Parabolic Scaling in Overdoped Cuprate: a Statistical Field Theory Approach

Yong Tao

doi:10.1007/s10948-019-05337-9

paper

Parabolic Scaling in Overdoped Cuprate: a Statistical Field Theory Approach

arXiv:2002.11469 · doi:10.1007/s10948-019-05337-9

Abstract

Recently, Bozovic et al. reported that [Nature 536, 309-311 (2016)], in the overdoped side of the single-crystal $L a_{2 - x} S r_{x} C u O_{4}$ (LSCO) films, the transition temperature $T_{c}$ and zero-temperature superfluid phase stiffness $ρ_{s} (0)$ will obey a two-class scaling law: $T_{c} = γ \cdot ρ_{s} (0)$ for $T_{c} \leq T_{Q}$ and $T_{c} \propto ρ_{s} (0)$ for $T_{c} \geq T_{M}$ , where $γ = (4.2 \pm 0.5) K^{1/2}$ , $T_{Q} \approx 15 K$ , and $T_{M} \approx 12 K$ . They further pointed out that the parabolic scaling observed in the highly overdoped side indicates a quantum phase transition from a superconductor to a normal metal. In this paper, we propose a quantum partition function (QPF) for zero-temperature Cooper pairs, by which one can effectively distinguish between mean-field and quantum critical behaviors. We theoretically show that the two-class scaling law can be exactly derived by using the QPF, and the theoretical values of $γ$ , $T_{Q}$ , and $T_{M}$ are well in accordance with experimental measure values. Our analyses indicate that the linear scaling $T_{c} \propto ρ_{s} (0)$ is a mean-field behavior, while the parabolic scaling $T_{c} = γ \cdot ρ_{s} (0)$ is a quantum critical behavior.

arXiv comment24 pages, 1 figure, 1 table

Parabolic Scaling in Overdoped Cuprate: a Statistical Field Theory Approach

Abstract

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