Fig. 2

Inter-Landau-level transition energy from multiple carriers. a Transition energy versus \(\sqrt B\) in the far-infrared range. Colored lines and labels are used to differentiate the origin of each feature. Red and blue dashed straight lines are guidelines for T-type transitions pointing to the origin of the plot, indicative of the two inequivalent massless Weyl fermions. Dark green dashed lines are fitting curves with linear-in-B evolution for M-type transitions, suggesting gapped electronic bands with band inversion. Red and blue solid lines are fitting curves for the intra-band transition involving the zeroth chiral Landau levels in Weyl nodes. In this plot, colors in red, blue, dark green (for curve, guidelines and labels) denote the contributions from Weyl node 1 (W1), Weyl node 2 (W2), and gapped band, respectively. Inset shows that W1 has a higher Fermi velocity than W2. Labels in purple present that the feature is contributed by both Weyl nodes, thus mixing red and blue. The label −n → n+1 denotes the initial and final Landau levels involved in the optical transition process. −(n+1) → n transition is also involved but not labeled for simplicity. Error bars are added based on both experimental resolution and fitting uncertainty. b The normalized reflection data from experiments (black) and the Magneto–Lorentz fitting (red). The energy of the inter-Landau level transition in a is described by the fitted energy (arrows) instead of apparent peak maxima. 2% is the change of the reflection under magnetic field. c Landau level dispersion of massless Weyl fermion in NbAs. Only the lowest nine branches are plotted for illustration. The arrows delineate the allowed optical inter-band transition processes between Landau levels at k _z  = 0. d, e Fan diagrams for W1 and W2 under different magnetic fields. Solid lines are guidelines pointing to the origin of the plot, indicative of the massless Weyl fermions and verifying the assignment of transition index. Labels indicate the transition and Landau level index