Quantum criticality of fermion velocities and critical temperature nearby a putative quantum phase transition in the $d$-wave superconductors

Abstract

Quantum critical behaviors induced by a putative quantum phase transition are vigilantly investigated, which separates a $d$-wave superconducting state and $d$-wave superconducting+$X$ state below the superconducting dome of the $d-$wave superconductors with tuning the non-thermal doping variable. Within the framework of renormalization group approach, we start with a phenomenological effective theory originated from the Landau-Ginzburg-Wilson theory and practice one-loop calculations to construct a set of coupled flows of all interaction parameters. After extracting related physical information from these coupled evolutions, we address that both fermion velocities and critical temperatures exhibit critical behaviors, which are robust enough against the initial conditions due to strong quantum fluctuations. At first, the evolution of Yukawa coupling between $X$-state order parameter and nodal fermions in tandem with quantum fluctuations heavily renormalize fermion velocities and generally drive them into certain finite anisotropic fixed point at the lowest-energy limit, whose concrete value relies upon the very quantum phase transition. In addition, these unique properties of fermion velocities largely reshape the fate of superfluid density, giving rise to either an enhancement or a dip of critical temperature. Moreover, we find that fermion-fermion interactions bring non-ignorable quantitative corrections to quantum critical behaviors despite they are subordinate to quantum fluctuations of order parameters.

22 pages; 15 figures

References in corpus (23)

• Theory of Intertwined Orders in High Temperature Superconductors
• Quantum criticality
• Electronic liquid crystal state in the high-temperature superconductor YBCO(6.45)
• Lattice symmetry breaking in cuprate superconductors: Stripes, nematics, and superconductivity
• Quantum Criticality
• Interacting fermions on the honeycomb bilayer: from weak to strong coupling
• Renormalization group theory of nematic ordering in d-wave superconductors
• Theory of the nodal nematic quantum phase transition in superconductors
• Electronic multicriticality in bilayer graphene
• Competition of Fermi surface symmetry breaking and superconductivity
• Experimental observables near a nematic quantum critical point in the pnictide and cuprate superconductors
• Stability of Quantum Critical Points in the Presence of Competing Orders
• Extended Hubbard model in undoped and doped monolayer and bilayer graphene: Selection rules and organizing principle among competing orders
• Quantum critical point shifts under superconductivity: the pnictides and the cuprates
• The fate of interaction-driven topological insulators under disorder
• Anomalous Scaling of the Penetration Depth in Nodal Superconductors
• Signatures of the nematic ordering transitions in the thermal conductivity of d-wave superconductors
• Stability of two-dimensional asymmetric materials with a quadratic band crossing point under four-fermion interaction and impurity scattering
• Velocity renormalization of nodal quasiparticles in d-wave superconductors
• Order parameter fluctuation and ordering competition in $\mathrm{B}{\mathrm{a}}_{1-\mathrm{x}}{\mathrm{K}}_{\mathrm{x}}\mathrm{F}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$
• Fermion-fermion interaction driven instability and criticality of quadratic band crossing systems with the breaking of time-reversal symmetry
• Two-loop disorder effects on the nematic quantum criticality in $d$-wave superconductors
• Color degeneracy of competing orders near topological defects cores in planar quadratic band touching systems

Cited by in corpus (2)

• Fermion-fermion interaction driven phase transitions in rhombohedral trilayer graphene
• Critical behavior around the fixed points driven by fermion-fermion interactions and disorders in the nodal-line superconductors