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

Abstract

We report on the electronic structure, density of states and transmission properties of the periodic one-dimensional Tight-Binding (TB) lattice with a single orbital per site and nearest-neighbor interactions, with a generic unit cell of $u$ sites. The determination of the eigenvalues is equivalent to the diagonalization of a real tridiagonal symmetric $u$-Toeplitz matrix with (cyclic boundaries) or without (fixed boundaries) perturbed upper right and lower 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 states and provide relevant analytical relations. We attach semi-infinite leads, determine and discuss the transmission coefficient at zero bias and investigate the peaks number and position, and the effect of the coupling strength and asymmetry as well as of the lead properties on the transmission profiles. We introduce a generic optimal coupling condition and demonstrate its physical meaning.

23 pages, 20 figures

References in corpus (8)

• Of Bulk and Boundaries: Generalized Transfer Matrices for Tight-Binding Models
• Point Mutations Effects on Charge Transport Properties of the Tumor-Suppressor Gene p53
• Electronic structure and carrier transfer in B-DNA monomer polymers and dimer polymers: Stationary and time-dependent aspects of wire model vs. extended ladder model
• Unbiased charge oscillations in DNA monomer-polymers and dimer-polymers
• Spectral duality and distribution of exponents for transfer matrices of block tridiagonal Hamiltonians
• Insulator-metal transition in biased finite polyyne systems
• One-dimensional models of disordered quantum wires: general formalism
• Wire and extended ladder model predict THz oscillations in DNA monomers, dimers and trimers

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