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Multi-Weyl semimetals are new types of Weyl semimetals which have anisotropic non-linear energy dispersion and a topological charge larger than one, thus exhibiting a unique quantum response. Using a unified lattice model, we calculate the optical conductivity numerically in the multi-Weyl semimetal phase and in its neighboring gapped states, and obtain the characteristic frequency dependence of each phase analytically using a low-energy continuum model. The frequency dependence of longitudinal and transverse optical conductivities obeys scaling relations that are derived from the winding number of the parent multi-Weyl semimetal phase and can be used to distinguish these electronic states of matter.
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The interband optical response of a three-dimensional Dirac cone is linear in photon energy ($Omega$). Here, we study the evolution of the interband response within a model Hamiltonian which contains Dirac, Weyl and gapped semimetal phases. In the pure Dirac case, a single linear dependence is observed, while in the Weyl phase, we find two quasilinear regions with different slopes. These regions are also distinct from the large-$Omega$ dependence. As the boundary between the Weyl (WSM) and gapped phases is approached, the slope of the low-$Omega$ response increases, while the photon-energy range over which it applies decreases. At the phase boundary, a square root behaviour is obtained which is followed by a gapped response in the gapped semimetal phase. The density of states parallels these behaviours with the linear law replaced by quadratic behaviour in the WSM phase and the square root dependence at the phase boundary changed to $|omega|^{3/2}$. The optical spectral weight under the intraband (Drude) response at low temperature ($T$) and/or small chemical potential ($mu$) is found to change from $T^2$ ($mu^2$) in the WSM phase to $T^{3/2}$ ($|mu|^{3/2}$) at the phase boundary.
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 study dc conductivity of a Weyl semimetal with uniaxial anisotropy (Fermi velocity ratio $xi= v_bot/v_parallel eq1$) considering the scattering of charge carriers by a wide class of impurity potentials, both short- and long-range. We obtain the ratio of transverse and longitudinal (with respect to the anisotropy axis) conductivities as a function of both $xi$ and temperature. We find that the transverse and longitudinal conductivities exhibit different temperature dependence in the case of short-range disorder. For general long-range disorder, the temperature dependence ($sim T^4$) of the conductivity turns out to be insensitive of the anisotropy in the limits of strong ($xigg$ and $ll1$) and weak ($xiapprox1$) anisotropy.
The optical properties of (001)-oriented NbP single crystals have been studied in a wide spectral range from 6 meV to 3 eV from room temperature down to 10 K. The itinerant carriers lead to a Drude-like contribution to the optical response; we can further identify two pronounced phonon modes and interband transitions starting already at rather low frequencies. By comparing our experimental findings to the calculated interband optical conductivity, we can assign the features observed in the measured conductivity to certain interband transitions. In particular, we find that transitions between the electronic bands spilt by spin-orbit coupling dominate the interband conductivity of NbP below 100 meV. At low temperatures, the momentum-relaxing scattering rate of the itinerant carriers in NbP is very small, leading to macroscopic characteristic length scales of the momentum relaxation of approximately 0.5 $mu$m.
In a slab geometry with large surface-to-bulk ratio, topological surface states such as Fermi arcs for Weyl or Dirac semimetals may dominate their low-energy properties. We investigate the collective charge oscillations in such systems, finding striking differences between Weyl and conventional electronic systems. Our results, obtained analytically and verified numerically, predict that the Weyl semimetal thin-film host a single $omegapropto sqrt{q}$ plasmon mode, that results from collective, anti-symmetric charge oscillations of between the two surfaces, in stark contrast to conventional 2D bi-layers as well as Dirac semimetals with Fermi arcs, which support anti-symmetric acoustic modes along with a symmetric optical mode. These modes lie in the gap of the particle-hole continuum and are thus spectroscopically observable and potentially useful in plasmonic applications.
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