  A criterion to determine the existence of zero-energy edge states is
discussed for a class of particle-hole symmetric Hamiltonians. A ``loop'' in a
parameter space is assigned for each one-dimensional bulk Hamiltonian, and its
topological properties, combined with the chiral symmetry, play an essential
role. It provides a unified framework to discuss zero-energy edge modes for
several systems such as fully gapped superconductors, two-dimensional d-wave
superconductors, and graphite ribbons. A variants of the Peierls instability
caused by the presence of edges is also discussed.
