Magneto-Optics of a Weyl Semimetal beyond the Conical Band Approximation: Case Study of TaP

Landau-level spectroscopy, the optical analysis of electrons in materials subject to a strong magnetic field, is a versatile probe of the electronic band structure and has been successfully used in the identification of novel states of matter such as Dirac electrons, topological materials or Weyl semimetals. The latter arise from a complex interplay between crystal symmetry, spin-orbit interaction, and inverse ordering of electronic bands. Here, we report on unusual Landau-level transitions in the monopnictide TaP that decrease in energy with increasing magnetic field. We show that these transitions arise naturally at intermediate energies in time-reversal-invariant Weyl semimetals where the Weyl nodes are formed by a partially gapped nodal-loop in the band structure. We propose a simple theoretical model for electronic bands in these Weyl materials that captures the collected magneto-optical data to great extent.

Figure 1

(a) The four zero-energy points of the Hamiltonian (1) appearing for a particular set of parameters at locations where both the diagonal and off-diagonal terms vanish. (b) The electronic band structure implied by the Hamiltonian (1) with two pairs of Weyl cones located at ${\mathbf{q}}^w=(\pm q_x^w,\pm q_y^w,0)$ and full electron-hole symmetry. Two pairs of saddle points as well as one local extremum at $\mathbf{q}=0$ (due to the band inversion) appear in the conduction (blue) and valence (red) bands, respectively.

Figure 2

(a) The LL spectrum as a function of $B$ calculated for $\mathrm{\Delta }=35\mathrm{meV}$, ${\gamma }_0=10\mathrm{meV}$, $\mathrm{\Gamma }=1\mathrm{meV}$, and $M=m_y=m_x/12=m_0/4$ where $m_0$ is the free electron mass. The number of LLs considered in our calculations has been limited to $N=700$. The horizontal lines denote energies of the band extrema and saddle points in the (zero-field) band structure, cf. Fig. 1. (b) The false color-plot of relative magneto-reflectivity, $R_B/R_0$, calculated for the system considered in the panel (a). The reference spectrum $R_0$ has been approximated by the reflectivity trace calculated at $B=1\mathrm{T}$ and for $\mathrm{\Gamma }=5\mathrm{meV}$. The background dielectric constant ${ϵ}_{\infty }=20$ has been considered. The horizontal arrow indicates the feature due to excitations between higher-energy saddle points. (c) The experimentally determined $R_B/R_0$ at $T=2\mathrm{K}$. (d) The schematic fan chart of experimentally observed inter-LL excitations. For relatively narrow lines, maxima in $R_B/R_0$ represent good estimates of transition energies. Excitations decreasing their energy with $B$ are represented by red solid lines.

Figure 3

(a) Infrared reflectivity of TaP measured at selected temperatures. The corresponding real part of conductivity and dielectric function are shown in parts (b) and (c), respectively. The measurements and analysis of this zero-field data closely followed the procedure described in Ref. [38].