Superconducting and excitonic quantum phase transitions in doped systems with Dirac electrons

TL;DR

This paper explores the phase transitions and coexistence of superconducting and excitonic orders in doped Dirac electron systems, revealing conditions for coexistence, phase diagrams, and analogies to high-energy physics phenomena.

Contribution

It provides a detailed phase diagram analysis of superconducting and excitonic interactions in doped Dirac systems, including coexistence conditions and qualitative comparisons to high-temperature superconductors.

Findings

Coexistence of superconductivity and excitonic order occurs at equal interaction strengths above a quantum critical point.

Superconducting gap exhibits a dome shape as doping increases, similar to high-temperature superconductors.

Superconductivity suppresses excitonic order as chemical potential increases.

Abstract

Material systems with Dirac electrons on a bipartite planar lattice and possessing superconducting and excitonic interactions are investigated both in the half-filling and doped regimes at zero temperature. Excitonic pairing is the analog of chiral symmetry breaking of relativistic fermion theories and produces an insulating gap in the electronic spectrum. Condensed matter systems with such competing interactions display phenomena that are analogous to the onset of the chiral condensate and of color superconductivity in dense quark matter. Evaluation of the free-energy (effective potential) allows us to map the phases of the system for different values of the couplings of each interaction. At half-filling, we show that Cooper pairs and excitons can coexist if the superconducting and excitonic interactions strengths are equal and above a quantum critical point, which is evaluated. If one of the interactions is stronger than the other, then only the corresponding order parameter is non-vanishing and we do not have coexistence. For nonzero values of chemical potential, the phase diagram for each interaction is obtained independently. Taking into account only the excitonic interaction, a critical chemical potential, as a function of the interaction strength, is obtained. If only the superconducting interaction is considered, the superconducting gap displays a characteristic dome as charge carriers are doped into the system and our results qualitatively reproduce the superconducting phase diagram of several compounds, like 122 pnictides and cuprate superconductors. We also analyze the possibility of coexistence between Cooper pairs and excitons and we show that, even if the excitonic interaction strength is greater than the superconducting interaction, as the chemical potential increases, superconductivity tends to suppress the excitonic order parameter.