  Second-order topological insulators (SOTIs) are the topological phases of
matter in d dimensions that manifest (d-2)-dimensional localized modes at the
intersection of the edges. We show that SOTIs can be designed via stacked Chern
insulators with opposite chiralities connected by interlayer coupling. To
characterize the bulk-corner correspondence, we establish a
Jacobian-transformed nested Wilson loop method and an edge theory that are
applicable to a wider class of higher-order topological systems. The
corresponding topological invariant admits a filling anomaly of the corner
modes with fractional charges. The system manifests a fragile topological phase
characterized by the absence of a Wannier gap in the Wilson loop spectrum.
Furthermore, we argue that the proposed approach can be generalized to
multilayers. Our work offers perspectives for exploring and understanding
higher-order topological phenomena.
