Tunneling of Hydrogen and Deuterium in Niobium: Embedded TLSs in Quantum Devices

Hydrogen (H) and deuterium (D) tunneling in niobium (Nb) trapped by oxygen (O) impurities is a potential source of two-level system (TLS) loss that can limit the performance of quantum devices operating in the 1-10 GHz regime [1]. We report our results based on density functional theory (DFT) and related methods for the trapping energies of H/D at interstitial sites, the double-well potential that determines H/D tunneling states, and the wave functions and tunnel-split levels of of H/D trapped by O at interstitial sites within BCC Nb. We show that O is localized at the octahedral site and that there are several possible sites where H can be trapped in the near vicinity of O. These include the pair of tetrahedral sites proposed by Magerl et al [2]. The calculated energy levels of the ground and first excited states, and thus the tunnel splittings for H and D, compare well with the results reported from low temperature heat capacity measurements and inelastic neutron scattering; JH = 0.19 meV and JD = 0.021 meV. The effects of O strain on the distribution of TLS levels are discussed.

[1] A. Abogoda, et al., DOI:10.48550/arXiv.2409.09014 (2024).

[2] A. Magerl et al., Phys. Rev. B 27, 927 (1983).