  Su-Schrieffer-Heeger (SSH) model on two-dimensional square lattice exhibits a
topological phase transition, which is related to the Zak phase determined by
bulk band topology. The strong modulation of electron hopping causes nontrivial
charge polarization even in the presence of inversion symmetry. The energy band
structures and topological edge states have been calculated numerically in
previous studies. Here, however, full energy spectrum and explicit form of wave
functions for two-dimensional bulk and one-dimensional ribbon geometries of SSH
model are analytically derived using wave mechanics approach. Explicit analytic
representations of wave functions provide the information of parity for each
subband, localization length and critical point of topological phase transition
in SSH ribbon. It is also shown that the dimensional crossover of topological
transition point for SSH model from one to two-dimension.
