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We present results of a theoretical study of photocurrents in the Weyl semimetals belonging to the gyrotropic symmetry classes. We show that, in weakly gyrotropic symmetry classes C$_{nv}$ ($n = 3,4,6$), the circular photocurrent transverse to the incidence direction appears only with account, in the electron effective Hamiltonian, for both linear and quadratic or cubic in quasi-momentum spin-dependent terms as well as a spin-independent term resulting in the tilt of the cone dispersion. A polarization-independent magneto-induced photocurrent is predicted which is also allowed in gyrotropic systems only. For crystals of the C$_{2v}$ symmetry, we consider a microscopic mechanism of the photocurrent in a quantized magnetic field which is generated under direct optical transitions between the ground and the first excited magnetic subbands. It is shown that this current becomes nonzero with allowance for anisotropic tilt of the dispersion cones.
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Fermions in nature come in several types: Dirac, Majorana and Weyl are theoretically thought to form a complete list. Even though Majorana and Weyl fermions have for decades remained experimentally elusive, condensed matter has recently emerged as fertile ground for their discovery as low energy excitations of realistic materials. Here we show the existence of yet another particle - a new type of Weyl fermion - that emerges at the boundary between electron and hole pockets in a new type of Weyl semimetal phase of matter. This fermion was missed by Weyl in 1929 due to its breaking of the stringent Lorentz symmetry of high-energy physics. Lorentz invariance however is not present in condensed matter physics, and we predict that an established material, WTe$_2$, is an example of this novel type of topological semimetal hosting the new particle as a low energy excitation around a type-2 Weyl node. This node, although still a protected crossing, has an open, finite-density of states Fermi surface, likely resulting in a plethora physical properties very different from those of standard point-like Fermi surface Weyl points.
We investigate higher-order Weyl semimetals (HOWSMs) having bulk Weyl nodes attached to both surface and hinge Fermi arcs. We identify a new type of Weyl node, that we dub a $2nd$ order Weyl node, that can be identified as a transition in momentum space in which both the Chern number and a higher order topological invariant change. As a proof of concept we use a model of stacked higher order quadrupole insulators to identify three types of WSM phases: $1st$-order, $2nd$-order, and hybrid-order. The model can also realize type-II and hybrid-tilt WSMs with various surface and hinge arcs. Moreover, we show that a measurement of charge density in the presence of magnetic flux can help identify some classes of $2nd$ order WSMs. Remarkably, we find that coupling a $2nd$-order Weyl phase with a conventional $1st$-order one can lead to a hybrid-order topological insulator having coexisting surface cones and flat hinge arcs that are independent and not attached to each other. Finally, we show that periodic driving can be utilized as a way for generating HOWSMs. Our results are relevant to metamaterials as well as various phases of Cd$_3$As$_2$, KMgBi, and rutile-structure PtO$_2$ that have been predicted to realize higher order Dirac semimetals.
Weyl semimetals are crystals in which electron bands cross at isolated points in momentum space. Associated with each crossing point (or Weyl node) is an integer topological invariant known as the Berry monopole charge. The discovery of new classes of Weyl materials is driving the search for novel properties that derive directly from the Berry charge. The circular photogalvanic effect (CPGE), whereby circular polarized light generates a current whose direction depends on the helicity of the absorbed photons, is a striking example of a macroscopic property that emerges from Weyl topology. Recently, it was predicted that the rate of current generation associated with optical transitions near a Weyl node is proportional to its monopole charge and independent of material-specific parameters. In Weyl semimetals that retain mirror symmetry this universal photogalvanic current is strongly suppressed by opposing contributions from energy equivalent nodes of opposite charge. However, when all mirror symmetries are broken, as in chiral Weyl systems, nodes with opposite topological charge are no longer degenerate, opening a window of photon energies where the topological CPGE can emerge. In this work we test this theory through measurement of the photon-energy dependence of the CPGE in the chiral Weyl semimetal RhSi. The spectrum is fully consistent with a topological CPGE, as it reveals a response in a low-energy window that closes at 0.65 eV, in quantitative agreement with the theoretically-derived bandstucture.
We investigate collective modes in three dimensional (3D) gapless multi-Weyl semimetals with anisotropic energy band dispersions (i.e., $Esim sqrt{ k_{parallel}^{2J} + k_z^2}$, where $k_{parallel}$ and $k_z$ are wave vectors and $J$ is a positive integer). For comparison, we also consider the gapless semimetals with the isotropic band dispersions (i.e., $Esim k^J$). We calculate analytically long-wavelength plasma frequencies incorporating interband transitions and chiral properties of carriers. For both the isotropic and anisotropic cases, we find that interband transitions and chirality lead to the depolarization shift of plasma frequencies. For the isotropic parabolic band dispersion (i.e., $N=2$, $Esim k^2$), the long-wavelength plasma frequencies lie outside the single particle excitation regions for all carrier densities, and thus the plasmons do not decay via Landau damping. For the higher-order band dispersions ($N ge 3$) the long-wavelength plasmons experience damping below a critical density. For systems with the anisotropic dispersion the density dependence of the long-wavelength plasma frequency along the direction of non-linear dispersion behaves like that of the isotropic linear band model ($N=1$), while along the direction of linear dispersion it behaves like that of the isotropic non-linear model ($N ge 2$). Plasmons along both directions remain undamped over a broad range of densities due to the chirality induced depolarization shift. Our results provide a comprehensive picture of how band dispersion and chirality affect plasmon behaviors in 3D gapless chiral systems with the arbitrary band dispersion.
We suggest the possibility of a linear magnetochiral effect in time reversal breaking Weyl semimetals. Generically the magnetochiral effect consists in a simultaneous linear dependence of the magnetotransport coefficients with the magnetic field and a momentum vector. This simultaneous dependence is allowed by the Onsager reciprocity relations, being the separation vector between the Weyl nodes the vector that plays such role. As a side consequence, we find a non vanishing positive longitudinal magnetoconductivity at Fermi energies above the point where the chirality of the Weyl nodes is globally lost.
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