Harmonic generation is a general characteristic of driven nonlinear systems, and serves as an efficient tool for investigating the fundamental principles that govern the ultrafast nonlinear dynamics. Here, we report on terahertz-field driven high-harmonic generation in the three-dimensional Dirac semimetal Cd3As2 at room temperature. Excited by linearly-polarized multi-cycle terahertz pulses, the third-, fifth-, and seventh-order harmonic generation is very efficient and detected via time-resolved spectroscopic techniques. The observed harmonic radiation is further studied as a function of pump-pulse fluence. Their fluence dependence is found to deviate evidently from the expected power-law dependence in the perturbative regime. The observed highly non-perturbative behavior is reproduced based on our analysis of the intraband kinetics of the terahertz-field driven nonequilibrium state using the Boltzmann transport theory. Our results indicate that the driven nonlinear kinetics of the Dirac electrons plays the central role for the observed highly nonlinear response.

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 C4 in our construction), but breaks the Lorentz symmetry, resulting in nonlinear band spectra (namely, E ∼ (p 2 x + p 2 y ) n/2 , but E ∼ |pz|, for example, where momenta p is measured from the Weyl nodes). Consequently, the effective field theory displays U (1) × SU (2) non-Abelian anomaly, yielding anomalous Hall effect, its non-Abelian generalization, and various chiral conductivities. The anomalous violation of conservation laws is determined by the monopole charge n and a specific algebraic property of the SU (2) Lie group, which we further substantiate by numerically computing the regular and "isospin" densities from the lattice models of mWSMs. These predictions are also supported from a strongly coupled (holographic) description of mWSMs. Altogether our findings unify the field theoretic descriptions of mWSMs of arbitrary monopole charge n (featuring n copies of the Fermi arc surface states), predict signatures of non-Abelian anomaly in table-top experiments, and pave the route to explore anomaly structures for multi-fold fermions, transforming under arbitrary half-integer or integer spin representations.

We study the longitudinal magnetotransport in three-dimensional multi-Weyl semimetals, constituted by a pair of (anti)-monopole of arbitrary integer charge (n), with n = 1, 2 and 3 in a crystalline environment. For any n > 1, even though the distribution of the underlying Berry curvature is anisotropic, the corresponding intrinsic component of the longitudinal magnetoconductivity (LMC), bearing the signature of the chiral anomaly, is insensitive to the direction of the external magnetic field (B) and increases as B 2 , at least when it is sufficiently weak (the semi-classical regime). In addition, the LMC scales as n 3 with the monopole charge. We demonstrate these outcomes for two distinct scenarios, namely when inter-particle collisions in the Weyl medium are effectively described by (a) a single and (b) two (corresponding to inter-and intra-valley) scattering times. While in the former situation the contribution to LMC from chiral anomaly is inseparable from the non-anomalous ones, these two contributions are characterized by different time scales in the later construction. Specifically for sufficiently large inter-valley scattering time the LMC is dominated by the anomalous contribution, arising from the chiral anomaly. The predicted scaling of LMC and the signature of chiral anomaly can be observed in recently proposed candidate materials, accommodating multi-Weyl semimetals in various solid state compounds.

We study non-perturbatively the anomalous Hall current and its high harmonics generated in Weyl and Dirac semimetals by strong elliptically polarized laser fields, in the context of kinetic theory. We find a novel crossover between perturbative and non-perturbative regimes characterized by the electric field strength E * = µω 2ev F (ω: laser frequency, µ: Fermi energy, vF : Fermi velocity). In the perturbative regime, the anomalous Hall current quadratically depends on the field strength (E), whereas the higher order corrections, as well as high harmonics, vanish at zero temperature. In the non-perturbative regime, the anomalous Hall current saturates and decays as (log E)/E, while even-order high harmonics are generated when inplane rotational symmetry is broken. Based on the analytical solution of the Boltzmann equation, we reveal the topological origin of the sharp crossover: the Weyl monopole stays inside or moves outside of the Fermi sphere, respectively, during its fictitious motion in the pertubative or non-pertubative regimes. Our findings establish a new non-linear response intrinsically connected to topology, characteristic to Weyl and Dirac semimetals.

Significance Weyl semimetals are a class of three-dimensional materials, whose low-energy excitations mimic massless fermions. In consequence they exhibit various unusual transport properties related to the presence of chiral anomalies, a subtle quantum phenomenon that denotes the breaking of the classical chiral symmetry by quantum fluctuations. In this work we present a universal description of transport in weakly disordered Weyl semimetals with several scattering mechanisms taken into account. Our work predicts the existence of a new anomaly-induced transport regime in these materials and gives a crisp experimental signature of a chiral anomaly in optical conductivity measurements. Finally, by also capturing the hydrodynamic regime of quasiparticles, our construction bridges the gap between developments in electronic fluid mechanics and three-dimensional semimetals.

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We report on terahertz high-harmonic generation in a Dirac semimetal as a function of the driving-pulse ellipticity and on a theoretical study of the field-driven intraband kinetics of massless Dirac fermions. Very efficient control of third-harmonic yield and polarization state is achieved in electron-doped Cd 3 As 2 thin films at room temperature. The observed tunability is understood as resulting from terahertz-field driven intraband kinetics of the Dirac fermions. Our study paves the way for exploiting nonlinear optical properties of Dirac matter for applications in signal processing and optical communications.

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