Single Dirac cone topological surface state and unusual thermoelectric property of compounds from a new topological insulator family

Angle resolved photoemission spectroscopy study on TlBiTe2 and TlBiSe2 from a thallium-based ternary chalcogenides family revealed a single surface Dirac cone at the center of the Brillouin zone for both compounds. For TlBiSe2, the large bulk gap (～200 meV) makes it a topological insulator with better mechanical properties than the previous binary 3D topological insualtor family. For TlBiTe2, the observed negative bulk gap indicates it as a semimetal, instead of a narrow-gap semiconductor as conventionally believed; this semimetality naturally explains its mysteriously small thermoelectric figure of merit comparing to other compounds in the family. Finally, the unique band structures of TlBiTe2 also suggest it as a candidate for topological superconductors.     

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.     

Hybrid Dispersion Dirac Semimetal and Hybrid Weyl Phases in Luttinger Semimetals: A Dynamical Approach

It is shown that hybrid Dirac and Weyl semimetals can be realized in a 3D Luttinger semimetal with quadratic band touching (QBT). This is illustrated using a periodic kicking scheme. In particular, the focus is on a momentum-dependent driving (nonuniform driving) and the realization of various hybrid Dirac and Weyl semimetals is demonstrated. A unique hybrid dispersion Dirac semimetal with two nodes is identified, where one of the nodes is linear while the other is dispersed quadratically. Next, it is shown that by tilting QBT via periodic driving and in the presence of an external magnetic field, one can realize various single/double hybrid Weyl semimetals depending on the strength of external field. Finally, it is noted that in principle, phases that are found in this work can also be realized by employing the appropriate electronic interactions.     

On a new type of massless Dirac fermions in crystalline topological insulators

A new type of massless Dirac fermions in crystalline three-dimensional topological insulators (three-dimensional → two-dimensional situation) has been predicted. The spectrum has fourfold degeneracy at the top of the two-dimensional Brillouin zone (M point) and twofold degeneracy near the M point. Crystal symmetry along with the time reversal invariance in three-dimensional topological insulators allows fourfold degenerate Dirac cones, which are absent in the classification of topological features in R.-J. Slager et al., Nat. Phys. 9, 98 (2013). The Hamiltonian in the cited work does not contain Dirac singularities with more than twofold degeneracy. For this reason, the corresponding topological classification is incomplete. The longitudinal magnetic field in the spinless case holds the massless dispersion law of fermions and does not lift fourfold degeneracy. In the spinor case, the magnetic field lifts fourfold degeneracy, holding only twofold degeneracy, and results in the appearance of a band gap in the spectrum of fermions.     

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.     

Weyl semimetal in a topological insulator multilayer

We propose a simple realization of the three-dimensional (3D) Weyl semimetal phase, utilizing a multilayer structure, composed of identical thin films of a magnetically doped 3D topological insulator, separated by ordinary-insulator spacer layers. We show that the phase diagram of this system contains a Weyl semimetal phase of the simplest possible kind, with only two Dirac nodes of opposite chirality, separated in momentum space, in its band structure. This Weyl semimetal has a finite anomalous Hall conductivity and chiral edge states and occurs as an intermediate phase between an ordinary insulator and a 3D quantum anomalous Hall insulator. We find that the Weyl semimetal has a nonzero dc conductivity at zero temperature, but Drude weight vanishing as T(2), and is thus an unusual metallic phase, characterized by a finite anomalous Hall conductivity and topologically protected edge states.     

Magneto-optical conductivity study in three-dimensional Dirac semimetals of ZrTe<Subscript>5</Subscript>

The three-dimensional (3D) Dirac semimetal material of ZrTe₅ provides a possible platform for studying 3D Dirac fermions. It can realize both the point-node semimetal phase and line-node semimetal phase when the intrinsic Zeeman interaction acts along different crystalline directions. In this work we present a study of magneto-optical conductivity in ZrTe₅. We calculate the optical conductivities in different phases, which exhibit a series of resonant peaks lying on a growing background whose origins are explored. For the Weyl semimetal phase, two striking signatures are found, one is the existence of an additional n = 0 LL transition and another is the double-strong peak structure related to the LL transition in one dispersion branch. While in the line-node semimetal phase, the weak peak appear and the strong peaks have higher degeneracy. We discuss the implications of these results in experiment.     

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.     

Effective models for nearly ideal Dirac semimetals

Topological materials (TMs) have gained intensive attention due to their novel behaviors compared with topologically trivial materials. Among various TMs, Dirac semimetal (DSM) has been studied extensively. Although several DSMs have been proposed and verified experimentally, the suitable DSM for realistic applications is still lacking. Thus finding ideal DSMs and providing detailed analyses to them are of both fundamental and technological importance. Here, we sort out 8 (nearly) ideal DSMs from thousands of topological semimetals in Nature 566(7745), 486 (2019). We show the concrete positions of the Dirac points in the Brillouin zone for these materials and clarify the symmetryprotection mechanism for these Dirac points as well as their low-energy effective models. Our results provide a useful starting point for future study such as topological phase transition under strain and transport study based on these effective models. These DSMs with high mobilities are expected to be applied in fabrication of functional electronic devices.     

Surface electronic structure of single-domain Si( 001) 2 × 2-Al: an angle-resolved photoelectron spectroscopy study using synchrotron radiation

The electronic structure of a single-domain Si(001)2 × 2-Al surface has been studied by angle-resolved photoelectron spectroscopy (ARPES) using synchrotron radiation. Through detailed ARPES measurements along various symmetry axes of the surface Brillouin zone, the existence and dispersions of five surface states are identified, one at binding energies a little less than 1 eV and the others between 1 and 2 eV. The origin of the surface states are discussed in terms of the Al-dimer structures on Si(001).     

Transport evidence of 3D topological nodal-line semimetal phase in ZrSiS

Topological nodal-line semimetal is a new emerging material, which is viewed as a three-dimensional (3D) analog of graphene with the conduction and valence bands crossing at Dirac nodes, resulting in a range of exotic transport properties. Herein, we report on the direct quantum transport evidence of the 3D topological nodal-line semimetal phase of ZrSiS with angular-dependent magnetoresistance (MR) and the combined de Hass-van Alphen (dHvA) and Shubnikov-de Hass (SdH) oscillations. Through fitting by a two-band model, the MR results demonstrate high topological nodal-line fermion densities of approximately 6×10²¹ cm⁻³ and a perfect electron/hole compensation ratio of 0.94, which is consistent with the semi-classical expression fitting of Hall conductance Gxy and the theoretical calculation. Both the SdH and dHvA oscillations provide clear evidence of 3D topological nodal-line semimetal characteristic.     

Unexpected low thermal conductivity and large power factor in Dirac semimetal Cd_3As_2

Thermoelectrics has long been considered as a promising way of power generation for the next decades. So far,extensive efforts have been devoted to the search of ideal thermoelectric materials, which require both high electrical conductivity and low thermal conductivity. Recently, the emerging Dirac semimetal Cd3As2, a three-dimensional analogue of graphene, has been reported to host ultra-high mobility and good electrical conductivity as metals. Here, we report the observation of unexpected low thermal conductivity in Cd3As2, one order of magnitude lower than the conventional metals or semimetals with a similar electrical conductivity, despite the semimetal band structure and high electron mobility. The power factor also reaches a large value of 1.58 m W·m-1·K-2at room temperature and remains non-saturated up to 400 K.Corroborating with the first-principles calculations, we find that the thermoelectric performance can be well-modulated by the carrier concentration in a wide range. This work demonstrates the Dirac semimetal Cd3As2 as a potential candidate of thermoelectric materials.     

Shubnikov-de Haas oscillations of massive Dirac fermions in a Dirac antiferromagnet SrMnSb2

We investigate the physical properties of massive Dirac fermions in SrMnSb₂ using transport, specific heat, electronic structure calculations, and Shubnikov-de Haas (SdH) oscillations. SrMnSb₂ is a candidate Dirac antiferromagnet, consisting of the MnSb layers and the distorted square net of Sb atoms with a zigzag chain structure. This structural distortion leads to gap opening at the band crossing point found in the square lattice of the sister compound SrMnBi₂ but leaves another Dirac band crossing near the Brillouin zone boundary. The small 2D Fermi surface with a light electron mass and a small Fermi energy is confirmed by the large resistivity anisotropy, the large Seebeck coefficient, and also the angle and temperature dependent SdH oscillations. The Berry phase obtained from the SdH oscillations is trivial, in contrast to the case of SrMnBi₂. The relatively large spin orbit coupling gap and the small Fermi energy in SrMnSb₂ is found to be essential to understand this contrasting behavior of the massive Dirac fermions as compared to SrMnBi₂. Our observations demonstrate that the Berry phase of the mobile electrons in SrMnSb₂ is sensitive to the Fermi level change and can be tuned by doping or deficiency.     

k=0处的类狄拉克锥

狄拉克锥在电子和经典波体系中分别被发现, 由于其线性能带关系, 伴随着很多独特的现象. 除了一般存在于布里渊区边界处的狄拉克锥, k=0处也存在包含线性能带关系的类狄拉克锥. 这个类狄拉克锥可以由单极子和偶极子的偶然简并而形成. k=0处的类狄拉克锥可以通过两维电介质光子晶体来实现, 利用等效媒质理论, 此时的光子晶体在类狄拉克点频率可以等效为介电常数和磁导率都为零的材料. 电介质双零折射率材料既可以避免阻抗的不匹配, 也可以避免体系推广到高频所引起的强烈损耗. 此外, k=0处的类狄拉克锥与双零折射率的概念可以从两维体系拓展到三维体系, 而且还可以从电磁波体系推广到声波和弹性波体系. 利用具有类狄拉克点的两维光子晶体, 在材料参数都偏离类狄拉克点条件的两个半无限大光子晶体所构成的界面中, 一定存在界面态. 这些界面态的存在可以通过层状多重散射理论得到的表面阻抗以及体能带的几何相位来彻底解释.     

Large linear magnetoresistance in a new Dirac material BaMnBi_2

Dirac semimetal is a class of materials that host Dirac fermions as emergent quasi-particles.Dirac cone-type band structure can bring interesting properties such as quantum linear magnetoresistance and large mobility in the materials.In this paper,we report the synthesis of high quality single crystals of BaMnBi_2 and investigate the transport properties of the samples.BaMnBi_2 is a metal with an antiferromagnetic transition at T_N = 288 K.The temperature dependence of magnetization displays different behavior from CaMnBi_2 and SrMnBi_2,which suggests the possible different magnetic structure of BaMnBi_2.The Hall data reveals electron-type carriers and a mobility μ(5K)= 1500 cm~2/V·s.Angle-dependent magnetoresistance reveals the quasi-two-dimensional(2D) Fermi surface in BaMnBi_2- A crossover from semiclassical MR~H~2dependence in low field to MR~H dependence in high field,which is attributed to the quantum limit of Dirac fermions,has been observed in magnetoresistance.Our results indicate the existence of Dirac fermions in BaMnBi_2.     

Double Dirac cones at k = 0 in pinned platonic crystals

In this paper, we compute the band structure for a pinned elastic plate which is constrained at the points of a hexagonal lattice. Existing work on platonic crystals has been restricted to square and rectangular array geometries, and an examination of other Bravais lattice geometries for platonic crystals has yet to be made. Such hexagonal arrays have been shown to support Dirac cone dispersion at the center of the Brillouin zone for phononic crystals, and we demonstrate the existence of double Dirac cones for the first time in platonic crystals here. In the vicinity of these Dirac points, there are several complex dispersion phenomena, including a multiple interference phenomenon between families of waves which correspond to free space transport and those which interact with the pins. An examination of the reflectance and transmittance for large finite gratings arranged in a hexagonal fashion is also made, where these effects can be visualized using plane waves. This is achieved via a recurrence relation approach for the reflection and transmission matrices, which is computationally stable compared to transfer matrix approaches.     

Tunable multiple layered Dirac cones in optical lattices

We show that multiple layered Dirac cones can emerge in the band structure of properly addressed multicomponent cold fermionic gases in optical lattices. The layered Dirac cones contain multiple copies of massless spin-1/2 Dirac fermions at the same location in momentum space, whose different Fermi velocity can be tuned at will. On-site microwave Raman transitions can further be used to mix the different Dirac species, resulting in either splitting of or preserving the Dirac point (depending on the symmetry of the on-site term). The tunability of the multiple layered Dirac cones allows us to simulate a number of fundamental phenomena in modern physics, such as neutrino oscillations and exotic particle dispersions with E~p(N) for arbitrary integer N.     

Strain engineering of topological properties in lead‐salt semiconductors

Rock‐salt chalcogenide SnTe represents the simplest realization of a topological insulator where a crystal symmetry allows for the appearance of surface metallic states. Here, we theoretically predict that strain, as realized in thin films grown on (001) substrates, may induce a transition to a topological crystalline insulating phase in related lead‐salt chalcogenides. Furthermore, relevant topological properties of the surface states, such as the location of the Dirac cones on the surface Brillouin zone or the decay length of edge states, appear to be tunable with strain, with potential implications for technological devices benefiting from those additional degrees of freedom. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Conical Diffraction from Approximate Dirac Cone States in a Superhoneycomb Lattice

Superhoneycomb lattice is an edge‐centered honeycomb lattice that represents a hybrid fermionic and bosonic system. It contains pseudospin‐1/2 and pseudospin‐1 Dirac cones, as well as a flat band in its band structure. In this paper, we cut the superhoneycomb lattice along short‐bearded boundaries and obtain the corresponding band structure. The states very close to the Dirac points represent approximate Dirac cone states that can be used to observe conical diffraction during light propagation in the lattice. In comparison with the previous literature, this research is carried out using the continuous model, which brings new results and is simple, direct, accurate, and computationally efficient.     

New family of Dirac and Weyl semimetals in XAuTe (X = Na,K, Rb) ternary honeycomb compounds

We propose a new family of 3D Dirac semimetals based on XAuTe(X = K, Na, Rb) ternary honeycomb compounds, determined based on first-principles calculations, which are shown to be topological Dirac semimetals in which the Dirac points are induced by band inversion. Dirac points with four-fold degeneracy that are protected by C3 rotation symmetry and located on the Γ-A high-symmetry path are found. Through spatial-inversion symmetry breaking, a K(Au0.5 Hg0.5)(Te0.5As0.5) superlattice structure composed of KHgAs and KAuTe compounds is proven to be a Weyl semimetal with type-II Weyl points, which connect electronand hole-like bands. In this superlattice structure, the six pairs of Weyl nodes are distributed along the K-Γ high-symmetry path on the kz = 0 plane. Our research expands the family of topological Dirac and type-II Weyl semimetals.