  We study type IIB supergravity solutions that are dual to two-dimensional
superconformal defects in $d=4$ SCFTs which preserve $\mathcal{N}=(0,2)$
supersymmetry. We consider solutions dual to defects in $\mathcal{N}=4$ SYM
theory that have non-trivial monodromy for $U(1)^3\subset SO(6)$ global
symmetry and we also allow for the possibility of conical singularities. In
addition, we consider the addition of fermionic and bosonic mass terms that
have non trivial dependence on the spatial directions transverse to the defect,
while preserving the superconformal symmetry of the defect. We compute various
physical quantities including the central charges of the defect expressed as a
function of the monodromy, the on-shell action as well as associated
supersymmetric Renyi entropies. Analogous computations are carried out for
superconformal defects in the $\mathcal{N}=1$, $d=4$ Leigh-Strassler SCFT. We
also show that the defects of the two SCFTs are connected by a line of bulk
marginal mass deformations and argue that they are also related by bulk RG
flow.
