Spectral anomaly for interacting fermions is characterized by the spectral function A ([k − k F ], ω) satisfying the scaling relation A (Λy1 [k − k F ], Λy2 ω) =ΛyA A ([k − k F ], ω), where y1, y2, and yA are the exponents defining the universality class. For a Fermi liquid y1 = 1, y2 = 1, yA = −1; all other values of the exponents are termed anomalous. In this paper, an example for which y1 = 1, y2 = 1, but yA = α − 1 is considered in detail. Attractive interaction added to such a critical system leads to a novel superconducting state, which is explored and its relevance to high temperature cuprate superconductors is discussed.
In the underdoped, overdoped, Zn-doped or stripe-forming regions of high-Tc cuprate superconductors (HTSC), the superfluid density ns/m* at T→ 0 shows universal correlations with Tc. Similar strong correlations exist between 2-dimensional superfluid density and superfluid transition temperature in thin films of 4 He in non-porous or porous media, and 4 He /3 He film adsorbed on porous media. Based on analogy between HTSC and He film systems, we propose a model for cuprates where: (1) the overdoped region is characterized by a phase separation similar to 4 He /3 He ; and (2) pair (boson) formation and fluctuating superconductivity occur at separate temperatures above Tc in the underdoped region.
Within the kinetic energy driven superconducting mechanism, the doping and temperature dependence of the superfluid density in cuprate superconductors is studied throughout the superconducting dome. It is shown that the superfluid density shows a crossover from the linear temperature dependence at low temperatures to a nonlinear one in the extremely low temperatures. In analogy to the dome-like shape of the doping dependent superconducting transition temperature, the maximal zero-temperature superfluid density occurs around the critical doping δ ≈ 0.195, and then decreases in both lower doped and higher doped regimes.
Superfluid Density of Strongly Underdoped Cuprate Superconductors from a Four-DimensionalXYModel