Magnetic Field Effects on the Superconducting and Quantum Critical Properties of Layered Systems with Dirac Electrons

TL;DR

This paper investigates how external magnetic fields influence the superconducting and quantum critical behaviors of layered Dirac electron systems, revealing phase diagrams and critical phenomena relevant to materials like Cu_xTiSe_2.

Contribution

It provides explicit expressions for the superconducting gap and phase diagrams as functions of temperature, magnetic field, and coupling, highlighting novel quantum phase transitions in Dirac electron systems.

Findings

Linear decay of critical magnetic field with temperature

Coupling-dependent critical temperature similar to high-Tc cuprates

Quantum phase transition at a critical line influenced by magnetic field

Abstract

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 ($\lambda_{\rm R}$). From this, we extract the $B \times \lambda_{\rm R}$, $T\times \lambda_{\rm R}$ and $B \times T$ 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 $Cu_xTiSe_2$ and also in intercalated graphite. The second one, presents a coupling dependent critical temperature $T_c$ that resembles the one observed in high-$T_c$ cuprates in the underdoped region and also in $Cu_xTiSe_2$. 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 $Cu_xTiSe_2$.