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

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.

23 pages, 11 figures

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Cited by in corpus (11)

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• Competition and duality correspondence between chiral and superconducting channels in (2+1)-dimensional four-fermion models with fermion number and chiral chemical potentials
• Absence of inhomogeneous chiral phases in 2+1-dimensional four-fermion and Yukawa models
• Interplay between superconductivity and chiral symmetry breaking in a (2+1)-dimensional model with compactified spatial coordinate
• Superconducting phase transitions induced by chemical potential in (2+1)-dimensional four-fermion quantum field theory
• Magnetic catalysis effect in (2+1)-dimensional Gross--Neveu model with Zeeman interaction
• Superconductivity phenomenon induced by external in-plane magnetic field in (2+1)-dimensional Gross--Neveu type model
• Superconductivity in graphene stacks: from the bilayer to graphite
• Competing effective interactions of Dirac electrons in the Spin-Fermion system
• Temperature vs. doping phase diagram of cuprate superconductors