  Surface bound states in the continuum (SBICs) have been found to occur in
diverse settings, but so far always at the interface of non-homogeneous media,
such as discrete lattices or periodic systems. Here we show that they can also
exist at the interface of homogeneous media, resulting in unique SBICs.
Specifically, we found that, contrary to general belief, leaky Dyakonov states
exist at the interface between materials that exhibit opposite signs of
anisotropy. In addition, properly breaking the anisotropy-symmetry leads to the
formation of both guided states and also SBICs embedded within the continuum. A
direct implication of our finding is the possibility to create SBICs and
Dyakonov states in a whole new class of materials and metamaterials.
