Universal Critical Quantum Properties of Cuprate Superconductors

Abstract

Using the scaling theory of quantum critical phenomena we explore the occurrence of universal critical behavior at the insulator-to-superconductor and superconductor-to-normal state transitions at zero temperature. Experimentally, these phase transitions are driven by doping and correspond to critical end points of the phase transition łine in the temperature-hole concentration plane. Provided that the order parameter is a complex scalar in two dimensions, and that the London relation between superfluid number density and magnetic penetration depth holds, the scaling theory predicts universal behavior close to the insulator-to-superconductor transition. In particular, transition temperature and zero temperature penetration depth are universally related and the sheet resistance adopts a universal value. These predictions agree remarkably well with available experimental data and provide useful constraints for a microscopic theory.PACS numbers: 74.62.Dh Many physical properties of cuprate superconductors depend on hole doping. The generic doping dependence of the transition temperature Tc is depicted in Fig. 1. At a certain doping level, the so-called underdoped limit, these materials undergo at the hole concentration x" and T > O a transition from insulator to anomalous metal, and at T = O a transition from insulator to superconductor. As x is increased, Tc rises and reaches its maximum at x m . This behavior is shared by many cuprates, . In some compounds a further increase in the doping level leads to more metallic normal-state properties [8,9], but T, decreases and vanishes in the overdoped limit xo. Here, these materials undergo at T = O a superconductor-to-normal-state transition. A prominent example is La2_x S rx C uO4 _ δ [2].Another essential and doping-dependent property is the effective mass an-

Electric field control of the LaAlO3/SrTiO3 interface ground state

“…The control parameter of the phase transition is the variation of the carrier concentration δn 2D = n 2D − n 2Dc , where n 2Dc is the sheet carrier density at the critical point. phenomena [20,21,22] the phase transition line T BKT (δV ) presented in Fig. 3 is expected to scale, in the vicinity of the quantum critical point (QCP), as…”

D-XY critical behavior in cuprate superconductors

“…Here the materials correspond to a stack of independent sheets of thickness d s As there is a phase transition line with an endpoint T c (x = x u ) = 0, one expects a doping driven 2D-XY insulator to superconductor transition at T = 0. For such a transition the scaling theory of quantum critical phenomena predicts [19][20][21] …”

Implications evinced by the phase diagram, anisotropy, magnetic penetration depths, isotope effects and conductivities of cuprate superconductors

“…Thus, given a family of cuprate superconductors, characterized by T c (x m ) and γ T (x m ), it gives a universal perspective on the interplay between anisotropy and superconductivity. [1,2,4,6,7] , ( , Tc (xm) = 37K, γT =0 (xm) = 14.9) [8,9] Close to 2D-QSI criticality various properties are not independent but related by [13][14][15][16][17][18]…”

“…8 well off the 2D-QSI behavior T c ∝ 1/λ 2 ab (0) now scale nearly onto a single line. Thus the approximate 3D-XY scaling relation (13), together with the empirical doping dependence of the c-axis correlation length (Eqs. (14) and (15)) are consistent with the available experimental data for La 2−x Sr x CuO 4 and uncovers the relevance of the anisotropy.…”