Two-loop disorder effects on the nematic quantum criticality in $d$-wave superconductors

Abstract

The gapless nodal fermions exhibit non-Fermi liquid behaviors at the nematic quantum critical point that is supposed to exist in some $d$-wave cuprate superconductors. This non-Fermi liquid state may be turned into a disorder-dominated diffusive metal if the fermions also couple to a disordered potential that generates a relevant perturbation in the sense of renormalization group theory. It is therefore necessary to examine whether a specific disorder is relevant or not. We study the interplay between critical nematic fluctuation and random chemical potential by performing renormalization group analysis. The parameter that characterizes the strength of random chemical potential is marginal at the one-loop level, but becomes marginally relevant after including the two-loop corrections. Thus even weak random chemical potential leads to diffusive motion of nodal fermions and the significantly critical behaviors of physical implications, since the strength flows eventually to large values at low energies.

16 pages, 12 figures

References in corpus (17)

• The electronic properties of graphene
• Electronic liquid crystal state in the high-temperature superconductor YBCO(6.45)
• Lattice symmetry breaking in cuprate superconductors: Stripes, nematics, and superconductivity
• Formation of a Nematic Fluid at High Fields in Sr3Ru2O7
• Effect of Disorder on Transport in Graphene
• Effect of electron-electron interactions on the conductivity of clean graphene
• Graphene via large N I: Renormalization
• Renormalization group theory of nematic ordering in d-wave superconductors
• Theory of the nodal nematic quantum phase transition in superconductors
• Disorder effect on 3-dimensional $Z_2$ quantum spin Hall systems
• Diffusive Quantum Criticality in Three Dimensional Disordered Dirac Semimetals
• Renormalization group approach to 2D Coulomb interacting Dirac fermions with random gauge potential
• Competition of Fermi surface symmetry breaking and superconductivity
• Experimental observables near a nematic quantum critical point in the pnictide and cuprate superconductors
• Quantum critical point shifts under superconductivity: the pnictides and the cuprates
• Signatures of the nematic ordering transitions in the thermal conductivity of d-wave superconductors
• Velocity renormalization of nodal quasiparticles in d-wave superconductors