  The non-Hermitian skin effect under open boundary conditions is widely
believed to originate from the intrinsic spectral topology under periodic
boundary conditions. If the eigenspectra under periodic boundary conditions
have no spectral windings (e.g., piecewise arcs) or a finite area on the
complex plane, there will be no non-Hermitian skin effect with open boundaries.
In this article, we demonstrate another scenario beyond this perception by
introducing a two-dimensional periodically driven model. The effective Floquet
Hamiltonian lacks intrinsic spectral topology and is proportional to the
identity matrix (representing a single point on the complex plane) under
periodic boundary conditions. Yet, the Floquet Hamiltonian exhibits a
second-order skin effect that is robust against perturbations and disorder
under open boundary conditions. We further reveal the dynamical origin of these
second-order skin modes and illustrate that they are characterized by a
dynamical topological invariant of the full time-evolution operator.
