Scaling of the superfluid density in strongly underdopedYBa2Cu3O6+y: Evidence for a Josephson phase

Abstract

Recent measurements on extremely-underdoped YBa2Cu3O6+y [Phys. Rev. Lett. 99, 237003 (2007)] have allowed the critical temperature Tc, superfluid density ρs0 ≡ ρs(T ≪ Tc) and dc conductivity σ dc (T Tc) to be determined for a series of electronic dopings for Tc ≃ 3 − 17 K. The general scaling relation ρs0/8 ≃ 4.4 σ dc Tc is observed, extending the validity of both the ab-plane and c-axis scaling an order of magnitude and creating a region of overlap for the first time. This suggests that severely underdoped materials may constitute a Josephson phase; as the electronic doping is increased a more uniform superconducting state emerges.PACS numbers: 89.75. Da,74.72.Bk,74.25.Gz,74.25.Nf Since the discovery of superconductivity at elevated temperatures in the cuprate materials, there has been a concerted effort to identify empirical scaling relations in the hope of providing insights to the mechanism for superconductivity in these materials. While the nature of the superconductivity remains elusive, it is now generally accepted that in the optimally-doped compounds the superconducting energy gap has a d-wave symmetry. Much of the current research in the cuprate materials focuses on the underdoped compounds where the development of a pseudogap 1 in the antinodal region in the normal state at a characteristic temperature T * leads to the formation of Fermi arcs (or pockets) centered around the nodal regions. 2,3 There is currently a considerable amount of debate as to whether or not the pseudogap represents preformed pairs that simply lack the coherence required for superconductivity, 3 or if superconductivity originates in the Fermi arcs (pockets) and the pseudogap reflects some alternative ground state that competes with superconductivity. 4,5,6 An important scaling relation in the underdoped cuprates is the Uemura relation, 7,8 which notes that the superfluid density at low temperature (ρ s0 ) is proportional to the critical temperature (T c ). The superfluid density is defined here as ρ s0 ≡ 1/λ 2 0 , where λ 0 = λ(T ≪ T c ) is the effective penetration depth. Alternatively, ρ s0 is also referred to as the superfluid stiffness where ρ s0 = 4πn s0 e 2 /m * c 2 , where n s0 is the density of the superconducting carriers and m * is an effective mass. The Uemura relation works well over much of the underdoped region, but does not apply in optimal and overdoped materials. 9 In addition, as the phase diagram for YBa 2 Cu 3 O 6+y has been extended to the severely underdoped regime, 10 the scaling of ρ s0 is observed to change from a linear to power-law relation. 11,12,13,14 In this work we demonstrate that the severelyunderdoped data for YBa 2 Cu 3 O 6+y is in fact consistent with a more general scaling relation ρ s0 /8 ≃ 4.4 σ dc T c where σ dc is the dc conductivity measured at T T c (note that in this representation both σ dc and T c are shown in units of cm −1 , so that the constant is dimensionless and ρ s0 has the units of cm −2 ). 15,16,17 In the cuprates this scaling relation is valid for the copperoxygen plane...

Do organic and other exotic superconductors fail universal scaling relations?

“…(1), to include the SC critical temperature T c , Only data points obtained from optical spectroscopies (IR and MW SI) are included in the plot. The data points are from: cuprates ab-plane [2,11,12], cuprates c-axis [2], pnictides [13,14], elements [2], TiN [15], Ba1−xKxBiO3 [16], MgB2 [17,18], organic SC [19][20][21], fullerenes [22], heavy fermion CeCoIn5 [23], negative-U induced SC TlxPb1−xTe [24] and Y2C2I2 [25].…”

Perspective on the phase diagram of cuprate high-temperature superconductors

“…This relation holds for the underdoped materials and orders different cuprate families with respect to their maximum T c . The Uemura relation and subsequent scaling laws have remained stimulating, up to now, and some were shown to be valid for other superconductors as well23456789. While there are various attempts at a theoretical explanation of the Uemura relation4101112, a connection to other experimentally probed properties of cuprates is still lacking, in particular to material chemistry parameters.…”