A novel efficient method to calculate the scattering matrix (SM) of arbitrary tight-binding Hamiltonians is proposed, including cases with multiterminal structures. In particular, the SM of two kind of fundamental structures are given, which can be used to obtain the SM of bigger systems iteratively. Also, a procedure to obtain the SM of layer-composed periodic leads is described. This method allows renormalization approaches, which permits computations over macroscopic length systems without introducing additional approximations. Finally, the transmission coefficient of a ring-shaped multiterminal system and the transmission function of a square-lattice nanoribbon with a reduced width region are calculated.
Phone number: þ52 55 5622 4634, Fax number: þ52 55 5616 1251In this paper, the dc electronic transport at zero temperature in aperiodic systems with macroscopic length is studied by using a real-space renormalization plus convolution method developed for the Kubo-Greenwood formula within the tight-binding formalism. We analytically prove the existence of transparent states in several generalized Fibonacci lattices, as well as in segmented linear chains, where they always appear if the number of bonds in each segment is even, regardless the ordering of segments. For two-dimensional square-lattice tapes with a periodic or non-periodic Fanoimpurity plane, we found a novel ballistic transport state in the dc conductance spectra.
This paper presents an accurate highly efficient method for solving the bound states in the one-dimensional Schrödinger equation with an arbitrary potential. We show that the bound state energies of a general potential well can be obtained from the scattering matrices of two associated scattering potentials. Such scattering matrices can be determined with high efficiency and accuracy, leading us to a new method to find the bound state energies. Moreover, it allows us to find the associated wavefunctions, their norm, and expected values. The method is validated by comparing solutions of the harmonic oscillator and the hydrogen atom with their analytical counterparts. The energies and eigenfunctions of Lennard-Jones potential are also computed and compared to others reported in the literature. This method is highly parallelizable and produces results that reach machine precision with low computational effort. A parallel implementation of this method written in FORTRAN is included in the Supplemental material to solve eigenstates of the Lennard-Jones potential.
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