  Skin effect that all eigenmodes within a frequency range become edge states
is dictated by the topological properties of complex eigenvalues unique in
non-Hermitian systems. The prevailing attempts to realize such a fascinating
effect are confined to either one-dimensional or nonreciprocal systems
exhibiting asymmetric couplings. Here, inspired by a recent model Hamiltonian
theory, we propose a realistic reciprocal two-dimensional (2D) photonic crystal
(PhC) system that shows the desired skin effect. Specifically, we establish a
routine for designing such non-Hermitian systems via revealing the inherent
connections between the non-trivial eigenvalue topology of order-2 exceptional
points (EPs) and the skin effects. Guided by the proposed strategy, we
successfully design a 2D PhC that possesses the EPs with nonzero eigenvalue
winding numbers. The spectral area along a specific wavevector direction is
then formed by leveraging the symmetry of the macroscopic geometry and the unit
cell. The projected-band-structure calculations are performed to demonstrate
that the desired skin effect exists at the specific crystalline interfaces. We
finally employ time-domain simulations to vividly illustrate this phenomenon by
exciting a pulse at the center of a finite-sized PhC. Our results form a solid
basis for further experimental confirmations and applications of the skin
effect.
