Direct evaluation of the isotope effect within the framework of density functional theory for superconductors

Martin Lüders, Pierluigi Cudazzo, Gianni Profeta, Alessandra Continenza, Sandro Massidda, Antonio Sanna, E. K.U. Gross

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Within recent developments of density functional theory, its numerical implementation and of the superconducting density functional theory is nowadays possible to predict the superconducting critical temperature, Tc, with sufficient accuracy to anticipate the experimental verification. In this paper we present an analytical derivation of the isotope coefficient within the superconducting density functional theory. We calculate the partial derivative of Tc with respect to atomic masses. We verified the final expression by means of numerical calculations of isotope coefficient in monatomic superconductors (Pb) as well as polyatomic superconductors (CaC6). The results confirm the validity of the analytical derivation with respect to the finite difference methods, with considerable improvement in terms of computational time and calculation accuracy. Once the critical temperature is calculated (at the reference mass(es)), various isotope exponents can be simply obtained in the same run. In addition, we provide the expression of interesting quantities like partial derivatives of the deformation potential, phonon frequencies and eigenvectors with respect to atomic masses, which can be useful for other derivations and applications.

Original languageAmerican English
Article number334001
JournalJournal of Physics Condensed Matter
Issue number33
StatePublished - 2019
Externally publishedYes

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© 2019 IOP Publishing Ltd.


  • CaC6
  • isotope effect
  • superconductivity


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