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

TL;DR

This paper investigates how an external magnetic field influences the superconducting phase diagram of quasi-two-dimensional Dirac electron systems, revealing a quantum phase transition and critical magnetic field behavior relevant to materials like Cu_xTiSe_2.

Contribution

It provides a theoretical analysis of magnetic field effects on superconductivity and quantum criticality in Dirac electron systems, including phase transition details and critical field behavior.

Findings

Quantum phase transition at zero temperature depending on magnetic field and coupling

Linear decay of critical magnetic field with temperature

Relevance to experimental observations in Cu_xTiSe_2 and intercalated graphite

Abstract

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.