Abstract Body

High-temperature superconductivity in cuprates is induced by carrier doping, and its physical properties depend on the carrier concentration (p). To understand the mechanism, it is necessary to clarify the p-dependence of various properties. The coherence length ξ_ab and the magnetic penetration depth λ_ab are fundamental parameters of superconductivity. However, the p-dependence of the upper critical field (H_c2||c ~ 1/ξ_ab²), for example, has only recently been established since it exceeds 100 T at low temperatures. λ_ab is also a fundamental parameter, but few studies have systematically evaluated it using single crystals. Furthermore, the details of the p-dependence of the superconducting parameters of B-i2212, one of the typical copper oxides, have not yet been established. Therefore, we attempted to systematically evaluate the p-dependence of ξ_ab and λ_ab for B-i2212 single crystals.

Bi-2212 single crystals were grown using the floating zone technique. One single crystal was cut into several pieces and post-annealed to prepare same quality samples with different carrier concentrations (p = 0.10-0.20). To determine H_c2, the irreversible magnetic field H_irr(T) was evaluated by magnetization hysteresis measurements (H // c) up to 24 T using the 25 T cryogen-free superconducting magnet (25T-CSM) at the High Field Laboratory for Superconducting Materials, Tohoku University. At low temperatures, where H_irr(T) > 24 T, the magnetic field dependence of the pinning force density F_p was evaluated and the Dew-Hughes’s scaling law^[1] was used to estimate H_irr(T). H_irr(0), extrapolated from the H_irr(T), was used as H_c2(0), as same as recent studies for Y- and Hg-based materials^[2,3]. The magnetic field penetration depth λ_ab was evaluated from the London model (dM/d(lnH) = Φ₀/8πμ₀λ_ab²) by measuring the magnetic field dependence of reversible magnetization at several temperatures. The d-wave model was used to fit the T-dependent super-fluid density 1/λ_ab²(T) to obtain 1/λ_ab²(0)^[4].

H_irr(0)≃H_c2(0) – p is plotted in Fig.(a) as orange circles. H_irr(0) increases with increasing p from 70 T at p ~ 0.10 (under dope, UD) to a maximum of 170 T at p ~ 0.20 (over dope, OD). In OD, the behavior of increasing H_irr despite decreasing T_c has also been reported for both Y- and Hg-based materials^[2,3]. The 1/λ_ab²(0) (blue diamonds) also shows a monotonous increase toward OD. This result is approximately consistent with the AC susceptibility^[5] and specific heat^[6] measurements of 1/λ_ab²(0) - p. The condensation energy (E_cond) was calculated from ξ and λ. The result of E_cond - p is shown in Fig. (b) (green circles), and T_c (open circles) is also shown. E_cond increased monotonically with p. While p ~ 0.12 (UD) and p~ 0.20 (OD) have similar T_c ~ 75 K, the E_cond values are 6 × 10⁴ J/m³ and 3.0 × 10⁵ J/m³, respectively, a fivefold difference.

As described above, we obtained a systematic p-dependence of the superconducting parameters. It was revealed that T_c and E_cond show completely different p-dependencies. These will be discussed including the other cuprates materials and the other physical properties.

Fig. (a) Doping dependence of irreversibility field H_irr (orange circles) and superfluid density 1/λ_ab² (blue diamonds) at T = 0 K.
Fig. (b) Doping dependence of condensation energy E_cond (green circles) with critical temperature T_c (open circles).

References

[1] D. D. Hughes, Phil. Mag. 30, 293 (1974)
[2] G. Grissonnaanche et. al. Nat. Commun. 5, 3280 (2014)
[3] M. K. Chan et. al. Proc. Natl. Aca. Sci. U.S.A. 117, 9782 (2020)
[4] R. J. Radtke et. al., PRB 53, R522 (1996).
[5] W. Anukool et. al., PRB 80, 024516 (2009).
[6] J. L. Tallon et. al., PRB 101, 174512 (2020).

Acknowledgment

This work was supported by the Japan society for the promotion of science (JSPS) ; grant in aid for scientific research (JP 21H01377)
This work was performed at the High Field Laboratory for Superconducting Materials, Institute for Materials Research, Tohoku University (Project 202112-HMKPA-0025)