1984
DOI: 10.1088/0305-4608/14/5/016
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Quick iterative scheme for the calculation of transfer matrices: application to Mo (100)

Abstract: The transfer matrix of a solid described by the stacking of principal layers is obtained by an iterative procedure which takes into account 2" layers after n iterations, in contrast to usual schemes where each iteration includes just one more layer. The Green function and density of states at the surface of the corresponding semi-infinite crystal are then given by well known formulae in terms of the transfer matrix. This method, especially convenient near singularities, is applied to the calculation of the spe… Show more

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Cited by 1,117 publications
(547 citation statements)
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References 22 publications
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“…Then the Green's functions are obtained using a highly convergent iterative method and we calculate the local density of states (LDOS) for both the edge principal layer and the bulk principal layer from them (25,26). This method is employed to describe an edge of the semiinfinite 2D system and it provides the clear connectivity between the edge states and the bulk states.…”
Section: Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…Then the Green's functions are obtained using a highly convergent iterative method and we calculate the local density of states (LDOS) for both the edge principal layer and the bulk principal layer from them (25,26). This method is employed to describe an edge of the semiinfinite 2D system and it provides the clear connectivity between the edge states and the bulk states.…”
Section: Resultsmentioning
confidence: 99%
“…To figure out the band topology of each phase, we employ the direct computation method of the Z 2 invariant on a lattice Brillouin zone (BZ) which is based on the recent development in the lattice gauge theory (23,24). Also, we examine the edge state dispersion from the edge Green's functions (25,26) and it is found to be consistent with the Z 2 invariants of the 2D bands. …”
mentioning
confidence: 99%
“…The MLWF hopping parameters for the bulk part can be constructed from the bulk ab initio calculation, and the ones for the surface slab can be constructed from the ab initio calculation of the slab, in which the surface correction to the lattice constants and band structure have been considered self-consistently and the chemical potential is determined by the charge neutrality condition. With these bulk and surface MLWF hopping parameters, we use an iterative method 23,24 to obtain the surface Green's function of the semi-infinite system. The imaginary part of the surface Green's function is the local density of states (LDOS), from which we can obtain the dispersion of the surface states.…”
Section: Topological Surface Statesmentioning
confidence: 99%
“…A principal layer is defined as the smallest group of neighboring atomic planes such that only nearest-neighbor interactions exist between PLs [14]. Here, we extend this concept also for one-dimensional systems, such as carbon nanotubes, considering that a PL in this case is the smallest group of neighboring atoms, instead of infinite slabs (see Fig.…”
Section: B Green's Function and The Density Matrixmentioning
confidence: 99%
“…In this implementation we have used the recursive algorithm described in Ref. [14], although other options can also be employed [12].…”
Section: Retarded Green's Function Of the Central Regionmentioning
confidence: 99%