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.Introduction. A Weyl semimetal (WSM) is a gapless topological state of matter possessing k-space singularities where its valence and conduction bands make contact at a point. This singularity is a k-space monopole providing a quantized source or sink of a Berry's flux and can occur only in materials in which either time reversal symmetry or inversion symmetry is broken. In the prototypical WSM, a twofold band degeneracy at the Weyl point is broken linearly in momentum in all directions and the node is characterized by the topological winding number (also referred to as chirality) ±1. A transition to an insulating phase is possible only if Weyl nodes with opposite chirality pairwise merge and annihilate. The gapped phase produced by this merger can be in a normal insulating state or a topological quantum anomalous Hall state. The linear dispersion around the Weyl point has important consequences for the low frequency optical properties, which have been explored theoretically and used as an experimental fingerprint of the topological state [1][2][3][4][5][6][7][8][9].A k-space merger of Weyl points with the same chirality produces a new type of Weyl semimetal, referred to as a multi-Weyl semimetal (m-WSM) [10, 11]. In these states, the merger of the nodes is robust if it is protected by a point group symmetry. The low energy dispersion can then be characterized by double (triple) Weyl nodes with linear dispersion along one symmetry direction and quadratic (cubic) dispersion along the remaining two directions. Because of the change in topological nature, the enhancement of the density of states, the anisotropic nonlinear energy dispersion and a modified spin-momentum locking structure, these states will have optical and transport signatures that distinguish them from elementary WSMs.In (a) Phase diagrams of J = 2 lattice models on the tz/m0 and mz/m0 plane and (b) evolution of the energy band structure from the 3D quantum anomalous Hall (QAH) phase to the normal insulator (NI) phase. Here, we use several values of mz/m0 corresponding to different phases, indicated by circled numbers in the phase diagram. QAH|WSM and WSM|NI denote the transition phase between 3D QAH and WSM, and WSM and NI, respectively. The phase diagram for J = 1 has a similar shape, but has a different phase boundary between the WSM and 3D QAH represe...

The stacking orders in few-layer graphene (FLG) strongly influences the electronic properties of the material. To explore the stacking-specific properties of FLG in detail, one needs powerful microscopy techniques that visualize stacking domains with sufficient spatial resolution. We demonstrate that infrared (IR) scattering scanning near-field optical microscopy (sSNOM) directly maps out the stacking domains of FLG with a nanometric resolution, based on the stacking-specific IR conductivities of FLG. The intensity and phase contrasts of sSNOM are compared with the sSNOM contrast model, which is based on the dipolar tip-sample coupling and the theoretical conductivity spectra of FLG, allowing a clear assignment of each FLG domain as Bernal, rhombohedral, or intermediate stacks for tri-, tetra-, and pentalayer graphene. The method offers 10-100 times better spatial resolution than the far-field Raman and infrared spectroscopic methods, yet it allows far more experimental flexibility than the scanning tunneling microscopy and electron microscopy.

We study the frequency-dependent conductivity of nodal line semimetals (NLSMs), focusing on the effects of carrier density and energy dispersion on the nodal line. We find that the low-frequency conductivity has a rich spectral structure which can be understood using scaling rules derived from the geometry of their Dupin cyclide Fermi surfaces. We identify different frequency regimes, find scaling rules for the optical conductivity in each, and demonstrate them with numerical calculations of the inter- and intraband contributions to the optical conductivity using a low-energy model for a generic NLSM.

No abstract

We investigate collective modes in three dimensional (3D) gapless multi-Weyl semimetals with anisotropic energy band dispersions (i.e., with a positive integer J). For comparison, we also consider the gapless semimetals with the isotropic band dispersions (i.e. E ~ kJ). 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 the long-wavelength plasmons do not decay via Landau damping, while for the higher-order band dispersions 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, while along the direction of linear dispersion it behaves like that of the isotropic non-linear model. 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.