Journal of Superconductivity and Novel Magnetism

, Volume 32, Issue 12, pp 3773–3777 | Cite as

Parabolic Scaling in Overdoped Cuprate Films

  • Yong TaoEmail author
Original Paper


It was recently reported that, in the highly overdoped side of single-crystal La2 − xSrxCuO4 films, the transition temperature Tc and zero-temperature superfluid phase stiffness ρs(0) will obey a parabolic scaling \( {T}_c=\gamma \bullet \sqrt{\rho_s(0)} \). Parabolic scaling indicates a quantum phase transition from a superconductor to a normal metal, for which there has been scant understanding (Nature 536:309–311, 2016). The current study shows that, using the quantum critical model for zero-temperature Cooper pairs (EPL 118:57007, 2017), parabolic scaling can be exactly derived, where γ = γ(εF, a) is uniquely determined by the Fermi energy εF and the minimal lattice constant a of superconducting materials. For single-crystal La2 − xSrxCuO4 films, we calculate the theoretical value of γ, which yields 4.29 ∙ K1/2 and is in accordance with an experimental measure value (4.2 ± 0.5) ∙ K1/2 with high accuracy. Our formula for γ can be further tested by investigating other BCS-like materials.


Quantum critical phenomena Cuprate films Quantum fluctuation Renormalization group 



The author acknowledges Professor Steven Weinberg for confirming the validity of the lattice spacing as the (ultraviolet) cut-off in solid-state physics.

Funding Information

This work was financially supported by the Fundamental Research Funds for the Central Universities (Grant No. SWU1409444 and Grant No. SWU1809020), the National Natural Science Foundation of China (Grant No. 71773099), and the State Scholarship Fund granted by the China Scholarship Council.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Economics and ManagementSouthwest UniversityChongqingChina
  2. 2.Department of Management, Technology, and EconomicsETH ZurichZurichSwitzerland

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