Influence of pinholes and weak-points in aluminum-oxide Josephson junctions

Josephson junctions are the key components used in superconducting qubits for quantum computing. The advancement of quantum computing is limited by a lack of stability and reproducibility of qubits, which ultimately originates in the amorphous tunnel barrier of the Josephson junctions and other material imperfections. Pinholes in the junction have been suggested as one of the possible contributors to these instabilities, but evidence of their existence and the effect they might have on transport is unclear. We use molecular dynamics to create three-dimensional atomistic models to describe $\mathrm{Al}\text{\ensuremath{-}}{\mathrm{AlO}}_{x}\text{\ensuremath{-}}\mathrm{Al}$ tunnel junctions, showing that pinholes form when oxidation of the barrier is incomplete. Following this, we use the atomistic model and simulate the electronic transport properties for tunnel junctions with different barrier thicknesses using the nonequilibrium Green's function formalism. We observe that pinholes may contribute to excess quasiparticle current flow in $\mathrm{Al}\text{\ensuremath{-}}{\mathrm{AlO}}_{x}\text{\ensuremath{-}}\mathrm{Al}$ tunnel junctions with thinner barriers, and in thicker barriers we observe weak-points that facilitate leakage currents even when the oxide is continuous. We find that the disordered nature of the amorphous barrier results in significant variations in the transport properties. Additionally, we determine the current-phase relationship for our atomistic structures, confirming that devices with pinholes and weak-points cause a deviation from the ideal sinusoidal Josephson relationship.