A recent study (link) identifies xenon as a realistic candidate for a “beyond the tonne scale” experiment, which could explore 0??? decay with a sensitivity of 10^29-10^30 year sensitivity. The main challenge for the realization of such a large detector is the efficient and affordable procurement of 100s of tons of xenon.
This study was conducted as part of the Snowmass 2021 activities to define the scientific landscape for particle physics for the next decade. Important input to this process was provided by a topical ACFI workshop in December 2020.