Competition between superconductivity and nematic order in high-$T_c$ superconductor

Abstract

We investigate the competition between d-wave superconductivity and nematic order in high-$T_c$ superconductor, and examine the role played by gapless fermionic degrees of freedom. Apart from the competitive interaction with the superconducting order parameter, the nematic order parameter couples strongly to gapless nodal quasiparticles. The interplay of these two kinds of interactions is analyzed by means of renormalization group method. In case the fermionic degree of freedom are entirely neglected, the competitive interaction between two bosonic order parameters is strongly relevant, and can lead to runaway behavior. However, these properties are fundamentally changed once the dynamics of fermions are taken into account. At the nematic quantum critical point where an extreme fermion velocity anisotropy occurs, the superconducting and nematic order parameters are decoupled from each other. Consequently, the phase transitions are continuous, and d-wave superconductivity can coexist with nematic order homogeneously. These results indicate that the gapless fermions can play an important role and should be carefully included in the theoretical description of competing orders.

21 pages, 6 figures, significantly revised

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Cited by in corpus (8)

• The fate of interaction-driven topological insulators under disorder
• Influence of Coulomb interaction on the anisotropic Dirac cone in graphene
• Order parameter fluctuation and ordering competition in $\mathrm{B}{\mathrm{a}}_{1-\mathrm{x}}{\mathrm{K}}_{\mathrm{x}}\mathrm{F}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$
• Coexistence of Nematic Order and Superconductivity in the Hubbard Model
• Renormalization group analysis of competition between distinct order parameters
• Two-loop disorder effects on the nematic quantum criticality in $d$-wave superconductors
• Variation of shear moduli across superconducting phase transitions
• On the existence of nematic-superconducting states in the Ginzburg-Landau regime