The materials science of Josephson junctions in-silico: modelling their formation and electrical response from an atomistic point of view

The key component of superconducting qubits is the Josephson junction, and at the moment most of these qubits use aluminium-oxide junctions. The electronic properties of such junctions are strongly dependent on the morphology of the barrier, both at the interfaces of the superconducting leads and within the metal oxide itself. Using computational techniques we analyse both how the junctions are formed and how their electrical response depends on the junction microstructure. We perform molecular dynamics simulations of the oxidation and deposition process, in order to develop atomistic models of aluminium-oxide tunnel junctions. By simulating the fabrication process, we aim to determine what characteristics naturally emerge from the fabrication process, and how they can be controlled by modifying the fabrication conditions. To understand the electrical response of these model junctions, we capture the physics of the oxide using a three-dimensional electrostatic potential computed from molecular dynamics simulations, and then use a non-equilibrium Green's functions formalism to determine the resulting charge movement through the junction. This allows us to study the influence of oxide density, stoichiometry, defects and pin-holes on the resulting circuit response. Our results provide new insights into the influence of fabrication conditions on the electrical response of metal-oxide barriers and the performance of superconducting qubits constructed from them.