Scaling of the superfluid density in high-temperature superconductors

C. C. Homes; S. V. Dordevic; T. Valla; M. Strongin

doi:10.1103/PhysRevB.72.134517

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Scaling of the superfluid density in high-temperature superconductors

C. C. Homes, S. V. Dordevic, T. Valla, M. Strongin

DOI 10.1103/PhysRevB.72.134517 · Physical Review B

T1

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Abstract

A scaling relation Nc≃4.4σdcTc has been observed in the copper-oxide superconductors, where Nc is the spectral weight associated with the formation of the superconducting condensate ρs=8Nc, Tc is the critical temperature, and σdc is the normal-state dc conductivity close to Tc. This scaling relation is examined within the context of a clean and dirty-limit BCS superconductor. These limits are well established for an isotropic BCS gap 2Δ and a normal-state scattering rate 1∕τ; in the clean limit 1∕τ⪡2Δ, and in the dirty limit 1∕τ>2Δ. The dirty limit may also be defined operationally as the regime where ρs varies with 1∕τ. It is shown that the scaling relation Nc or ρs∝σdcTc, which follows directly from the Ferell-Glover-Tinkham sum rule, is the hallmark of a BCS system in the dirty-limit. While the gap in the copper-oxide superconductors is considered to be d wave with nodes and a gap maximum Δ0, if 1∕τ>2Δ0 then the dirty-limit case is preserved. The scaling relation implies that the copper-oxide superconductors are likely to be in the dirty limit and, as a result, that the energy scale associated with the formation of the condensate scales linearly with Tc. The a−b planes and the c axis also follow the same scaling relation. It is observed that the scaling behavior for the dirty limit and the Josephson effect (assuming a BCS formalism) are essentially identical, suggesting that in some regime these two pictures may be viewed as equivalent.

Source-reported materials — not catalogue approval

Formula	Reported Tc (K)	Pressure (GPa)	Type
YBa2Cu3O6.95 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	70	Pressure not reported	unknown
YBa2Cu3O6.95 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	80	Pressure not reported	unknown
YBa2Cu3O6.95 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	85	Pressure not reported	unknown
YBa2Cu3O6.95 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	93.5	Pressure not reported	unknown
YBa2Cu3O6.60 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	59	Pressure not reported	unknown
YBa2Cu3O6.95 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	93.2	Pressure not reported	unknown
YBa2Cu3O7-δ Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	92	Pressure not reported	unknown
Pr-YBa2Cu3O7-δ Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	40	Pressure not reported	unknown
Pr-YBa2Cu3O7-δ Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	75	Pressure not reported	unknown
YBa2Cu4O8 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	80	Pressure not reported	unknown
Bi2Ca2SrCu2O8+δ Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	90	Pressure not reported	unknown
Bi2Ca2SrCu2O8+δ Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	91	Pressure not reported	unknown
Bi2Ca2SrCu2O8+δ Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	85	Pressure not reported	unknown
Y/Pb-Bi2Ca2SrCu2O8+δ Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	35	Pressure not reported	unknown
Y-Bi2Ca2SrCu2O8+δ Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	40	Pressure not reported	unknown
Y-Bi2Ca2SrCu2O8+δ Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	43	Pressure not reported	unknown
Tl2Ba2CuO6+δ Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	88	Pressure not reported	unknown
Nd1.85Ce0.15CuO4 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	23	Pressure not reported	unknown
Pr1.85Ce0.15CuO4 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	19	Pressure not reported	unknown
Pr1.85Ce0.15CuO4 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	21	Pressure not reported	unknown
Pr1.87Ce0.15CuO4 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	16	Pressure not reported	unknown
La1.87Sr0.13CuO4 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	32	Pressure not reported	unknown
La1.86Sr0.14CuO4 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	36	Pressure not reported	unknown
Ba0.62K0.38BiO3 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	31	Pressure not reported	unknown
Ba0.60K0.40BiO3 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	28	Pressure not reported	unknown
Ba0.54K0.46BiO3 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	21	Pressure not reported	unknown
Nb Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	8.3	Pressure not reported	unknown
Nb Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	9.3	Pressure not reported	unknown
Pb Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	7.2	Pressure not reported	unknown