  We propose a concept of interfacial symmetries such as interfacial
particle-hole symmetry and interfacial time-reversal symmetry, which appear in
interfaces between two regions related to each other by particle-hole or
time-reversal transformations. These symmetries result in novel dispersion of
interface states. In particular for the interfacial particle-hole symmetry the
gap closes along a loop ("Fermi loop") at the interface. We numerically
demonstrate this for the Fu-Kane-Mele tight-binding model. We show that the
Fermi loop originates from a sign change of a Pfaffian of a product between the
Hamiltonian and a constant matrix.
