Exact solution for the resolvent matrix of a generalized tridiagonal Hamiltonian

Dy, K. S.; Wu, Shiyu; Spratlin, T.

doi:10.1103/physrevb.20.4237

Cited by 88 publications

(37 citation statements)

References 12 publications

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“…A number of well-established, numerically exact procedures exist to find the solution of such an equation [23,25]. The power of the realspace Green's function technique is that once G 00 is calculated, all other elements G nn can be found through recursion of the Dyson equation.…”

Section: Surface Green's Functionmentioning

confidence: 99%

Complex band structure of topologically protected edge states

et al. 2014

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One of the great successes of modern condensed matter physics is the discovery of topological insulators (TIs). A thorough investigation of their properties could bring such materials from fundamental research to potential applications. Here, we report on theoretical investigations of the complex band structure (CBS) of two-dimensional (2D) TIs. We utilize the tight-binding form of the Bernevig, Hughes, and Zhang model as a prototype for a generic 2D TI. Based on this model, we outline the conditions that the CBS must satisfy in order to guarantee the presence of topologically protected edge states. Furthermore, we use the Green's function technique to show how these edge states are localized, highlighting the fact that the decay of the edge-state wave functions into the bulk of a TI is not necessarily monotonic and, in fact, can exhibit an oscillatory behavior that is consistent with the predicted CBS of the bulk TI. These results may have implications for electronic and spin transport across a TI when it is used as a tunnel barrier.

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Section: Surface Green's Functionmentioning

confidence: 99%

Complex band structure of topologically protected edge states

et al. 2014

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“…30,37 This method has the obvious drawback of being limited by the possibility of computing analytically the necessary determinants. 38,39 We present in what follows a method that overcomes the technical difficulties above mentioned.…”

Section: Determination Of the Lattice Green's Functionmentioning

confidence: 99%

Lattice Green’s function approach to the solution of the spectrum of an array of quantum dots and its linear conductance

2009

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In this paper we derive general relations for the band-structure of an array of quantum dots and compute its transport properties when connected to two perfect leads. The exact lattice Green's functions for the perfect array and with an attached adatom are derived. The expressions for the linear conductance for the perfect array as well as for the array with a defect are presented. The calculations are illustrated for a dot made of three atoms. The results derived here are also the starting point to include the effect of electron-electron and electron-phonon interactions on the transport properties of quantum dot arrays. Different derivations of the exact lattice Green's functions are discussed.

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“…any block-tridiagonal matrix) is DWSZ method [40][41][42]. Unlike the standard Q R a l g o r i t h m [ 3 2 , 3 3 ] , b a s e d o n i t e r a t i v e o r t h o g o n a l s i m i l a r i t y t r a n s f o r m a t i o n s , it allows u:-i n calculate one selected eigenvector and does not require computer memory space for any N x N matrix.…”

Section: The Number Of Eigenvalues Of S'tm (9) Less Than X Is Equal Tmentioning

confidence: 99%

New Numerical Matrix Methods of Solving the Quasi-One-Dimensional Effective-Mass Equation

et al. 1999

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New efficient numerical methods of computing eigenvalues and eigenvectors of quasi-one-dimensional effective-mass Hamiltonian with arbitrary coordinate dependence of charge carrier mass are presented. Within the proposed approach the effective-mass equation is replaced by a nonsymmetric or symmetric matrix eigenproblem which can be analysed numerically with the help of existing computer routines. The presented methods are verified in special semiconductor heterostructure cases that are solvable within other approaches. A generalization of the presented methods for nonparabolic materials is also discussed.

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Exact solution for the resolvent matrix of a generalized tridiagonal Hamiltonian

Cited by 88 publications

References 12 publications

Complex band structure of topologically protected edge states

Complex band structure of topologically protected edge states

Lattice Green’s function approach to the solution of the spectrum of an array of quantum dots and its linear conductance

New Numerical Matrix Methods of Solving the Quasi-One-Dimensional Effective-Mass Equation

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