Bottom-up modeling of topological material-based Josephson junctions

Superconducting circuits with Josephson junctions are currently one of the most promising platforms for realizing scalable qubit architectures, with the low-energy states of the circuit forming the qubit states. The qubit properties are strongly dependent on the characteristics of the integrated Josephson junctions, which are in turn dictated by the design of the structure and the materials used. In this context, we will explore the properties of Josephson junctions based on topological materials, such as (magnetic) topological insulators, and benchmark their performance in superconducting qubit architectures. These materials have various interesting and unique properties that may provide significant advantages over the conventional materials, e.g., they can host topologically protected ballistic channels and elusive Majorana fermion-like quasiparticles.

To obtain the detailed characteristics of topological material-based (two-terminal as well as multiterminal) Josephson junctions and optimize their design for integration in superconducting qubit architectures, we will simulate topological material-based Josephson junctions from the bottom up, employing tight-binding models and the Green's function formalism. The envisioned modeling approach allows us to take into account all the relevant material as well as structural properties that can be tailored to experimentally realizable designs. Furthermore, the impact of an external magnetic field and various imperfections (e.g., impurities or disorder) can be considered. 

Based on these simulation results, the properties of various superconducting qubit architectures, such as transmon qubits, will be extracted and benchmarked against the conventional designs.