  A higher order topological insulator is an extended notion of the
conventional topological insulator, which belongs to a special class of
topological insulators where the conventional bulk-boundary correspondence is
not applicable. The bulk topological index may be described by the Wannier
center located at a high symmetry point of the crystal. In this paper we
propose minimal models for the second-order topological insulator in two
dimensions and the third-order topological insulator in three dimensions. They
are anisotropic two-band models with two different hopping parameters. The
two-dimensional model is known to capture the essential physics of phosphorene
near the Fermi level. It has so far been recognized as a trivial insulator due
to the absence of topological edge states in nanoribbons. However, we
demonstrate the emergence of topological boundary states in zero dimension,
i.e., in nanodisks. In particular, the diamond structure exhibits such
topological states at two corners, each of which carries a 1/2 fractional
charge. We predict that these corner states will be observed in the diamond
structure of phosphorene.
