Quantum criticality and superconductivity in quasi-two-dimensional Dirac electronic systems

Abstract

We present a theory describing the superconducting (SC) interaction of Dirac electrons in a quasi-two-dimensional system consisting of a stack of N planes. The occurrence of a SC phase is investigated both at T = 0 and T = 0, in the case of a local interaction, when the theory must be renormalized and also in the situation where a natural physical cutoff is present in the system. In both cases, at T = 0, we find a quantum phase transition connecting the normal and SC phases at a certain critical coupling. The phase structure is shown to be robust against quantum fluctuations. The SC gap is determined for T = 0 and T = 0, both with and without a physical cutoff and the interplay between the gap and the SC order parameter is discussed. Our theory qualitatively reproduces the SC phase transition occurring in the underdoped regime of the high-Tc cuprates. This fact points to the possible relevance of Dirac electrons in the mechanism of high-Tc superconductivity.

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

“…Notice that in the limit B → 0 both the quantum critical point and the superconducting gap reduce to the ones found previously [3] in the absence of a magnetic field. Conversely, for each value of the physical coupling parameter λ R , there is a critical magnetic field above which superconductivity is destroyed.…”

“…We have shown in [3], that the mean-field phase structure obtained at zero magnetic field is robust against quantum fluctuations. The same arguments apply here and, therefore, we reach the same conclusion in the presence of an applied magnetic field.…”

“…The second and third terms, respectively, contain the coupling of the magnetic field to orbital and spin degrees of freedom. As in [3], we assume there is an effective superconducting interaction whose origin will not influence the results of this work. g is the superconducting coupling constant, which is supposed to depend on some external control parameter.…”

“…In order to make the lagrangian smooth, we define g ≡ λ/N. We use the same convention for the Dirac matrices as in [3].…”

“…This will drastically affect the physical properties of such materials. In a previous work [3], we investigated the superconducting properties of a quasi-two-dimensional system of Dirac electrons and showed that they are completely different from the ones presented by usual Schrödinger electrons. There is, in particular, a quantum phase transition connecting the normal and superconducting phases, which is controlled by the magnitude of the effective superconducting interaction coupling parameter.…”