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Tailoring Superconductivity with Two-Level Systems

Joshuah T. Heath1,2,*, Alexander C. Tyner1,2, S. Pamir Alpay3,4, Peter Krogstrup5, and Alexander V. Balatsky1,2,†

  • *Contact author: joshuah.heath@mu.ie
  • †Contact author: balatsky@hotmail.com
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Phys. Rev. Lett. 136, 216001 – Published 26 May, 2026

DOI: https://doi.org/10.1103/zdgk-b66f

Abstract

We investigate the impact of two-level systems (TLSs) on superconductivity, treating them as soft modes localized in real space. We show that these defects can either enhance or suppress the superconducting critical temperature, depending on their surface density and average frequency. Using thin-film aluminium as a case study, we quantitatively describe how TLSs modify both the critical temperature and the zero-temperature superconducting gap. Our results thus highlight new opportunities for tailoring material properties through TLS engineering.

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  122. Note that this frequency range corresponds to that of collective vibronic modes resulting from dangling bonds, as discussed in Ref. [70]. While such energies may be directly proportional to the tunnelling amplitudes of TLSs, we do not explicitly incorporate the microscopic specifics of asymmetry energies or tunnelling amplitudes into our study.

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Phys. Rev. Lett. 136, 216001– Published 26 May, 2026
  • Received 7 November 2025
  • Accepted 26 March 2026
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