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Anharmonic lattice dynamics and superconductivity in strained bulk and surface niobium

Mihir Ranjan Sahoo1, Roman Lucrezi2, Pedro Nunes Ferreira1, Chia-Nien Tsai3, Matthew Julian4, Rohit P. Prasankumar4, Mahmoud I. Hussein3,5, and Christoph Heil1,*

  • *Contact author: christoph.heil@tugraz.at
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Phys. Rev. B 114, 254508 – Published 9 November, 2026

DOI: https://doi.org/10.1103/tn2d-vjy1

Abstract

Using first-principles calculations, we investigate how homogeneous strain and crystallographic surface orientation modify the vibrational and superconducting properties of niobium. For bulk Nb, tensile strain strongly softens the phonon spectrum and enhances the electron-phonon coupling, increasing the superconducting transition temperature within the harmonic approximation from 9.5 K at equilibrium to 14.6 K at ∼6% lattice expansion. Anharmonic corrections are small near equilibrium but become increasingly significant under tensile strain and considerably reduce this enhancement at large expansion. For ultrathin Nb slabs with low-index (001), (110), and (111) surface orientations, harmonic phonon calculations exhibit imaginary modes, showing that anharmonic lattice effects are essential. To treat these effects efficiently, we train Nb-specific machine-learning interatomic potentials on bulk and slab first-principles configurations and use them to accelerate stochastic self-consistent harmonic approximation calculations, thereby obtaining anharmonically renormalized phonon modes that are combined with density-functional perturbation theory electron–phonon matrix elements to construct the Eliashberg spectral function. Among the three clean free-standing slabs examined, Nb(001) exhibits the strongest electron-phonon coupling and the highest calculated transition temperature of 10.1 K, while Nb(110) and Nb(111) show progressively reduced pairing strength. Finally, by analyzing the Eliashberg spectral function and the functional derivative δTc/δα2F(ω), we identify the phonon energy ranges most effective for superconducting pairing. Our results show that strain, surface termination, and anharmonic phonon renormalization provide complementary and interrelated microscopic routes for tuning superconductivity in Nb.

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Phys. Rev. B 114, 254508– Published 9 November, 2026
  • Received 1 June 2026
  • Revised 19 October 2026
  • Accepted 21 October 2026
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