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Trapping and Tunneling of Hydrogen, Deuterium and Oxygen in Niobium

Abdulaziz Abogoda, J. A. Sauls

TL;DR

This work addresses the microscopic origin of two-level tunneling systems in Nb by identifying O–H/O–D trapping configurations using a DFT-trained MACE machine-learning interatomic potential, uncovering a lower-energy edge trapping site in addition to the known Magerl face site. It computes a 3D potential-energy surface for O–H/O–D tunneling and solves the 3D Schrödinger equation to obtain tunnel splittings, finding J_H and J_D values of 0.414 meV (≈100 GHz) and 0.024 meV (≈5.80 GHz) for the face site, and 0.275 meV (≈66.5 GHz) and 0.014 meV (≈3.39 GHz) for the edge site, with good agreement to 1D NEB results and experimental TLS data. The edge site is energetically favored (trapping energy around -62 vs -11 for the face), and a static-lattice treatment yields trends similar to NEB but may overestimate barriers due to neglect of lattice dynamics. The authors argue for future work using adiabatic potential-energy surfaces and phonon coupling to capture H/D tunneling more accurately, highlighting implications for TLS-related losses in Nb-based superconducting devices.

Abstract

We investigate isolated O-H and O-D pairs trapped in BCC Nb using a machine-learning interatomic potential (MLIP) trained to density-functional theory (DFT). The MLIP enables large-supercell analysis and identification of trapping sites within BCC Nb, as well as efficient mapping of three-dimensional (3D) potential-energy surfaces. In addition to the pair of tetrahedral``face'' sites previously identified based on DFT, we identify a lower-energy pair of ``edge'' trapping sites and confirm the stability of H and D at these trapping sites with DFT. We solve the Schrödinger equation for H and D in the 3D potential that surrounds the trapping sites. Solutions based on the static-lattice limit yield tunnel splittings in the range $J/h \in\{3-100\}$ GHz for both trapping sites.

Trapping and Tunneling of Hydrogen, Deuterium and Oxygen in Niobium

TL;DR

This work addresses the microscopic origin of two-level tunneling systems in Nb by identifying O–H/O–D trapping configurations using a DFT-trained MACE machine-learning interatomic potential, uncovering a lower-energy edge trapping site in addition to the known Magerl face site. It computes a 3D potential-energy surface for O–H/O–D tunneling and solves the 3D Schrödinger equation to obtain tunnel splittings, finding J_H and J_D values of 0.414 meV (≈100 GHz) and 0.024 meV (≈5.80 GHz) for the face site, and 0.275 meV (≈66.5 GHz) and 0.014 meV (≈3.39 GHz) for the edge site, with good agreement to 1D NEB results and experimental TLS data. The edge site is energetically favored (trapping energy around -62 vs -11 for the face), and a static-lattice treatment yields trends similar to NEB but may overestimate barriers due to neglect of lattice dynamics. The authors argue for future work using adiabatic potential-energy surfaces and phonon coupling to capture H/D tunneling more accurately, highlighting implications for TLS-related losses in Nb-based superconducting devices.

Abstract

We investigate isolated O-H and O-D pairs trapped in BCC Nb using a machine-learning interatomic potential (MLIP) trained to density-functional theory (DFT). The MLIP enables large-supercell analysis and identification of trapping sites within BCC Nb, as well as efficient mapping of three-dimensional (3D) potential-energy surfaces. In addition to the pair of tetrahedral``face'' sites previously identified based on DFT, we identify a lower-energy pair of ``edge'' trapping sites and confirm the stability of H and D at these trapping sites with DFT. We solve the Schrödinger equation for H and D in the 3D potential that surrounds the trapping sites. Solutions based on the static-lattice limit yield tunnel splittings in the range GHz for both trapping sites.
Paper Structure (6 sections, 4 figures, 1 table)

This paper contains 6 sections, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. MLIP training
  3. Trapping Sites
  4. Tunnel Splittings
  5. Summary and Outlook
  6. Acknowledgments

Figures (4)

  • Figure 1: (a) The Magerl or "face" site, and (b) the "edge" site. Red is O, gray is H, dark green is Nb in ideal BCC lattice, and light green are displaced Nb according to the method in section \ref{['sec-splittings']}.
  • Figure 2: Contour plots of the PES of H in (a) the face configuration and (b) the edge configuration. while centered on the bottom of the energy well in the z axis. Each contour represents 50. The Gray box is the simulation box. The conventional cell is extracted from the center of the 4x4x4 supercell with the boundaries representing the dimensions of an unperturbed cell. Open circles mark the in-plane projection of atomic sites, green is Nb, red is O.
  • Figure 3: Cross sections of wavefunctions (w.f.) of the face configuration $z=z_\text{max}$ were $z_\text{max}$ is the $z$ coordinate at which $|\phi|$ attains its maximum. Top (bottom) row is H (D). Left column shows the ground state (symmetric w.f.), while the right column shows the excited state (antisymmetric w.f.). Densities in panels: (a) $\phi_{\mathrm{H},0}$, (b) $\phi_{\mathrm{H},1}$, (c) $\phi_{\mathrm{D},0}$, and (d) $\phi_{\mathrm{D},1}$. The gray rectangle is the simulation box. The conventional cell is extracted from the center of the 4x4x4 supercell with the boundaries representing the dimensions of an unperturbed unit cell. Open circles mark the in-plane projection of atomic sites: green is Nb, red is O.
  • Figure 4: Descriptions are the same as those in Fig. \ref{['fig-wf-T3']}, but for the edge configuration.