Nanoscale Conducting and Insulating Domains on YbB_{6}

YbB_{6} is a predicted topological insulator, with experimental evidence for conducting surface states of yet-unproven origin. However, its lack of a natural cleavage plane, and resultant surface-dependent polarity, has obscured its study. We use scanning tunneling microscopy to image the cleaved surface of YbB_{6}, which exhibits several coexisting terminations with distinct atomic structures. Our spectroscopic measurements reveal band bending between the terminations, resulting in both conducting and fully gapped domains. In the conducting domains, we observe spectral peaks that are suggestive of Van Hove singularities arising from Rashba spin-split quantum well states. The insulating domains rule out the possibility that YbB_{6} is a strong topological insulator, while the spin-polarized conducting domains suggest possible utility for spintronic devices.