We analyze the thermoelectric response of Dirac and Weyl semimetals using the semiclassical approach, focusing on the extrinsic contributions due to skew-scattering and side jump. Our results apply to linear response Nernst effect in ferromagnetic Dirac materials such as Fe$_3$Sn$_2$, Weyl semimetal Co$_3$Sn$_2$S$_2$ and to second order response of monolayer graphene on hBN with trigonal warping. Our analysis indicates that the extrinsic contributions can be a significant component of anomalous Nernst response and used to explain an enhanced thermoelectric response.
Weyl semimetals host linear energy dispersions around Weyl nodes, as well as monopoles of Berry curvature in momentum space around these points. These features give rise to unique transport signatures in a Weyl semimetal, such as transverse transport without an applied magnetic field, known as anomalous transport. The type-II Weyl semimetal, recently experimentally demonstrated in several materials, is classified by a tilting of the Weyl nodes. This paper provides a theoretical study on thermoelectric transport in time-reversal breaking type-II Weyl semimetals. Our results examine the balance …
The spin Nernst effect describes a transverse spin current induced by the longitudinal thermal gradient in a system with the spin-orbit coupling. Here we study the spin Nernst effect in a mesoscopic four-terminal cross-bar Weyl semimetal device under a perpendicular magnetic field. By using the tight-binding Hamiltonian combining with the nonequilibrium Green's function method, the three elements of the spin current in the transverse leads and then spin Nernst coefficients are obtained. The results show that the spin Nernst effect in the Weyl semimetal has the essential difference with the tra…
The discovery of Weyl fermions in transition metal monoarsenides/phosphides without inversion symmetry represents an exceptional breakthrough in modern condensed matter physics. However, exploring the inherent nature of these quasiparticles is experimentally elusive because most of the experimental probes rely on analysing Fermi arc topology or controversial signatures such as the appearance of the chiral anomaly and the giant magnetoresistance. Here we show that the prototypical type-I Weyl semimetals TaP and TaAs possess a giant anomalous Nernst signal with a characteristic saturation platea…
Weyl semimetals expand research on topologically protected transport by adding bulk Berry monopoles with linearly dispersing electronic states and topologically robust, gapless surface Fermi arcs terminating on bulk node projections. Here, we show how the Nernst effect, combining entropy with charge transport, gives a unique signature for the presence of Dirac bands. The Nernst thermopower of NbP (maximum of 800 microV K-1 at 9 T, 109 K) exceeds its conventional thermopower by a hundredfold and is significantly larger than the thermopower of traditional thermoelectric materials. The Nernst eff…
We report a robust anomalous Nernst effect in Co2MnGa thin films in the thickness regime between 20 and 50 nm. The anomalous Nernst coefficient varied in the range of -2.0 to -3.0 uV/K at 300 K. We demonstrate that the anomalous Hall and Nernst coefficients exhibit similar behavior and fulfill the Mott relation. We simultaneously measure all four transport coefficients of the longitudinal resistivity, transversal resistivity, Seebeck coefficient, and anomalous Nernst coefficient. We connect the values of the measured and calculated Nernst conductivity by using the remaining three magneto-therm…
In this paper, we present a simple model of a three-dimensional insulating magnetic structure which represents a magnonic analog of the layered electronic system described in [Phys. Rev. Lett. {\bf 107}, 127205 (2011)]. In particular, our model realizes Weyl magnons as well as surface states with a Dirac spectrum. In this model, the Dzyaloshinskii-Moriya interaction is responsible for the separation of opposite Weyl points in momentum space. We calculate the intrinsic (due to the Berry curvature) transport properties of Weyl and so-called anomalous Hall effect (AHE) magnons. The results are co…
The magneto-thermoelectric properties of Heusler compound thin films are very diverse. Here, we discuss the anomalous Nernst response of Co$_2$MnGa thin films. We systematically study the anomalous Nernst coefficient as a function of temperature, and we show that unlike the anomalous Hall effect, the anomalous Nernst effect in Co$_2$MnGa strongly varies with temperature. We exploit the on-chip thermometry technique to quantify the thermal gradient, which enables us to directly evaluate the anomalous Nernst coefficient. We compare these results to a reference CoFeB thin film. We show that the 5…
Topological Weyl semimetals (WSM), a new state of quantum matter with gapless nodal bulk spectrum and open Fermi arc surface states, have recently sparked enormous interest in condensed matter physics. Based on the symmetry and fermiology, it has been proposed that WSMs can be broadly classified into two types, type-I and type-II Weyl semimetals. While the undoped, conventional, type-I WSMs have point like Fermi surface and vanishing density of states (DOS) at the Fermi energy, the type-II Weyl semimetals break Lorentz symmetry explicitly and have tilted conical spectra with electron and hole …
We study the anomalous Nernst and thermal Hall effects in a linearized low-energy model of a tilted Weyl semimetal, with two Weyl nodes separated in momentum space. For inversion symmetric tilt, we give analytic expressions in two opposite limits: for a small tilt, corresponding to a type-I Weyl semimetal, the Nernst conductivity is finite and independent of the Fermi level, while for a large tilt, corresponding to a type-II Weyl semimetal, it acquires a contribution depending logarithmically on the Fermi energy. This result is in a sharp contrast to the nontilted case, where the Nernst respon…
Chiral anomaly or Adler-Bell-Jackiw anomaly in Weyl semimetals (WSMs) has a significant impact on the electron transport behaviors, leading to remarkable longitudinal or planar electrical and thermoelectric transport phenomena in the presence of electromagnetic gauge fields. These phenomena are consequences of the imbalanced chiral charge and energy induced by chiral anomaly in the presence of parallel electric ($\mathbf{E}$) and magnetic ($\mathbf{B}$) fields ($\mathbf{E \cdot B }\neq 0$) or $(\mathbf{B \cdot \nabla }T\neq 0)$ ($\mathbf{\nabla}T$ is the thermal gradient). We here propose anot…
In this paper, we discuss the effect of a periodically driving circularly polarized laser beam in the high frequency limit, on the band structure and thermal transport properties of type-I and type-II Weyl semimetals (WSMs). We develop the notion of an effective Fermi surface stemming from the time-averaged Floquet Hamiltonian and discuss its effects on the steady-state occupation numbers of electrons and holes in the linearized model. In order to compute the transport coefficients averaged over a period of the incident laser source, we employ the Kubo formalism for Floquet states and show tha…
Dirac and Weyl semimetals display a host of novel properties. In Cd$_3$As$_2$, the Dirac nodes lead to a protection mechanism that strongly suppresses backscattering in zero magnetic field, resulting in ultrahigh mobility ($\sim$ 10$^7$ cm$^2$ V$^{-1}$ s$^{-1}$). In applied magnetic field, an anomalous Nernst effect is predicted to arise from the Berry curvature associated with the Weyl nodes. We report observation of a large anomalous Nernst effect in Cd$_3$As$_2$. Both the anomalous Nernst signal and transport relaxation time $τ_{tr}$ begin to increase rapidly at $\sim$ 50 K. This suggests a…
WTe$_2$ is one of a series of recently discovered high mobility semimetals, some of whose properties are characteristic of topological Dirac or Weyl metals. One of its most interesting properties is the unsaturated giant magnetoresistance that it exhibits at low temperatures. An important question is the degree to which this property can be ascribed to a conventional semi-metallic model in which a highly compensated, high mobility metal exhibits large magnetoresistance. Here we show that the longitudinal thermopower (Seebeck effect) of semi-metallic WTe$_2$ exfoliated flakes exhibits periodic …
We theoretically investigate a pure spin Hall current driven by a longitudinal temperature gradient, i.e., the spin Nernst effect (SNE), in a paramagnetic state of a collinear antiferromagnetic insulator with the Dzyaloshinskii-Moriya interaction. The SNE in a magnetic ordered state in such an insulator was proposed by Cheng {\it et al.} [R. Cheng, S. Okamoto, and D. Xiao, Phys. Rev. Lett. 117, 217202 (2016)]. Here we show that the Dzyaloshinskii-Moriya interaction can generate a pure spin Hall current even without magnetic ordering. By using a Schwinger boson mean-field theory, we calculate t…
Unlike the conventional (linear) anomalous Nernst effect, the non-linear anomalous Nernst effect (NLANE) can survive in an inversion symmetry broken system even in the presence of time-reversal symmetry. Using semiclassical Boltzmann transport theory, we derive the general expression of the non-linear anomalous Nernst coefficient as the second-order response function to the applied temperature gradient. We find that the non-linear Nernst current, which flows perpendicular to the temperature gradient even in the absence of a magnetic field, arises due to the Berry curvature of the states near t…
Berry curvature acts analogous to a magnetic field in the momentum-space, and it modifies the flow of charge carriers and entropy. This induces several intriguing magnetoelectric and magnetothermal transport phenomena in Weyl semimetals. %, including the planar Hall and planar Nernst effect. Here, we explore the impact of the Berry curvature and orbital magnetization on the thermopower in tilted type-I and type-II Weyl semimetals, using semiclassical Boltzmann transport formalism. We analytically calculate the full magnetoconductivity matrix and use it to obtain the thermopower matrix for diff…
Weyl semimetals are paradigmatic topological gapless phases in three dimensions. We here address the effect of disorder on charge transport in Weyl semimetals. For a single Weyl node with energy at the degeneracy point and without interactions, theory predicts the existence of a critical disorder strength beyond which the density of states takes on a nonzero value. Predictions for the conductivity are divergent, however. In this work, we present a numerical study of transport properties for a disordered Weyl cone at zero energy. For weak disorder our results are consistent with a renormalizati…
We investigate the electric and thermal transport properties in a disordered Weyl ferromagnet on an equal footing by using the Keldysh formalism in curved spacetime. In particular, we calculate the anomalous thermal Hall conductivity, which consists of the Kubo formula and the heat magnetization, without relying on the Wiedemann-Franz law. We take nonmagnetic impurities into account within the self-consistent $T$-matrix approximation and reproduce the Wiedemann-Franz law for the extrinsic Fermi-surface and intrinsic Fermi-sea terms, respectively. This is the first step towards a unified theory…
Finding fingerprints of disordered Weyl semimetals (WSMs) is an unsolved task. Here we report such findings in the level statistics and the fractal nature of electron wavefunction around Weyl nodes of disordered WSMs. The nearest-neighbor level spacing follows a new universal distribution $P_c(s)=C_1 s^2\exp[-C_2 s^{2-γ_0}]$ originally proposed for the level statistics of critical states in the integer quantum Hall systems or normal dirty metals (diffusive metals) at metal-to-insulator transitions, instead of the Wigner-Dyson distribution for diffusive metals. Numerically, we find $γ_0=0.62\pm…
We study magnetotransport in a disordered Weyl semimetal taking into account localization effects exactly. In the vicinity of a Weyl node, a single chiral Landau level coexists with a number of conventional non-chiral levels. Disorder scattering mixes these topologically different modes leading to peculiar localization effects. We derive the average conductance as well as the full distribution function of transmission probabilities along the field direction. Remarkably, we find that localization of the non-chiral modes is greatly enhanced in a strong magnetic field with the typical localizatio…
A large Berry curvature in the vicinity of the Fermi energy is required in order to obtain a large anomalous Hall and Nernst effect. This Berry curvature can be induced by Weyl points and gapped nodal lines. One of the possible mechanisms takes place in systems with a symmetry group where mirror planes lead to protected nodal line structures. When these mirror symmetries are broken, e. g. via fixing a magnetization direction, a gap in the former nodal line can create Weyl points and a large Berry curvature along the gapped lines. In this work we study this effect in a minimal effective model a…
Although Lorentz invariance forbids the presence of a term that tilts the energy-momentum relation in the Weyl Hamiltonian, a tilted dispersion is not forbidden and, in fact, generic for condensed matter realizations of Weyl semimetals. We here investigate the combined effect of such a tilted Weyl dispersion and the presence of potential disorder. In particular, we address the influence of a tilt on the disorder-induced phase transition between a quasi-ballistic phase at weak disorder, in which the disorder is an irrelevant perturbation, and a diffusive phase at strong disorder. Our main resul…
In magnetic Weyl semimetals, where magnetism breaks time-reversal symmetry, large magnetically sensitive anomalous transport responses are anticipated that could be useful for topological spintronics. The identification of new magnetic Weyl semimetals is therefore in high demand, particularly since in these systems Weyl node configurations may be easily modified using magnetic fields. Here we explore experimentally the magnetic semimetal PrAlGe, and unveil a direct correspondence between easy-axis Pr ferromagnetism and anomalous Hall and Nernst effects. With sizes of both the anomalous Hall co…
We study the intrinsic and extrinsic Hall effects in disordered magnetic Weyl semimetals numerically. We show that in Weyl metals, where the Fermi energy deviates from the Weyl point, the Hall and longitudinal conductances exhibit a specific relation, which is distinguished from the well-known relation in integer quantum Hall systems. Around the Weyl point, the Hall conductance increases with increasing longitudinal conductance. This increasing behavior indicates the existence of additional contributions to the Hall conductance from the subbands of Weyl cones besides that from the bulk Berry c…
As they do not rely on the presence of any crystal symmetry, Weyl nodes are robust topological features of an electronic structure that can occur at any momentum and energy. Acting as sinks and sources of Berry curvature, Weyl nodes have been predicted to strongly affect the transverse electronic response, like in the anomalous Hall or Nernst effects. However, to observe large anomalous effects the Weyl nodes need to be close to or at the Fermi-level, which implies the band structure must be tuned by an external parameter, e.g. chemical doping or pressure. Here we show that in a ferromagnetic …
A theory of the fluctuation-induced Nernst effect is developed for arbitrary magnetic fields and temperatures beyond the upper critical field line in a two-dimensional superconductor. First, we derive a simple phenomenological formula for the Nernst coefficient, which naturally explains the giant Nernst signal due to fluctuating Cooper pairs. The latter is shown to be large even far from the transition and may exceed by orders of magnitude the Fermi liquid terms. We also present a complete microscopic calculation (which includes quantum fluctuations) of the Nernst coefficient and give its asym…
Double Weyl nodes are topologically protected band crossing points which carry chiral charge $\pm2$. They are stabilized by $C_4$ point group symmetry and are predicted to occur in $\mathrm{SrSi_2}$ or $\mathrm{HgCr_{2}Se_{4}}$. We study their fate in the presence of quenched disorder by numerical transport calculations and scaling arguments. We find that a double Weyl node is unstable in a disordered environment and splits into a pair of emergent simple Weyl nodes which carry equal chiral charge of $\pm1$. This pair of simple Weyl nodes is robust to disorder up to a certain critical disorder …
In metallic ferromagnets, the Berry curvature of underlying quasiparticles can cause an electric voltage perpendicular to both magnetization and an applied temperature gradient, a phenomenon called the anomalous Nernst effect (ANE). Here, we report the observation of a giant ANE in the full-Heusler ferromagnet Co$_2$MnGa, reaching $S_{yx}\sim -6$ $μ$V/K at room $T$, one order of magnitude larger than the maximum value reported for a magnetic conductor. With increasing temperature, the transverse thermoelectric conductivity or Peltier coefficient $α_{yx}$ shows a crossover between $T$-linear an…
We develop a topological theory for disordered Weyl semimetals in the framework of gauge invariance of replica formalism and boundary-bulk correspondence of Chern insulators. An anisotropic topological $θ$-term is analytically derived for the effective non-linear sigma model. It is this nontrivial topological term that ensures the bulk transverse transport of Weyl semimetals to be robust against disorders. Moreover, we establish a general diagram that reveals the intrinsic relations among topological terms in the non-linear sigma models and gauge response theories respectively for $(2n + 2)$-d…
In disordered Weyl semimetals, mechanisms of topological origin lead to the protection against Anderson localization, and at the same time to different types of transverse electromagnetic response -- the anomalous Hall, and chiral magnetic effect. We here apply field theory methods to discuss the manifestation of these phenomena at length scales which are beyond the scope of diagrammatic perturbation theory. Specifically we show how an interplay of symmetry breaking and the chiral anomaly leads to a field theory containing two types of topological terms. Generating the unconventional response …
We study the dynamics of Dirac and Weyl electrons in disordered point-node semimetals. The ballistic feature of the transport is demonstrated by simulating the wave-packet dynamics on lattice models. We show that the ballistic transport survives under a considerable strength of disorder up to the semimetal-metal transition point, which indicates the robustness of point-node semimetals against disorder. We also visualize the robustness of the nodal points and linear dispersion under broken translational symmetry. The speed of the wave packets slows down with increasing disorder strength, and va…
Weyl semimetals have been intensely studied as a three dimensional realization of a Dirac-like excitation spectrum where the conduction bands and valence bands touch at isolated Weyl points in momentum space. Like in graphene, this property entails various peculiar electronic properties. However, recent theoretical studies have suggested that resonant scattering from rare regions can give rise to a non-zero density of states even at charge neutrality. Here, we give a detailed account of this effect and demonstrate how the semimetallic nature is suppressed at the lowest scales. To this end, we …
Tilting the Weyl cone breaks the Lorentz invariance and enriches the Weyl physics. Here, we report the observation of a magnetic-field-antisymmetric Seebeck effect in a tilted Weyl semimetal, Co$_3$Sn$_2$S$_2$. Moreover, it is found that the Seebeck effect and the Nernst effect are antisymmetric in both the in-plane magnetic field and the magnetization. We attribute these exotic effects to the one-dimensional chiral anomaly and phase space correction due to the Berry curvature. The observation is further reproduced by a theoretical calculation, taking into account the orbital magnetization.
Double Weyl nodes are topologically protected band crossing points which carry chiral charge $\pm2$. They are stabilized by $C_{4}$ point group symmetry and are predicted to occur in $\mathrm{SrSi_{2}}$ or $\mathrm{HgCr_{2}Se_{4}}$. We study their stability and physical properties in the presence of a disorder potential. We investigate the density of states and the quantum transport properties at the nodal point. We find that, in contrast to their counterparts with unit chiral charge, double Weyl nodes are unstable to any finite amount of disorder and give rise to a diffusive phase, in agreeme…
In disordered Weyl semimetals, mechanisms of topological origin lead to novel mechanisms of transport, which manifest themselves in unconventional types of electromagnetic response. Prominent examples of transport phenomena particular to the Weyl context include the anomalous Hall effect, the chiral magnetic effect, and the formation of totally field dominated regimes of transport in which the longitudinal conductance is proportional to an external magnetic field. In this paper, we discuss the manifestations of these phenomena at large length scales including the cases of strong disorder and/o…
Amorphous Fe-Sn nanofilms for anomalous-Nernst heat-flux sensing
Toyota Technological Institute（名古屋工业大学）；Graduate School of Engineering, Nagoya Institute of Technology（名古屋工业大学大学院工学研究科）；Quantum-Phase Electronics Center (QPEC) and Department of Applied Physics, The University of Tokyo（东京大学量子相电子中心及应用物理系）；Institute for Materials Research, Tohoku University（东北大学材料科学研究所）；Department of Chemistry, Rikkyo University（立教大学化学系）
Quantum phase transitions of three-dimensional (3D) Weyl semimetals (WSMs) subject to uncorrelated on-site disorder are investigated through quantum conductance calculations and finite-size scaling of localization length. Contrary to previous claims that a direct transition from a WSM to a diffusive metal (DM) occurs, an intermediate phase of Chern insulator (CI) between the two distinct metallic phases should exist due to internode scattering that is comparable to intranode scattering. The critical exponent of localization length is $ν\simeq 1.3$ for both the WSM-CI and CI-DM transitions, in …
Three-dimensional Dirac and Weyl semimetals exhibit a disorder-induced quantum phase transition between a semimetallic phase at weak disorder and a diffusive-metallic phase at strong disorder. Despite considerable effort, both numerically and analytically, the critical exponents $ν$ and $z$ of this phase transition are not known precisely. Here we report a numerical calculation of the critical exponent $ν=1.47\pm0.03$ using a minimal single-Weyl node model and a finite-size scaling analysis of conductance. Our high-precision numerical value for $ν$ is incompatible with previous numerical studi…
Using the Feynman diagram techniques, we derive the finite-temperature conductivity and magnetoconductivity formulas from the quantum interference and electron-electron interaction, for a three-dimensional disordered Weyl semimetal. For a single valley of Weyl fermions, we find that the magnetoconductivity is negative and proportional to the square root of magnetic field at low temperatures, as a result of the weak antilocalization. By including the contributions from the weak antilocalization, Berry curvature correction, and Lorentz force, we compare the calculated magnetoconductivity with a …
Non-Hermiticity in Weyl Hamiltonian leads to the realization of Weyl exceptional rings and flat bands inside the Weyl exceptional rings. Recently, the platform of non-Hermitian physics is extended to many-body or disordered systems where quasiparticles possess finite lifetime. Here, we clarify that the deviation from unitarity limit in a disordered Weyl semimetal leads to the generation of Weyl exceptional rings regardless of the detail of the scattering potential. In the case of topological Dirac semimetals, hybrid rings and flat bands without vorticity of complex-energy eigenvalues are reali…
Weyl semimetals are gapless quasi-topological materials with a set of isolated nodal points forming their Fermi surface. They manifest their quasi-topological character in a series of topological electromagnetic responses including the anomalous Hall effect. Here we study the effect of disorder on Weyl semimetals while monitoring both their nodal/semi-metallic and topological properties through computations of the localization length and the Hall conductivity. We examine three different lattice tight-binding models which realize the Weyl semimetal in part of their phase diagram and look for un…
Isolated Weyl cones in a disordered environment do not show the phenomenon of Anderson localization due to the abscence of backscattering processes. However, besides the conventional three dimensional diffusive metal, an additional semimetallic phase can form. In this paper we study the effect of tilt on the physics of disorder in isolated Weyl cones. Our main finding is that while the semimetallic phase remains a stable phase, tilt decreases the size of the semimetallic region. Conversely, disorder increases the effective tilt of the quasiparticle excitations.
Weyl semimetal, a three-dimensional electronic system with relativistic linear energy dispersion around gapless points carrying nontrivial Berry charge, is predicted to exhibit a wealth of unique response and transport properties.A crucial question is whether those properties are robust against disorder and whether Anderson localization occurs.In this work, the effects of nonperturbative topological (vortex loop) excitations and Berry phase in disordered time-reversal invariant 3d Weyl semimetal are studied.It is shown that the chiral symmetry is restored in the nonlinear sigma model describin…
The presence of disorder in semiconductors can dramatically change their physical properties. Yet, models faithfully accounting for it are still scarce and computationally inefficient. We present a mathematical and computational model able to simulate the optoelectronic response of semiconductor alloys of several tens of nanometer sidelength, while at the same time accounting for the quantum localization effects induced by the compositional disorder at the nano-scale. The model is based on a Wigner-Weyl analysis of the structure of electron and hole eigenstates in phase space made possible by …
The thermoelectric transport coefficients are calculated in a generic lattice model of multi-Weyl semimetals with a broken time-reversal symmetry by using the Kubo's linear response theory. The contributions connected with the Berry curvature-induced electromagnetic orbital and heat magnetizations are systematically taken into account. It is shown that the thermoelectric transport is profoundly affected by the nontrivial topology of multi-Weyl semimetals. In particular, the calculation reveals a number of thermal coefficients of the topological origin which describe the anomalous Nernst and th…
Topological Weyl semimetals, besides manifesting chiral anomaly, can also accommodate a disorder-driven unconventional quantum phase transition into a metallic phase. A fundamentally and practically important question in this regard concerns an experimentally measurable quantity that can clearly distinguish these two phases. We show that the optical conductivity while serving this purpose can also play the role of a bonafide order parameter across such disorder-driven semimetal-metal quantum phase transition by virtue of displaying distinct scaling behavior in semimetallic and metallic phases,…
Having the chiral anomaly induced magneto-transport phenomena extensively studied in single Weyl semimetal (WSM) as characterized by topological charge $n=1$, we here address the transport properties in the context of multi-Weyl semimetals (m-WSMs) where $n>1$. Using semiclassical Boltzmann transport formalism with the relaxation time approximation, we investigate several intriguing transport properties such as longitudinal magneto-conductivity (LMC), planar Hall conductivity (PHC), thermo-electric coefficients (TECs) and planar Nernst coefficient (PNC) for m-WSMs in the co-planar setups with …
Several lattices, such as the dice or the Lieb lattice, possess Dirac cones and a flat band crossing the Dirac point, whose effective model is the pseudospin-1 Dirac-Weyl equation. We investigate the fate of the flat band in the presence of disorder by focusing on the density of states (DOS) and dc conductivity. While the central hub-site does not reveal the presence of the flat band, the sublattice resolved DOS on the non-central sites exhibits a narrow peak with height ~ 1/\sqrt{g} with g the dimensionless disorder variance. Although the group velocity is zero on the flat band, the dc conduc…
