Magnetic field effects on the superconducting and quantum critical properties of layered systems with Dirac electrons

We study the effects of an external magnetic field on the superconducting properties of a quasi-two-dimensional system of Dirac electrons at an arbitrary temperature. An explicit expression for the superconducting gap is obtained as a function of temperature, magnetic field and coupling parameter (λR)(λR). From this, we extract the B×λRB×λR, T×λRT×λR and B×TB×T phase diagrams. The last one shows a linear decay of the critical field for small values thereof, which is similar to the behavior observed experimentally in the copper doped dichalcogenide CuxTiSe2 and also in intercalated graphite. The second one, presents a coupling dependent critical temperature TcTc that resembles the one observed in high-TcTc cuprates in the underdoped region and also in CuxTiSe2. The first one, exhibits 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. This should be observed in planar materials containing Dirac electrons, such as CuxTiSe2.