  Edge states of semi-infinite nanowires in tight binding limit are examined.
We argue that understanding these edge states provides a pathway to generic
comprehension of surface states in many semi-infinite physical systems. It is
shown that the edge states occur within the gaps of the corresponding bulk
spectrum (thus also called the midgap states). More importantly, we show that
the presence of these midgap states reflects an underlying generalized
supersymmetry. This supersymmetric structure is a generalized rotational
symmetry among sublattices and results in a universal tendency: all midgap
states tend to vanish with periods commensurate with the underlying lattice.
Based on our formulation, we propose a structure with superlattice in hopping
to control the number of localized electronic states occurring at the ends of
the nanowires. Other implications are also discussed. In particular, it is
shown that the ordinarily recognized impurity states can be viewed as disguised
midgap states.
