The internship deals with a theoretical understanding of the Schwinger effect in Dirac matter (graphene and other 2D crystals). Its original high-energy version consists of the spontaneous creation of electron-positron pairs in the presence of a strong static electric field. While the effect has never been observed with true electron-positron pairs as a consequence of their large mass gap, recent experiments on mesoscopic quantum transport have unveiled the analogous effect with electron-hole pairs in graphene, within a collaboration led by the LPENS mesoscopic physics group and the theory group at LPS, Orsay. The present Master project aims at a deeper theoretical understanding of the effect, namely if an AC voltage is added to the constant one that creates the strong electric field. Indeed, one expects then a frequency-assisted version of the effect and eventually a crossover to yet another relativistic quantum effect that is the Compton effect. The theoretical approach to these phenomena is mainly analytical.