Perfect valley- and spin-resolved nonlocal Cooper pair splitting in superconducting transition metal dichalcogenides heterojunctions

Abstract In this study, we extend the multi-mode scattering matrix method to study transition metal dichalcogenides based quantum Hall/superconductor/quantum Hall triple terminal heterojunctions. In particular, we focus on the quantum limit case where only the lowest Landau levels are involved in the scattering processes. Due to the valley- and spin-polarized chiral edge states in the quantum limit regime, the Andreev reflection and the elastic cotunneling can be completely shut down. The allowed crossed Andreev reflection and the normal reflection can be tuned by the junction structure parameters, the external magnetic field, and the chemical potentials in the quantum Hall and the superconducting lead. Importantly, the perfect valley- and spin-resolved nonlocal Cooper pair splitting is allowed for the observation with energies lying in the spin splitting band gaps and without applying any bias voltage. The proposed large and even perfect (efficiency = 100% and purity = 100%) valley- and spin-resolved nonlocal Cooper pair splitting can provide a reliable setup for future low-consumption quantum information and quantum computing applications based on group-VI dichalcogenides material.