They correspond to a twist in the phase in the mass of the Dirac fermions, akin to cosmic strings in particle physics.     

In-plane transport and enhanced thermoelectric performance in thin films of the topological insulators Bi₂Te₃ and Bi₂Se₃

Several small-band-gap semiconductors are now known to protect metallic surface states as a consequence of the topology of the bulk electron wave functions. The known "topological insulators" with this behavior include the important thermoelectric materials Bi?Te? and Bi?Se?, whose surfaces are observed in photoemission experiments to have an unusual electronic structure with a single Dirac cone. We study in-plane (i.e., horizontal) transport in thin films made of these materials. The surface states from top and bottom surfaces hybridize, and conventional diffusive transport predicts that the tunable hybridization-induced band gap leads to increased thermoelectric performance at low temperatures. Beyond simple diffusive transport, the conductivity shows a crossover from the spin-orbit-induced antilocalization at a single surface to ordinary localization.     

Noninertial Effects on a Dirac Neutral Particle Inducing an Analogue of the Landau Quantization in the Cosmic String Spacetime

We discuss the behavior of external fields interacting with a Dirac neutral particle with a permanent electric dipole moment in order to achieve relativistic bound state solutions in a noninertial frame and in the presence of a topological defect spacetime. We show that the noninertial effects of the Fermi?CWalker reference frame induce a radial magnetic field even in the absence of magnetic charges, which is influenced by the topology of the cosmic string spacetime. We then discuss the conditions that the induced fields must satisfy to yield the relativistic bound states corresponding to the Landau?CHe?CMcKellar?CWilkens quantization in the cosmic string spacetime. Finally, we obtain the Dirac spinors for positive-energy solutions and the Gordon decomposition of the Dirac probability current.     

Plasma oscillations of edge Dirac fermions

The dispersion law of one-dimensional plasmons in a quasi-one-dimensional system of massless Dirac fermions has been calculated. Two model two-dimensional systems where bands of edge states filled with such Dirac fermions appear at the edge have been considered. Edge states in the first system, topological insulator, are due to topological reasons. Edge states in the second system, system of massive Dirac fermions, have Tamm origin. It has been shown that the dispersion laws of plasmons in both systems in the long-wavelength limit differ only in the definition of the parameters (velocity and localization depth of Dirac fermions). The frequency of plasmons is formally quantum (ω ∝ ? ^?1/2) and, in the case of the Coulomb interaction between electrons, depends slightly on the Fermi level E _F. The dependence on E _F is stronger in the case of short-range interaction. The quantum features of oscillations of massless one-dimensional Dirac fermions are removed by introducing the mass of Dirac fermions at the Fermi level and their density. Correspondence to the dispersion law of classical one-dimensional plasma oscillations in a narrow stripe of “Schrödinger” electrons has been revealed.     

On the interaction of the Dirac oscillator with the Aharonov–Casher system in topological defect backgrounds

In this paper, we study the influence of the Aharonov–Casher effect [Y. Aharonov, A. Casher, Phys. Rev. Lett. 53 (1984) 319] on the Dirac oscillator in three different scenarios of general relativity: the Minkowski spacetime, the cosmic string spacetime and the cosmic dislocation spacetime. In this way, we solve the Dirac equation and obtain the energy levels for bound states and the Dirac spinors for positive-energy solutions. We show that the relativistic energy levels depend on the Aharonov–Casher geometric phase. We also discuss the influence of curvature and torsion on the relativistic energy levels and the Dirac spinors due to the topology of the cosmic string and cosmic dislocation spacetimes.     

Dawson–Furnstahl计算方案与Dirac空穴理论的联系

在相对论无规位相近似中,有两种顾及负能态贡献的方法.一种是由Dawson和Furnstahl(DF)提出的计算方案.他们假定Dirac海是空的.另外一种就是Dirac空穴理论,它认为负能海的全充满的.这两种方法在顾及负能态贡献上看似完全对立.文章中考察了这两种方法的关系,并给出了DF方法的适用范围.     

Entropies of a Toroidal Black Hole Due to Scalar and Dirac Fields

Using the thin film brick-wall model, the entropies of a toroidal black hole due to scalar and Dirac fields are investigated. The entropy due to the scalar field is one fourth of the horizon area, and that due to the Dirac field is seven eighth of the area. These results are similar to that in black holes with horizon topology S ². The cutoff in toroidal black hole is chosen as the same as one in black holes with horizon topology S ², which seems to mean that the thin film brick-wall model is universal.     

Fragility of surface states and robustness of topological order in Bi2Se3 against oxidation

Topological surface states are protected against local perturbations, but this protection does not extend to chemical reaction over the whole surface, as demonstrated by theoretical studies of the oxidation of Bi(2)Se(3) and its effects on the surface spin polarization and current. While chemisorption of O(2) largely preserves the topological surface states, reaction with atomic O removes the original surface states and yields two new sets of surface states. One set forms a regular Dirac cone but is topologically trivial. The other set, while topologically relevant, forms an unusual rounded Dirac cone. The details are governed by the hybridization interaction at the interface.     

Finite 1D-Lattice Physics as Induced by Dirac–Markov Operators

Finite 1D-lattice physics as induced by Dirac operators was examined. We identified the Dirac operators with Bi-Graded Markovian matrices. The Dirac operators dictate the time evolution of states in Markovian-like processes. By applying these Dirac operators to finite 1D-lattices, we find differences between the vacuum physical spinorial states over lattices with an even number of sites as compared to an odd number of sites. Solitonic states that are created by particle pairing appear on lattices with an even number of sites. On lattices with an odd number of sites, we find global solitonic states and global spin wave states, as well as a global steady oscillation of the spinorial wave function. This demonstrates how the lattice world, in a few number of sites, dramatically affects the vacuum physical states. All these vacuum states can be realized as entangled local particles over the lattice.     

二维声子晶体中Zak相位诱导的界面态

界面态具有巨大的实际应用价值,因此寻找界面态是一个既有科学意义也有应用前景的课题.在本文中,我们通过把二维正方晶格声子晶体的结构单元进行倾斜,构造出具有线性狄拉克色散的斜方晶格体系.狄拉克色散引起体能带Zak相位的π跃变,使得位于狄拉克锥投影能带两边的带隙具有不同符号的表面阻抗,从而导致由正方晶体体系与由其“倾斜”的斜方晶格体系构成的界面处存在确定性的界面态.