Isotope Effects in Underdoped Cuprate Superconductors: A Quantum Critical Phenomenon

Abstract

We show that the unusual doping dependence of the isotope effects on transition temperature and zero temperature in -plane penetration depth naturally follows from the doping driven 3D-2D crossover, the 2D quantum superconductor to insulator transition (QSI) in the underdoped limit and the change of the relative doping concentration upon isotope substitution. Close to the QSI transition both, the isotope coefficient of transition temperature and penetration depth approach the coefficient of the relative dopant concentration, and its divergence sets the scale. These predictions are fully consistent with the experimental data and imply that close to the underdoped limit the unusual isotope effect on transition temperature and penetration depth uncovers critical phenomena associated with the quantum superconductor to insulator transition in two dimensions. PACS numbers: 74.20. Mn, 74.25Dw, The observation of an unusual isotope effect in underdoped cuprate superconductors on transition temperature [1][2][3] and zero temperature penetration depth [4][5][6][7] poses a challenge to the understanding of high temperature superconductivity. In this letter we show that this behavior naturally follows from the doping driven 3D-2D crossover, the 2D superconductor to insulator (QSI) transition in the underdoped limit and the change of the relative doping concentration upon isotope substitution. Thus, the unusual isotope effect on superconducting properties of underdoped cuprates is derived to be a quantum critical phenomenon driven by variation of the dopant concentration.Consider [23], only the underdoped and optimally doped regimes appear to be accessible. As shown in Fig.1 for La 2−x Sr x CuO 4 the effective mass anisotropy, measured in terms of γ = M c /M ab increases drastically by approaching the underdoped limit. This property, also observed in HgBa 2 CuO 4+δ [20] and YBa 2 Cu 3 O 7−x [22], appears to be generic and reveals the crossover from three (3D) to two dimensional (2D) behavior.In our considerations the starting point is the critical endpoint of the phase transition line T c (x), where at T = 0 and x = x u , driven by variation of the dopant concentration x, the QSI transition occurs. Close to this critical endpoint the bulk superconductors correspond to a stack of independent superconducting slabs of thickness d s . Moreover, close to such a critical point, low energy properties depend only on the spatial dimensionality of the system, the number of components of the order parameter and the range of the interaction. The theory of quantum critical phenomena predicts that the transition temperature and zero temperature in -plane penetration depth scale as [24,17,18] z is the dynamic critical exponent, ν the exponent of the diverging length, a and b nonuniversal critical amplitudes, andmeasures the distance from the quantum critical point at x u , where in cuprate superconductors the QSI transition occurs. For a complex scalar order parameter and in D=2 the critical amplitudes a and b and the slab thickness d s ...

Oxygen isotope effect on the superconductivity and stripe phase inLa1.6−xNd0.4SrxCuWang1, Zhang2, Yang3 et al. 2007Phys. Rev. B9120View full textAdd to dashboardCite

“…The suppression of T C compared with La 2−x Sr x CuO 4 [32] is attributed to the static stripe phase induced by the substitution of Nd for La atoms [7]. The abnormal suppression on T C near 1/8 doping can be clearly seen in our samples, that is, the T c is the least for the sample with x=0.125.…”

“…This used to be successful in explaining the isotope effect in most of conventional superconductors, but failed in explaining the isotope effect in high T C superconductor [32]. Especially in La 2−x Sr x CuO 4 [26,27,28,29] the isotope exponent around 1/8 doping is about 1.…”

Gutzwiller scheme for electrons and phonons: The half-filled Hubbard-Holstein model

“…This problem has recently received a renewed attention, after a number of experiments on high-T c superconducting cuprates testified for a non trivial role of the e-ph coupling in the underdoped region, where correlation effects are important and standard e-ph theories are hardly reliable 3,4,5,6,7 . Indeed a full theoretical understanding of lattice effects in strongly-correlated systems is still lacking when the two interactions have intermediate or large strength.…”

Universal properties of cuprate superconductors

“…Thus, the isotope effect does not provide information on the pairing mechanism. Moreover, the empirical fact that β is very small close to optimum doping [27] implies that the combined effects on penetration depths and specific heat nearly cancel in this regime.…”