  A Creutz ladder, is a quasi one dimensional system hosting robust topological
phases with localized edge modes protected by different symmetries such as
inversion, chiral and particle-hole symmetries. Non-trivial topology is
observed in a large region of the parameter space defined by the horizontal,
diagonal and vertical hopping ampitudes and a transverse magnetic flux that
threads through the ladder. In this work, we investigate higher order topology
in a two dimensional extrapolated version of the Creutz ladder. To explore the
topological phases, we consider two different configurations, namely a torus
(periodic boundary) and a ribbon (open boundary) to look for hints of gap
closing phase transitions. We also associate suitable topological invariants to
characterize the non-trivial sectors. Further, we find that the resultant phase
diagram hosts two different topological phases, one where the higher order
topological excitations are realized in the form of robust corner modes, along
with (usual) first order excitations demonstrated via the presence of edge
modes in a finite lattice, for the other.
