Low Concentrations of H, D and O Two-Level Systems in Nb

Hydrogen and deuterium trapped by oxygen or nitrogen are known to form two-level tunneling systems in niobium, with tunnel splittings in the 5-10 GHz range for isolated O-H TLS impurities [1]. Here we report new results for the distribution of tunnel splittings and asymmetry energies for finite concentratios of O-H and O-D TLS impurities. We construct highly accurate machine-learning interatomic potentials (MLIPs) [1,2] validated with density-functional theory (DFT) to map the local potential-energy landscape for H bound to impurity complexes (O and N) in Nb. With these MLIPs we performed three-dimensional quantum-nuclear calculations of ground states and tunneling pathways to extract the TLS parameters. We generate statistical ensembles by sampling realistic impurity configurations. The resulting distributions provide a microscopic bridge between atomic-scale structure and  embedded O-H and O-D TLS distributions that are a source of decoherence in superconducting devices.

[1] Abogoda et al., PRB 111, L020103 (2025).

[2] Batatia et al., NeurIPS (2022).

[3] Batatia et al., arXiv (2022).