Title: Extended Kitaev chain with longer-range hopping and pairing,
Abstract: We consider the Kitaev chain model with finite and infinite range in the
hopping and pairing parameters, looking in particular at the appearance of
Majorana zero energy modes and massive edge modes. We study the system both in
the presence and in the absence of time reversal symmetry, by means of
topological invariants and exact diagonalization, disclosing very rich phase
diagrams. In particular, for extended hopping and pairing terms, we can get as
many Majorana modes at each end of the chain as the neighbors involved in the
couplings. Finally we generalize the transfer matrix approach useful to
calculate the zero-energy Majorana modes at the edges for a generic number of
coupled neighbors.