We investigate the behavior of low-energy electrons in two-dimensional molybdenum disulfide when submitted to an external magnetic field. Highly degenerate Landau levels form in the material, between which light-induced excitations are possible. The dependence of excitations on light polarization and energy is explicitly determined, and it is shown that it is possible to induce valley and spin polarization, i.e. to excite electrons of selected valley and spin. Whereas the effective low-energy model in terms of massive Dirac fermions yields dipole-type selection rules, higher-order band corrections allow for the observation of additional transitions. Furthermore, inter-Landau-level transitions involving the n = 0 levels provide a reliable method for an experimental measurement of the gap and the spin-orbit gap of molybdenum disulfide.

We study the "Higgs" amplitude mode in the relativistic quantum O(N ) model in two space dimensions. Using the nonperturbative renormalization group and the Blaizot-Méndez-Galain-Wschebor approximation (which we generalize to compute four-point correlation functions), we compute the O(N )-invariant scalar susceptibility at zero temperature in the vicinity of the quantum critical point. In the ordered phase, we find a well-defined Higgs resonance for N = 2 and 3 and determine its universal properties. No resonance is found for N 4. In the disordered phase, the spectral function exhibits a threshold behavior with no Higgs-like peak. We also show that for N = 2, the Higgs mode manifests itself as a very broad peak in the longitudinal susceptibility in spite of the infrared divergence of the latter. We compare our findings with results from quantum Monte Carlo simulations and = 4 − (d + 1) expansion near d = 3.