Topological semimetals are a new class of metallic materials, which exist at band fillings that ordinarily correspond to insulators or compensated accidental semimetals with zero Luttinger volume. Their metallicity is a result of nontrivial topology in momentum space and crystal symmetry, wherein topological charges may be assigned to point band-touching nodes, preventing gap opening, unless protecting crystal symmetries are violated. These topological charges, however, are defined from noninteracting band eigenstates, which raises the possibility that the physics of topological semimetals may be modified qualitatively by electron-electron interactions. Here we ask the following question: what makes the topological semimetals nontrivial beyond band theory? Alternatively, can strong electron-electron interactions open a gap in topological semimetals without breaking the protecting symmetries or introducing topological order? We demonstrate that the answer is generally no, and what prevents it is their topological response, or quantum anomalies. While this is familiar in the case of magnetic Weyl semimetals, where the topological response takes the form of an anomalous Hall effect, analogous responses in other types of topological semimetals are more subtle and involve crystal symmetry as well as electromagnetic gauge fields. Physically these responses are detectable as fractional symmetry charges induced on certain gauge defects. We discuss the cases of type-I Dirac semimetals and time-reversal invariant Weyl semimetals in detail. For type-I Dirac semimetals, we also show that the anomaly vanishes, in a nontrivial manner, if the momenta of the Dirac nodes satisfy certain exceptional conditions.
This chapter describes topological (Dirac and Weyl) semimetals from the viewpoint of their observable electromagnetic response. We argue that this response may be represented by topological terms with unquantized (non-integer) coefficients and make a connection with the Luttinger's theorem, which relates the size of the Fermi surface of an ordinary metal to the number of electrons per unit cell. We discuss observable transport phenomena, associated with this topological response.
Dirac and Weyl semimetals with linearly crossing bands are the focus of much recent interest in condensed matter physics. Although they host fascinating phenomena, their physics can be understood in terms of weakly interacting electrons. In contrast, more than 40 years ago, Abrikosov pointed out that quadratic band touchings are generically strongly interacting. We have performed terahertz spectroscopy on films of the conducting pyrochlore Pr$_2$Ir$_2$O$_7$, which has been shown to host a quadratic band touching. A dielectric constant as large as $\tilde{\varepsilon }/ε_0 \sim 180 $ is observe…
We construct the effective field theory for time-reversal symmetry breaking multi-Weyl semimetals (mWSMs), composed of a single pair of Weyl nodes of (anti-)monopole charge $n$, with $n=1,2,3$ in crystalline environment. From both the continuum and lattice models, we show that a mWSM with $n>1$ can be constructed by placing $n$ flavors of linearly dispersing simple Weyl fermions (with $n=1$) in a bath of an $SU(2)$ non-Abelian static background gauge field. Such an $SU(2)$ field preserves certain crystalline symmetry (four-fold rotational or $C_4$ in our construction), but breaks the Lorentz s…
We study the effect of long-ranged interactions on Weyl semimetals. Such interactions can give rise to unpaired Weyl nodes, which we demonstrate by explicitly constructing a system with just a single node - a situation that is fundamentally forbidden by fermion doubling in non-interacting band structures. Adding a magnetic field, we investigate the fate of the chiral anomaly. Remarkably, as long as a system exhibits a single Weyl node in the absence of magnetic fields, arbitrarily weak fields qualitatively restore the lowest Landau level structure of a non-interacting Weyl semimetal. This unde…
Kondo lattice models have established themselves as an ideal platform for studying the interplay between topology and strong correlations such as in topological Kondo insulators or Weyl-Kondo semimetals. The nature of these systems requires the use of non-perturbative techniques which are few in number, especially in high dimensions. Motivated by this we study a model of Dirac fermions in $3+1$ dimensions coupled to an arbitrary array of spins via a generalization of functional non-Abelian bosonization. We show that there exists an exact transformation of the fermions which allows us to write …
Luttinger's theorem connects a basic microscopic property of a given metallic crystalline material, the number of electrons per unit cell, to the volume, enclosed by its Fermi surface, which defines its low-energy observable properties. Such statements are valuable since, in general, deducing a low-energy description from microscopics, which may perhaps be regarded as the main problem of condensed matter theory, is far from easy. In this paper we present a unified framework, which allows one to discuss Luttinger theorems for ordinary metals, as well as closely analogous exact statements for to…
Topological semimetals have revealed a wide array of novel transport phenomena, including electron hydrodynamics, quantum field theoretic anomalies, and extreme magnetoresistances and mobilities. However, the scattering mechanisms central to these behaviors remain largely unexplored. Here we reveal signatures of significant phonon-electron scattering in the type-II Weyl semimetal WP$_{2}$ via temperature-dependent Raman spectroscopy. Over a large temperature range, we find that the decay rates of the lowest energy $A_{1}$ modes are dominated by phonon-electron rather than phonon-phonon scatter…
We present experimental evidence of an intriguing phase transition between distinct topological states in the type-II Weyl semimetal MoTe2. We observe anomalies in the Raman phonon frequencies and linewidths as well as electronic quasielastic peaks around 70 K, which, together with structural, thermodynamic measurements, and electron-phonon coupling calculations, demonstrate a temperature-induced transition between two topological phases previously identified by contrasting spectroscopic measurements. An analysis of experimental data suggests electron-phonon coupling as the main driving mechan…
Field-induced magnetic phase transitions and transport anomalies in GdAlSi
Zhejiang University（浙江大学）；Zhejiang University of Technology（浙江工业大学）；Anhui University（安徽大学）；Institute of Physical Science and Information Technology, Anhui University（安徽大学物理科学与信息技术研究院）；State Key Laboratory of Silicon and Advanced Semiconductor Materials, Zhejiang University（浙江大学硅材料与先进半导体技术国家重点实验室）；Hefei National Laboratory（合肥国家实验室）
Quantum materials with strong transport responses to disparate physical quantities are of great fundamental significance and may hold technological potentials. The interplay between interactions and topology drive such responses through the effects of spontaneous symmetry breaking and the associated domain configurations on quantum transport. Here we provide a comprehensive description of the magnetism of Mn3Ge, an antiferromagnetic kagomebased semimetal with room temperature transport anomalies associated with topologically protected Weyl nodes. Using polarized neutron diffraction, we show th…
Recently, anomalies in the temperature dependences of the carrier density and/or mobility derived from analysis of the magnetoresistivities using the conventional two-band model have been used to unveil intriguing temperature-induced Lifshitz transitions in various materials. For instance, two temperature-driven Lifshitz transitions were inferred to exist in the Dirac nodal-line semimetal ZrSiSe, based on two-band model analysis of the Hall magnetoconductivities where the second band exhibits a change in the carrier type from holes to electrons when the temperature decreases below T = 106 K an…
Peierls Transition and Magnetism in a Dirac Semimetal: CaMnBi$_2$
Brookhaven National Laboratory（布鲁克海文国家实验室）；Ames National Laboratory（埃姆斯国家实验室）；Iowa State University（爱荷华州立大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；National Institute of Standards and Technology（美国国家标准与技术研究院）；Ruhr-University Bochum（波鸿鲁尔大学）
Anomalous (3+1)d Fermionic Topological Quantum Field Theories via Symmetry Extension
Beijing Institute of Mathematical Sciences and Applications（北京数学与交叉科学研究院）；London Institute for Mathematical Sciences, Royal Institution（伦敦数学研究所，皇家学会）；Center of Mathematical Sciences and Applications, Harvard University（哈佛大学数学与应用研究中心）
The body-centered-tetragonal antiferromagnet EuGa$_4$ was recently identified as a Weyl nodal-line semimetal that exhibits the topological Hall effect below its reported antiferromagnetic (AFM) ordering temperature $T_{\rm N}= 15$-16.5 K which we find to be $T_{\rm N} = 16.4(2)$ K. The Eu$^{+2}$ ions are located at the corners and body center of the unit cell. EuGa$_4$ exhibits A-type AFM order below $T_{\rm N}$, where the Eu$^{2+}$ spin-7/2 moments are ferromagnetically aligned in the $ab$ plane with the Eu moments in adjacent Eu planes along the $c$ axis aligned antiferromagnetically. Low-fi…
Optical conductivity of the metallic pyrochlore iridate Pr$_2$Ir$_2$O$_7$: Influence of spin-orbit coupling and electronic correlations on the electronic structure
We report on a systematic study of the thermodynamic, electronic and charge transport properties of high-quality single crystals of BaNiS$_2$, the metallic end-member of the quasi-twodimensional BaCo$_{1-x}$Ni$_x$S$_2$ system characterized by a metal-insulator transition at $x_{cr}=0.22$. Our analysis of magnetoresistivity and specific heat data consistently suggests a picture of compensated semimetal with two hole- and one electron-bands, where electron-phonon scattering dominates charge transport and the minority holes exhibit, below $\sim$100 K, a very large mobility, $μ_h\sim$ 15000 cm$^2$…
