Intrinsic anomalous Hall effect in type-II Weyl semimetals

Recently, a new type of Weyl semimetal called type-II Weyl semimetal has been proposed. Unlike the usual (type-I) Weyl semimetal, which has a point-like Fermi surface, this new type of Weyl semimetal has a tilted conical spectrum around the Weyl point. Here we calculate the anomalous Hall conductivity of a Weyl semimetal with a tilted conical spectrum for a pair of Weyl points, using the Kubo formula. We find that the Hall conductivity is not universal and can change sign as a function of the parameters quantifying the tilts. Our results suggest that even for the case where the separation between the Weyl points vanishes, tilting of the conical spectrum could give rise to a finite anomalous Hall effect, if the tilts of the two cones are not identical.     

磁性外尔半金属材料研究现状与展望

外尔半金属是拓扑半金属家族中的一员。理想的外尔半金属费米面附近有且仅有非简并价带和导带形成的孤立能带交叉点,其低能激发准粒子可以用描述手性外尔费米子的外尔方程来刻画。在三维固体中形成外尔半金属态需要破缺时间反演、中心反演以及它们的组合对称操作。外尔点(即能带交叉点)具有拓扑稳定性和确定的手性或磁荷,且左右手性外尔点需成对出现。非磁性外尔半金属TaAs家族材料的发现,使得研究具有手征性的电子态,及其导致的新物性、新现象成为可能。与非磁性外尔半金属相比,磁性外尔半金属可以仅仅具有一对外尔点,是最简单的外尔半金属,有利于物理机理的分析。磁性外尔半金属可用于实现具有本征磁性的量子反常霍尔效应,提供了通过外磁场来调控外尔点及其相关效应的新手段。文章介绍了磁性外尔半金属的理论模型、拓扑数计算等基本原理,简要回顾了一些典型材料的理论计算和实验研究进展,并介绍了磁性拓扑量子化学理论和磁性拓扑材料的高通量计算,最后讨论了磁性外尔半金属的发展前景和未来的研究方向。     

Goos-Hänchen and Imbert-Fedorov shifts in tilted Weyl semimetals

We establish the beam models of Goos-Hänchen (GH) and Imbert-Fedorov (IF) effects in tilted Weyl semimetals (WSMs), and systematically study the influences of Weyl cone tilting and chemical potential on the GH and IF shifts at a certain photon energy 1.96 eV. It is found that the GH and IF shifts in tilted type-I and type-Ⅱ WSMs are both almost symmetric about the Weyl cone tilting. Meanwhile, the GH and IF shifts in type-I WSMs almost do not change with the tilt degree of Weyl cones, while those in type-Ⅱ WSMs are extremely dependent on tilt degree. These trends are mainly due to the nearly symmetric distribution of WSMs conductivities, where the conductivities keep stable in type-I WSMs and gradually decrease with tilt degree in type-Ⅱ WSMs. By adjusting the chemical potential, the boundary between type-I and type-Ⅱ WSMs widens, and the dependence of the beam shifts on the tilt degree can be manipulated. Furthermore, by extending the relevant discussions to a wider frequency band, the peak fluctuation of GH shifts and the decrease of IF shifts occur gradually as the frequency increases, and the performance of beam shifts at photon energy 1.96 eV is equally suitable for other photon frequencies. The above findings provide a new reference for revisiting the beam shifts in tilted WSMs and determining the types of WSMs.     

漫谈第二类Weyl半金属

近日,清华大学物理系研究人员及合作者在Weyl半金属研究中取得新进展：首次在实验上观测到第二类Weyl半金属(MoTe₂)上的拓扑费米弧,在真实材料中证实了破坏洛伦兹不变性的第二类Weyl 费米子的存在。相关文章于2016 年9 月6 日在NaturePhysics 上发表。这是继去年第一类Weyl费米子得到证实之后凝聚态物理研究上的又一重大突破。什么是第二类Weyl费米子？它与第一类Weyl费米子有何区别？作者通过本文来做一个简单的介绍。     

Tunable anisotropic anomalous Nernst effect and orbital magnetization in Floquet Weyl semimetals

Weyl semimetals and nodal line semimetals display a host of novel properties. Floquet Weyl semimetals with tunable Weyl points can be obtained from nodal line semimetals under the circularly polarized off-resonant light. Here we theoretically investigate the anomalous Nernst effect and orbital magnetization in Floquet Weyl semimetals. Due to the anisotropy of the band structure in Floquet Weyl semimetals, highly anisotropic Berry phase mediated anomalous Nernst effect and orbital magnetization in the absence of magnetic field are observed, indicating orientation-dependent applications in the design of nanodevices. The amplitude and sign of anomalous Nernst coefficient and orbital magnetization can be tuned by the light direction, amplitude and polarization. The effect of the chemical potential on anomalous Nernst coefficient and orbital magnetization is also discussed. The light-modulated anomalous Nernst effect and orbital magnetization make Floquet Weyl semimetals potential candidates for thermoelectric devices.     

Chiral magnetic effect without chirality source in asymmetric Weyl semimetals

We describe a new type of the chiral magnetic effect (CME) that should occur in Weyl semimetals (WSMs) with an asymmetry in the dispersion relations of the left- and right-handed (LH and RH) chiral Weyl fermions. In such materials, time-dependent pumping of electrons from a non-chiral external source can generate a non-vanishing chiral chemical potential. This is due to the different capacities of the LH and RH chiral Weyl cones arising from the difference in the density of states in the LH and RH cones. The chiral chemical potential then generates, via the chiral anomaly, a current along the direction of an applied magnetic field even in the absence of an external electric field. The source of chirality imbalance in this new setup is thus due to the band structure of the system and the presence of (non-chiral) electron source, and not due to the parallel electric and magnetic fields. We illustrate the effect by an argument based on the effective field theory, and by the chiral kinetic theory calculation for a rotationally invariant WSM with different Fermi velocities in the left and right chiral Weyl cones; we also consider the case of a WSM with Weyl nodes at different energies. We argue that this effect is generically present in WSMs with different dispersion relations for LH and RH chiral Weyl cones, such as SrSi₂ recently predicted as a WSM with broken inversion and mirror symmetries, as long as the chiral relaxation time is much longer than the transport scattering time.     

Collective modes of type-ⅡWeyl fermions with repulsive S-wave interaction

Three-dimensional type-ⅡWeyl fermions possess overtilted cone-like low-energy band dispersion.Unlike the closed ellipsoidal Fermi surface for type-ⅠWeyl fermions,the Fermi surface is an open hyperboloid for type-ⅡWeyl fermions.We evaluate the spin and density susceptibility of type-ⅡWeyl fermions with repulsive S-wave interaction by means of Green’s functions.We obtain the particle–hole continuum along the tilted momentum direction and perpendicular to the tilted momentum direction respectively.We find the zero sound mode in some repulsive interaction strengths by numerically solving the pole equations of the susceptibility within the random-phase approximation.     

Investigation of point-contact Andreev reflection on magnetic Weyl semimetal Co_3Sn_2S_2

Magnetic Weyl semimetals(WSMs) with broken time-reversal symmetry(TRS) hosting topological band structures are expected to provide an ideal platform for investigating topological superconductivity and spintronics. However, the experimental verification of magnetic WSMs is very challenging. Very recently, the kagome magnet Co_3Sn_2S_2 was confirmed to be a magnetic WSM by both angle-resolved photoemission spectroscopy and scanning tunneling spectroscopy and consequently has become the focus of great attention. This paper reports a point-contact Andreev-reflection spectroscopy(PCARS) investigation on the(001) surface and the side surface of the Co_3Sn_2S_2 single crystals, respectively. The measurements from the sample's(001) and side surfaces provide experimental evidence for transport spin polarization in the Co_3Sn_2S_2 magnetic WSM. Furthermore, the superconducting proximity effect in the Co_3Sn_2S_2 single crystal is successfully detected. The point-contact spectra(PCS) along the in-plane direction cannot be well fitted by theoretical models based on s-wave pairing, indicating that possible triplet p-wave superconductivity may be triggered at the interface, which paves the way for the future exploration of the topological superconductivity and Majorana states in broken TRS WSMs.     

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.     

拓扑Weyl半金属简介

材料体系的拓扑量子行为是当前凝聚态物理研究的热点。作为一种新型拓扑量子态,Weyl半金属最近引起了人们的关注。文章以烧绿石结构铱氧化物A₂Ir₂O₇(其中A=Y或稀土元素)为例,介绍了Weyl半金属的奇特性质：Weyl点受拓扑保护稳定;Weyl半金属有着受拓扑保护的表面态,即非闭合的费米弧;Weyl半金属的反常霍尔效应与Weyl点的位置有关,和能带的细节无关;Weyl半金属特有的输运性质。文章还介绍了人们预言的几种Weyl半金属以及相关的实验进展。     

Lifshitz transitions via the type-II dirac and type-II Weyl points

The type-II Weyl and type-II Dirac points emerge in semimetals and in relativistic systems. In particular, the type-II Weyl fermions may emerge behind the event horizon of black holes. The type-II Weyl and Dirac points also emerge as the intermediate states of the topological Lifshitz transitions. In one case, the type-II Weyl point connects the Fermi pockets, and the Lifshitz transition corresponds to the transfer of the Berry flux between the Fermi pockets. In the other case, the type-II Weyl point connects the outer and inner Fermi surfaces. At the Lifshitz transition, the Weyl point is released from both Fermi surfaces. They loose their Berry flux, which guarantees the global stability, and without the topological support, the inner surface disappears after shrinking to a point at the second Lifshitz transition. These examples reveal the complexity and universality of topological Lifshitz transitions, which originate from the ubiquitous interplay of a variety of topological characters of the momentum-space manifolds.     

Symmetrical broken and nonlinear response of Weyl semimetal TaAs influenced by the topological surface states and Weyl nodes

A Weyl semimetal (WSM) features Weyl fermions in its bulk and topological surface states on surfaces, and is novel material hosting Weyl fermions, a kind of fundamental particles. The WSM was regarded as a three‐dimensional version of “graphene” under the illusion. In order to explore its promising photoelectric properties and applications in photonics and photoelectronics, here, we study the anisotropic linear and nonlinear optical responses of a WSM TaAs, which are determined by the relationship and balance between its topological surface states and Weyl nodes. We demonstrate that topological surface states which break the bulk symmetry are responsible for the anisotropy of the mobility, and the anisotropic nonlinear response shows saturable characteristic with extremely large saturable intensity. We also find that the mobility is anisotropic with the magnitude of 10⁴ cm²V⁻¹s⁻¹ at room temperature and can be accelerated by the optical field. By analyzing the symmetry, the nonlinear response is mainly contributed by the fermions close to the Weyl nodes, and is related to the Pauli's blocking of fermions, electron‐electron interaction. This work experimentally discovers the anisotropic ultrahigh mobility of WSMs in the optical field and may start the field for the applications of WSMs in photonics and photoelectronics.

     

Hybrid Weyl semimetal under crossed electric and magnetic fields: Field tuning of spectrum type

There are two types (WSM-I and WSM-II) of the WSMs. The WSMs of different types have various topological and transport properties. Besides pure WSM-I and WSM-II, there exists a novel type, dubbed “hybrid Weyl semimetal”, which contains the Weyl points of both types. In this Letter we consider the hybrid WSM under crossed magnetic and electric fields. The electromagnetic field induces transition between different types of spectrum in Weyl point (WP). Thus, hybrid phase of the WSM can be tunable using the electromagnetic field. Finally, we proposed a new field-induced type of hybrid WSM in which two different regimes of spectrum coexist. In this case, the spectrum near the first WP corresponds to electric regime (no Landau levels) and the spectrum in the second WP with opposite chirality corresponds to magnetic regime (there are Landau levels).     

Electron transport in Dirac and Weyl semimetals

Recently, the Dirac and Weyl semimetals have attracted extensive attention in condensed matter physics due to both the fundamental interest and the potential application of a new generation of electronic devices. Here we review the exotic electrical transport phenomena in Dirac andWeyl semimetals. Section 1 is a brief introduction to the topological semimetals(TSMs). In Section 2 and Section 3, the intriguing transport phenomena in Dirac semimetals(DSMs) andWeyl semimetals(WSMs) are reviewed, respectively. The most widely studied Cd_3A_(s2) and the TaAs family are selected as representatives to show the typical properties of DSMs and WSMs, respectively. Beyond these systems, the advances in other TSM materials,such as ZrTe_5 and the MoTe_2 family, are also introduced. In Section 4, we provide perspectives on the study of TSMs especially on the magnetotransport investigations.     

外尔半金属及其输运特性

外尔半金属是继石墨烯以及拓扑绝缘体之后的又一个研究热点。相比于后两者,外尔半金 属独特的三维无能隙线性色散能带结构使得它有很多奇特的性质,如：手性反常、手性磁效应、 反弱局域化、手性朗道能级和负磁阻效应等。实际样品中无序总是不可避免的,所以考虑无序对 体系的影响是很有必要的。我们回顾了无序下第一类以及第二类外尔半金属的相变特性,并获得 了完整的相图,这些无序诱导的相变丰富了拓扑安德森绝缘体和安德森金属绝缘体相变的物理内 涵。我们同样回顾了长程短程无序影响下的第一类外尔半金属体系的输运,发现了一种不能采用 玻尔兹曼输运方程来描述的输运过程。我们介绍Imbert-Fedorov 位移这一光学中的效应在外尔 半金属中的实现,这为更好地应用外尔半金属提供了更多的可能性,随后采用波包散射,我们解 释了外尔半金属中的超高载流子迁移率问题的原因,最后我们给出一个简要的总结。     

Holographic topological semimetals

The holographic duality allows to construct and study models of strongly coupled quantum matter via dual gravitational theories.In general such models are characterized by the absence of quasiparticles, hydrodynamic behavior and Planckian dissipation times. One particular interesting class of quantum materials are ungapped topological semimetals which have many interesting properties from Hall transport to topologically protected edge states. We review the application of the holographic duality to this type of quantum matter including the construction of holographic Weyl semimetals, nodal line semimetals, quantum phase transition to trivial states(ungapped and gapped), the holographic dual of Fermi arcs and how new unexpected transport properties,such as Hall viscosities arise. The holographic models promise to lead to new insights into the properties of this type of quantum matter.     

Quantum transport in topological semimetals under magnetic fields

Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topological semimetals, according to the strength of the magnetic field. At weak magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak anti-localization effect and negative magnetoresistivity related to the nontrivial Berry curvature. We propose a fitting formula for the magnetoconductivity of the weak anti-localization. We expect that the weak localization may be induced by inter-valley effects and interaction effect, and occur in double-Weyl semimetals. For the negative magnetoresistance induced by the nontrivial Berry curvature in topological semimetals, we show the dependence of the negative magnetoresistance on the carrier density. At strong magnetic fields, specifically, in the quantum limit, the magnetoconductivity depends on the type and range of the scattering potential of disorder. The high-field positive magnetoconductivity may not be a compelling signature of the chiral anomaly. For long-range Gaussian scattering potential and half filling, the magnetoconductivity can be linear in the quantum limit. A minimal conductivity is found at the Weyl nodes although the density of states vanishes there.     

Topological Nodal Line Semimetal in Non-Centrosymmetric PbTaS_2

Topological semimetals are a new type of matter with one-dimensional Fermi lines or zero-dimensional Weyl or Dirac points in momentum space. Here using first-principles calculations, we find that the non-centrosymmetric PbTaS2 is a topological nodal line semimetal. In the absence of spin-orbit coupling(SOC), one band inversion happens around a high symmetrical H point, which leads to forming a nodal line. The nodal line is robust and protected against gap opening by mirror reflection symmetry even with the inclusion of strong SOC. In addition, it also hosts exotic drumhead surface states either inside or outside the projected nodal ring depending on surface termination. The robust bulk nodal lines and drumhead-like surface states with SOC in PbTaS_2 make it a potential candidate material for exploring the freakish properties of the topological nodal line fermions in condensed matter systems.