Weyl nodes come in pairs of opposite chirality. For broken time reversal symmetry (TR) they are displaced in momentum space by $\bf{Q}$ and the anomalous DC Hall conductivity $σ_{xy}$ is proportional to $\bf{Q}$ at charge neutrality. For finite doping there are additive corrections to $σ_{xy}$ which depend on the chemical potential as well as on the tilt ($C$) of the Dirac cones and on their relative orientation. If inversion symmetry (I) is also broken the Weyl nodes are shifted in energy by an amount $Q_{0}$. This introduces further changes in $σ_{xy}$ and we provide simple analytic formulas for these modifications for both type I ($C<1$) and type II ($C>1$, overtilted) Weyl. For type I when the Weyl nodes have equal magnitude but oppositely directed tilts, the correction to $σ_{xy}$ is proportional to the chemical potential $μ$ and completely independent of the energy shift $Q_{0}$. When instead the tilts are parallel, the correction is linear in $Q_{0}$ and $μ$ drops out. For type II the corrections involve both $μ$ and $Q_{0}$, are nonlinear and also involve a momentum cut off. We discuss the implied changes to the Nernst coefficient and to the thermal Hall effect of a finite $Q_{0}$.
We theoretically propose that giant magnetochiral anisotropy is achieved in Weyl semimetals in noncentrosymmetric crystals as a consequence of the chiral anomaly. The magnetochiral anisotropy is the nonlinearity of the resistivity $ρ$ that depends on the current $\boldsymbol{I}$ and the magnetic field $\boldsymbol{B}$ as $ρ=ρ_0 (1 + γ\boldsymbol{I} \cdot \boldsymbol{B})$, and can be applied to rectifier devices controlled by $\boldsymbol{B}$. We derive the formula for the coefficient $γ$ in noncentrosymmetric Weyl semimetals. The obtained formula for $γ$ shows that the magnetochiral anisotropy…
We have performed high-resolution angle-resolved photoemission spectroscopy (ARPES) on noncentrosymmetric Weyl semimetal candidate NbP, and determined the electronic states of both Nb- and P-terminated surfaces corresponding to the "opposite" surfaces of a polar crystal. We revealed a drastic difference in the Fermi-surface topology between the opposite surfaces, whereas the Fermi arcs on both surfaces are likely terminated at the surface projection of the same bulk Weyl nodes. Comparison of the ARPES data with our first-principles band calculations suggests notable difference in electronic st…
Even if Weyl semimetals are characterized by quasiparticles with well-defined chirality, exploiting this experimentally is severely hampered by Weyl lattice-fermions coming in pairs with opposite chirality, typically causing the net chirality picked up by experimental probes to vanish. Here we show this issue can be circumvented in a controlled manner when both time-reversal- and inversion- symmetry are broken. To this end, we investigate chirality-disbalance in the carbide family RMC$_2$ (R a rare-earth and M a transition metal), showing several members to be Weyl semimetals. Using the noncen…
Magnetic Weyl semimetals are predicted to host emergent electromagnetic fields at heterogeneous strained phases or at the magnetic domain walls. Tunability and control of the topological and magnetic properties is crucial for revealing these phenomena, which are not well understood or fully realized yet. Here, we use a scanning SQUID microscope to image spontaneous magnetization and magnetic susceptibility of CeAlSi, a noncentrosymmetric ferromagnetic Weyl semimetal candidate. We observe large metastable domains alongside stable ferromagnetic domains. The metastable domains most likely embody …
We study the dynamic chiral magnetic conductivity (DCMC) and natural optical activity in an inversion-broken tilted Weyl semimetal (WSM). Starting from the Kubo formula, we derive the analytical expressions for the DCMC for two different directions of the incident electromagnetic wave. We show that the angle of rotation of the plane of polarization of the transmitted wave exhibits remarkable anisotropic behavior and is larger along the tilt direction. This striking anisotropy of DCMC which results in anisotropic optical activity and rotary power, can be experimentally observed as a topological…
The noncentrosymmetric RAlPn (R = rare earth, Pn = Si, Ge) family, predicted to host nonmagnetic and magnetic Weyl states, provide an excellent platform for investigating the relation between magnetism and Weyl physics. By using high field magnetotransport measurements and first principles calculations, we have unveiled herein both type-I and type-II Weyl states in the nonmagnetic LaAlSi. By a careful comparison between experimental results and theoretical calculations, nontrivial Berry phases associated with the Shubnikov-de Haas oscillations are ascribed to the electron Fermi pockets related…
We present the topology of spin-split Fermi surface of CaAgAs as determined by de Haas-van Alphen (dHvA) effect measurements combined with ab initio calculations. We have determined the torus-shaped nodal-line Fermi surface from the dHvA oscillations of $β$ and $γ$ orbits. The former orbit encircles the nodal-line, while the latter does not. Nevertheless, a nontrivial Berry phase is found for both orbits. The nontrivial phase of $β$ arises from the orbital characters, which can be expressed as a pseudospin rotating around the nodal-line. On the other hand, the phase of $γ$ is attributed to the…
We calculate the A.C. optical response to circularly polarized light of a Weyl semimetal (WSM) with varying amounts of tilt of the Dirac cones. Both type-I and II (overtilted) WSM are considered in a continuum model with broken time reversal (TR) symmetry. The Weyl nodes appear in pairs of equal energies but of opposite momentum and chirality. For type-I the response of a particular node to right (RHP) and left (LHP) hand polarized light are distinct only in a limited range of photon energy $Ω$, $\frac{2}{1+C_{2}/v}<\fracΩμ<\frac{2}{1-C_{2}/v}$ with $μ$ the chemical potential and $C_{2}$ the t…
Topological magnetic Weyl semimetals have been proposed to host controllable chiral domain walls which bear a great prospect in device applications. To exploit them in applications, it is important to have a proper way to tune and manipulate these domain walls. One possible means is through magnetoelastic coupling. The involvement of rare earth in the lately proposed $R$Al$X$ ($R$=rare earth, $X$=Si and Ge) family magnetic Weyl semimetals may provide such a platform. Here we present transport and thermodynamic properties of CeAlGe under hydrostatic pressure. We find that pressure enhances the …
NbP is one member of a new class of nodal loop semimetals characterized by the cooperative effects of spin-orbit coupling (SOC) and a lack of inversion center. Here transport and spectroscopic properties of NbP are evaluated using density functional theory methods. SOC together with the lack of inversion symmetry splits degeneracies, giving rise to "Russian doll nested" Fermi surfaces containing 4*10$^{-4}$ electron (hole) carriers/f.u. Due to the modest SOC strength in Nb, the Fermi surfaces map out the Weyl nodal loops. Calculated structure around T$^*$~100 K in transport properties reproduc…
A large number of half-Heusler compounds have been recently proposed as three-dimensional (3D) topological insulators (TIs) with tunable physical properties.However, no transport measurements associated with the topological surface states have been observed in these half-Heusler candidates due to the dominating contribution from bulk electrical conductance. Here we show that, by reducing the mobility of bulk carriers, a two-dimensional (2D) weak antilocalization (WAL) effect, one of the hallmarks of topological surface states, was experimentally revealed from the tilted magnetic field dependen…
We consider a Weyl semimetal (WSM) with finite doping and tilt within a continuum model Hamiltonian with both broken time reversal and inversion symmetry. We calculate the absorptive part of the anomalous AC Hall conductivity as a function of photon energy ($Ω$) for both type I and type II Weyl semimetal. For a given Weyl node, changing the sign of its chirality or of its tilt changes the sign of its contribution to the absorptive Hall conductivity with no change in magnitude. For a noncentrosymmetric system we find that there are ranges of photon energies for which only the positive or only t…
We study both noncentrosymmetric and time-reversal breaking Weyl semimetal systems under a strong magnetic field with the Coulomb interaction. The three-dimensional bulk system is reduced to many mutually interacting quasi-one-dimensional wires. Each strongly correlated wire can be approached within the Tomonaga-Luttinger liquid formalism. Including impurity scatterings, we inspect the localization effect and the temperature dependence of the electrical resistivity. The effect of a large number of Weyl points in real materials is also discussed.
We calculate the optical conductivity of type-I and type-II multi-Weyl semimetals(m-WSMs) in time-reversal(TR) broken case at finite doping. It is found that both longitudinal and Hall conductivities are renormalized by J(monopole charge) perpendicular to Weyl nodes separation and longitudal conductivity along nodes has non-trivial dependence on J. The Kerr rotations in thin films and bulk have different dependence on system parameters. The Kerr rotation in ultra-thin films is independent of monopole charge J and depends only on Fermi velocity v F while in bulk it dependent on monopole charge …
Dynamics and textures of magnetic domain walls (DWs) may largely alter the electronic behaviors in a Weyl semimetal system via emergent gauge fields. However, very little is known about even the basic properties of these domain walls in Weyl materials. In this work, we imaged the spontaneous magnetization and magnetic susceptibility of a ferromagnetic (FM) Weyl semimetal CeAlSi using scanning SQUID microscopy. We observed the ferromagnetic DWs lined-up with the [100] direction (or other degenerate directions). We also discovered the coexistence of stable and metastable domain phases, which ari…
We attentively investigate the effects of short-range fermion-fermion interactions on the low-energy properties of both two-dimensional type-I and type-II tilted Dirac semimetals by means of the renormalization group framework. Practicing the standard renormalization group procedures via taking into account all one-loop corrections gives rise to the coupled energy-dependent evolutions of all interaction parameters, which are adopted to carefully examine whether and how the fermion-fermion interactions influence the low-energy physical behaviors of tilted Dirac fermions. After carrying out the …
We study the effective symmetry profiles of superconducting pair correlations and the flow of charge supercurrent in ballistic Weyl semimetal systems with a tilted dispersion relation. Utilizing a microscopic method in the ballistic regime and starting from both opposite-pseudospin and equal-pseudospin phonon-mediated opposite-spin electron-electron couplings, we calculate the anomalous Green's function to study various superconducting pair correlations that Weyl semimetal systems may develop. The momentum-space profile reveals that by properly manipulating the parameters of Weyl semimetal sys…
Weyl semimetal (WSM) feature tilted Dirac cones and can be type I or II depending on the magnitude of the tilt parameter ($C$). The boundary between the two types is at $C=1$ where the cones are tipped and there is a Lifshitz transition. The topological charge of a WSM is one. In multi-Weyl it can be two or more depending on the value of the winding number $J$. We calculate the absorptive part of the AC optical conductivity both along the tilt direction ($σ_{zz}$) and perpendicular to it ($σ_{xx}$) as a function of the tilt ($C$) and chemical potential ($μ$). For zero tilt there is a discontin…
We report the effect of Dirac cone tilting on interlayer magnetoresistance in α-(BEDT-TTF)$_2$I$_3$, which is a Dirac semimetal under pressure. Fitting of the experimental data by the theoretical formula suggests that the system is close to a type-II Dirac semimetal.
We study the chiral magnetic effect (CME) in tilted multi-Weyl Semimetals (WSM) employing a two-band lattice model. We focus on the type-II phase of mWSMs, introduced by incorporating a Lorentz symmetry violating tilt term. We add to the understanding of the CME (and anomalous Hall effect) in the type-II phase of mWSMs and near the Lifshitz transition by varying tilt. Like the elementary WSM, our results also indicate that the Berry curvature drives the CME for higher monopole charges. We find a peak in the CME at the transition point and discuss its significance using the density of states. A…
In highly conductive metals with sufficiently strong momentum-conserving scattering, the electron momentum is regarded as a long-lived quantity, whose dynamics is described by an emergent hydrodynamic theory. In this paper, we develop an electron hydrodynamic theory for noncentrosymmetric metals, where a novel class of electron fluids is realized by lowering crystal symmetries and the resulting geometrical effects. The obtained hydrodynamic equation suggests a nontrivial analogy between electron fluids in noncentrosymmetric metals and chiral fluids in vacuum, and predicts novel hydrodynamic tr…
We investigate the effects of quenched disorder on a non-interacting tilted Dirac semimetal in two dimensions. Depending on the magnitude of the tilting parameter, the system can have either Fermi points (type-I) or Fermi lines (type-II). In general, there are three different types of disorders for Dirac fermions in two dimensions, namely, the random scalar potential, the random vector potentials along and perpendicular to the tilting direction, and the random mass. We study the effects of weak disorder in terms of the renormalization group, which is performed by integrating out the modes with…
The chiral magnetic effect is a one of the exotic bulk transport properties of the Weyl semimetals. Because of the Nielsen-Ninomiya "no-go theorem", the total chiral magnetic current is absent in the equilibrium state. One of the mechanisms for generating this current is the chiral anomaly. This phenomenon is the anomalous nonconservation of chiral charge for massless relativistic particles. It can be realized by parallel magnetic and electric fields, and it leads to such new transport phenomenon as the negative longitudinal magnetoresistance. Using a simple theory (we consider both linearized…
Weyl semimetal (WSM) is expected to be an ideal spintronic material owing to its spin currents carried by the bulk and surface states with spin-momentum locking. A photocurrent generation in noncentrosymmetric WSM was also predicted owing to its broken inversion symmetry and linear energy dispersion which are unique to Weyl systems. In our recent measurements, the circular photogalvanic effect (CPGE) has been demonstrated in WSM of TaAs. The CPGE voltage is proportional to the helicity of the incident light and reverses its direction on changing the radiation helicity from left handed to right…
Topological Weyl semimetals (TWS) can be classified as type-I TWS, in which the density of states vanishes at the Weyl nodes, and type-II TWS where an electron and a hole pocket meet with finite density of states at the nodal energy. The dispersions of type-II Weyl nodes are tilted and break Lorentz invariance, allowing for physical properties distinct from those in a type-I TWS. We present minimal lattice models for both time-reversal-breaking and inversion-breaking type-II Weyl semimetals, and investigate their bulk properties and topological surface states. These lattice models capture the …
There is considerable interest in the intersection of correlations and topology, especially in metallic systems. Among the outstanding questions are how strong correlations drive novel topological states and whether such states can be readily controlled. Here we study the effect of a Zeeman coupling on a Weyl-Kondo semimetal in a nonsymmorphic and noncentrosymmetric Kondo-lattice model. A sequence of distinct and topologically nontrivial semimetal regimes are found, each containing Kondo-driven and Fermi-energy-bound Weyl nodes. The nodes annihilate at a magnetic field that is smaller than wha…
We report on the single crystal growth and transport properties of a topological semimetal CaAgBi which crystallises in the hexagonal $ABC-$type structure with the non-centrosymmetric space group $\mathit{P6_3mc}$ (No. 186). The transverse magnetoresistance measurements with current in the basal plane of the hexagonal crystal structure reveal a value of about 30 % for I // [10-10] direction and about 50 % for I // [1-210] direction at 10 K in an applied magnetic field of 14 T. The magnetoresistance shows a cusp-like behavior in the low magnetic-field region, suggesting the presence of weak ant…
The transition metal monopnictide family of Weyl semimetals recently has been shown to exhibit anomalously strong second-order optical nonlinearity, which is theoretically attributed to a highly asymmetric polarization distribution induced by their polar structure. We experimentally test this hypothesis by measuring optical second harmonic generation (SHG) from TaAs across a pressure-tuned polar-to-nonpolar structural phase transition. Despite the high-pressure structure remaining noncentrosymmetric, the SHG yield is reduced by more than 60 % by 20 GPa as compared to the ambient pressure value…
We present a systematic investigation of the magnetoresponses of the Weyl points (WPs) with a topological charge of n = 2, 3 and 4, and with both linear and quadratic energy tilt. The linear tilt always tends to squeeze the Landau levels (LLs) of both conduction and valence bands of all the WPs, and eventually leads to LL collapse in the type-II phase. However, the quadratic energy tilt has more complex influences on the LLs of the unconventional WPs. For charge-n (n = 2, 4) WP, the influence of the quadratic tilt on the LLs of conduction and valence bands are opposite, i.e. if the LLs of cond…
The emergent Weyl fermions in condensed matter generally break the Lorentz invariance resulting in a tilted (type-I) or over-tilted (type-II) energy dispersion. The tilting energy spectrums can lead to exotic quantum interference effects in a junction set up. Here, we theoretically investigate the Josephson current in a Weyl superconductor-Weyl (semi)metal-Weyl superconductor junction of a time-reversal (TR) broken type-I Weyl semimetal. We demonstrate that the Cooper pairs of BCS-like pairing acquire a finite momentum in case of inversion symmetric tilt. Consequently, the system exhibits tilt…
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 subject of topological materials has attracted immense attention in condensed-matter physics, because they host new quantum states of matter containing Dirac, Majorana, or Weyl fermions. Although Majorana fermions can only exist on the surface of topological superconductors, Dirac and Weyl fermions can be realized in both 2D and 3D materials. The latter are semimetals with Dirac/Weyl cones either not tilted (type I) or tilted (type II). Although both Dirac and Weyl fermions have massless nature with the nontrivial Berry phase, the formation of Weyl fermions in 3D semimetals require either …
Insulating states can be topologically nontrivial, a well-established notion that is exemplified by the quantum Hall effect and topological insulators. By contrast, topological metals have not been experimentally evidenced until recently. In systems with strong correlations, they have yet to be identified. Heavy fermion semimetals are a prototype of strongly correlated systems and, given their strong spin-orbit coupling, present a natural setting to make progress. Here we advance a Weyl-Kondo semimetal phase in a periodic Anderson model on a noncentrosymmetric lattice. The quasiparticles near …
Recently, topological semimetals become hot topic in condensed matter physics, including Dirac semimetal, Weyl semimetal, and nodal line semimetal (NLSM). In this paper, a new type of node- line semimetal - type-II NLSM is proposed based on a two-band cubic lattice model. For type-II NLSM, the zero energy bulk states have a closed loop in momentum space but the (local) Weyl cones on nodal line become tilted. The effect of magnetic field and that of correlation on type-II NLSM are studied. In particular, after considering repulsive interaction and additional spin degrees of freedom, different t…
Second harmonic generation (SHG) is a fundamental nonlinear optical phenomenon widely used both for experimental probes of materials and for application to optical devices. Even-order nonlinear optical responses including SHG generally require breaking of inversion symmetry, and thus have been utilized to study noncentrosymmetric materials. Here, we study theoretically the SHG in inversion-symmetric Dirac and Weyl semimetals under a DC current which breaks the inversion symmetry by creating a nonequilibrium steady state. Based on analytic and numerical calculations, we find that Dirac and Weyl…
We investigate the mutual influence of tilt, disorder, and Coulomb interaction in a type-I Dirac semimetal (DSM) with $x$-direction tilt by performing a renormalization group analysis. The interplay between disorder and ordinary tilt generates an effective tilt along the $x$-direction, which is the physically observable one. There exist two types of disorder which increase the effective tilt and drive a phase transition from the DSM phase to the diffusive metal phase. The diffusive phase transition stops the increase of the effective tilt and the surface of the original Dirac cone in the diffu…
We present details of materials synthesis, crystal structure, and anisotropic magnetic properties of single crystals of CeAlGe, a proposed type-II Weyl semimetal. Single-crystal x-ray diffraction confirms that CeAlGe forms in noncentrosymmetric I4$_1$md space group, in line with predictions of non-trivial topology. Magnetization, specific heat and electrical transport measurements were used to confirm antiferromagnetic order below 5 K, with an estimated magnon excitation gap of $Δ$ = 9.11 K from heat capacity and hole-like carrier density of 1.44 $\times$ 10$^{20}$ cm$^{-3}$ from Hall effect m…
We study structural and magnetic properties of rare-earth based semimetals RAuGe (R = Y, Gd-Tm, and Lu) using flux-grown single crystals. These compounds belong to the noncentrosymmetric polar space group P63mc. We confirm the systematic structural evolution at room temperature as a function of ionic radius of rare earths to clarify the isopointal crossover between two polar structures: three-dimensional LiGaGe-type and quasi-two-dimensional NdPtSb-type. Magnetism shows a characteristic anisotropy in reasonable agreement with the crystal electric field (CEF) theory; the easy-plane-type anisotr…
Spin-charge conversion via spin-orbit interaction is one of the core concepts in the current spintronics research. The efficiency of the interconversion between charge and spin current is estimated based on Berry curvature of Bloch wavefunction in the linear-response regime. Beyond the linear regime, nonlinear spin-charge conversion in the higher-order electric field terms has recently been demonstrated in noncentrosymmetric materials with nontrivial spin texture in the momentum space. Here we report the observation of the nonlinear charge-spin conversion in a nominally centrosymmetric oxide m…
