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We report on the electronic structure, density of states and transmissionproperties of the periodic one-dimensional Tight-Binding (TB) lattice with asingle orbital per site and nearest-neighbor interactions, with a generic unitcell of $u$ sites. The determination of the eigenvalues is equivalent to thediagonalization of a real tridiagonal symmetric $u$-Toeplitz matrix with(cyclic boundaries) or without (fixed boundaries) perturbed upper right andlower left corners. We solve the TB equations via the Transfer Matrix Method,producing, analytical solutions and recursive relations for its eigenvalues,closely related to the Chebyshev polynomials. We examine the density of statesand provide relevant analytical relations. We attach semi-infinite leads,determine and discuss the transmission coefficient at zero bias and investigatethe peaks number and position, and the effect of the coupling strength andasymmetry as well as of the lead properties on the transmission profiles. Weintroduce a generic optimal coupling condition and demonstrate its physicalmeaning.

Energy structure, density of states and transmission properties of the periodic 1D Tight-Binding lattice with a generic unit cell of $u$ sites