Effects of a Magnetic Field on Superconductivity and Quantum Criticality in Quasi-Two-Dimensional Systems with Dirac Electrons

We study the effects of an external magnetic field on thensuperconducting phase diagram of a quasi-two-dimensional system of Dirac electrons at an arbitrary temperature. At zero temperature, there is a quantum phase transition connecting a normal and a superconducting phase, occurring at a critical line that corresponds to a magnetic field dependent critical coupling parameter, which should be observed in planar materials containing Dirac electrons, such as $Cu_xTiSe_2$. Moreover, the superconducting gap is obtained as a function of temperature, magnetic field and coupling parameter ($\lambda_{\rm R}$). From this, we extract the critical magnetic field $B_{ c }$ as a function of the temperature. For small values of $B_{ c }$, we obtain a linear decay of the critical field, which is similar to the behavior observed experimentally in the copper doped dichalcogenide $Cu_xTiSe_2$ and also in intercalated graphite.