Universal properties of cuprate superconductors

Abstract

To provide an understanding of the universal properties emerging from the empirical correlations and phase diagrams of cuprate superconductors, we invoke the scaling theory of finite temperature and quantum critical phenomena. The universal features are traced back to the existence of quantum critical lines, representing the end lines of the finite temperature transition surface. At the respective quantum critical lines 2D superconductor to insulator (2D-QSI) transitions and 3D superconductor to normal state (3D-QSN) transitions occur. The flow to this quantum critical points is tuned by doping, substitution and anisotropy. It is shown that the empirical correlations, like the dependence of Tc on dopant and substitution concentration, the dependence of Tc on zero temperature in-plane penetration depth, etc., reflect universal properties associated with the flow to these quantum critical points and of the crossover from one to the other. A detailed account of the flow to 2D-QSI and 3D-QSN criticality is a challenge for microscopic theories attempting to solve the puzzle of superconductivity in these materials.

11 pages, 6 figures; Invited paper msR-2002

Cited by in corpus (16)

• Magnetic-force-microscope study of interlayer "kinks" in individual vortices in underdoped cuprate YBa${}_2$Cu${}_3$O${}_{6+x}$ superconductor
• Probing inhomogeneities in type II superconductors by means of thermal fluctuations, magnetic fields and isotope effects
• Dependence of the superconducting critical temperature on the number of layers in homologous series of high-Tc cuprates
• Pressure and isotope effect on the anisotropy of MgB${}_2$
• Finite size effect in Bi2Sr2CaCu2O(8+d) and YBa2Cu3O6.7 probed by the in-plane and out of plane penetration depths
• Evidence for Kosterlitz-Thouless and 3D-xy critical behavior in Bi2212
• Relationship between the isotope effects on transition temperature, specific heat and penetration depths
• Implications evinced by the phase diagram, anisotropy, magnetic penetration depths, isotope effects and conductivities of cuprate superconductors
• Relevance of electron-lattice coupling in cuprates superconductors
• Critical charge instability on verge of the Mott transition and the origin of quantum protection in high-$T_c$ cuprates
• Relationship between and implications of the isotope and pressure effects on transition temperature, penetration depths and conductivities
• Evidence for 3D-xy critical properties in underdoped YBa2Cu3O7+x
• Dependence of the superconducting effective mass on doping in cuprates
• On the occurrence of Berezinskii-Kosterlitz-Thouless behavior in highly anisotropic cuprate superconductors
• Implications of the isotope effects on the magnetization, magnetic torque and susceptibility
• Magnetic field induced finite size effect in type-II superconductors