Continuous-wave Landau-level laser in graphene

We prove the general feasibility and demonstrate the design of a continuous-wave terahertz laser operating between Landau levels in graphene placed on a polar substrate. Steady state population inversion under a continuous wave optical pumping becomes possible due to surface-phonon mediated relaxation of carriers. Our microscopic kinetics simulations including all relevant scattering processes show the existence of a steady state gain of magnitude up to 5{\%} per monolayer. The laser concept is transferable to other materials with massless Dirac fermions, notably to surface states in 3D topological insulators such as Bi$_{\mathrm{2}}$Se$_{\mathrm{3}}$.