Scattering matrix of arbitrary tight-binding Hamiltonians

García, Carlos Ramírez; Medina-Amayo, Luis A.

doi:10.1016/j.aop.2017.01.015

Cited by 7 publications

(24 citation statements)

References 16 publications

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“…Consider a general infinite periodic wire, as schematically shown in Figure (a). S‐matrix of this wire can be obtained as a result of recurrent (infinite) application of the assembly method by using unit layers of Figure (b) or 2(c), where

A_{i}^{false(+ false)}

and

A_{i}^{false(- false)}

are respectively the amplitude coefficients of the right incoming and outgoing waves of attached chains, while

B_{i}^{false(+ false)}

and

B_{i}^{false(- false)}

are those of the left‐side, being

i = 1, 2, \dots, Q

. S‐matrix of the unit layer ( S ) relates the coefficients of incoming and outgoing waves of external chains as

(\begin{matrix} A^{(-)} \\ B^{(-)} \end{matrix}) = S (\begin{matrix} A^{(+)} \\ B^{(+)} \end{matrix}) = (\begin{matrix} {boldS}_{11} & {boldS}_{12} \\ {boldS}_{21} & {boldS}_{22} \end{matrix}) (\begin{matrix} A^{(+)} \\ B^{(+)} \end{matrix})

being

{boldA}^{false(\pm false)}

and

{boldB}^{false(\pm false)}

column vectors of Q rows such as

{(A^{(\pm)})}_{i} = A_{i}^{(\pm)}

and

…”

Section: Extended States Of General Infinite Periodic Wiresmentioning

confidence: 99%

“…Therefore, extended states of a general periodic wire can be determined by obtaining the Bloch solutions of Equation , where amplitude coefficients of inner‐sites may be calculated from that of frontier‐sites . On the other hand, notice that choice of layer is not unique.…”

Section: Extended States Of General Infinite Periodic Wiresmentioning

confidence: 99%

“…Recently, we have proposed a new efficient method to determine S‐matrices of complex arbitrary models described by tight‐binding Hamiltonians by using S‐matrices of simpler sublayers, which are joined together to form the total S‐matrix of the system. This layer assembly method allows us to determine the S‐matrix of systems with complex geometries, including multiterminal cases.…”

Section: Introductionmentioning

confidence: 99%

“…It is worth mentioning that analytical expressions of S‐matrices of two kind of fundamental building blocks, the site‐ and bond‐layers, allow calculation of S‐matrices of arbitrary tight‐binding systems by following the assembly process . An example of the application of this process to calculate S‐matrix of layer A in Figure using exclusively S‐matrices is given in the Supporting Information, where the mentioned building‐block analytical expressions are also given.…”

Section: Introductionmentioning

confidence: 99%

“…In consequence, by calculating the S‐matrix of semi‐infinite leads, with one end connected to external chains, it is possible to determine transport properties of general systems where incoming and outgoing waves are not restricted to those of atomic chains. The particular case of layered leads has already been developed, where sites are connected to their equivalent ones in adjacent layers by the same hopping integral …”

Section: Introductionmentioning

confidence: 99%

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Determining Transport Properties of Complex Multiterminal Systems: S‐Matrix of General Tight‐Binding Periodic Leads

García¹

2017

Annalen der Physik

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Calculation of the scattering matrix (S-matrix) of a system allows direct determination of its transport properties. Within the scattering theory, S-matrices relate amplitudes of incoming and outgoing waves in semi-infinite leads attached to a scattering region. Recently, an assembly method to calculate S-matrices of arbitrary tight-binding systems connected to atomic chains has been proposed, were the S-matrices of subsystems are used to obtain S-matrix of the total system. In this paper, a new efficient method to obtain S-matrices of general periodic leads is established, which can be used in the mentioned assembly method, allowing to address coherent quantum transport of arbitrary multiterminal systems with complex geometries trough Landauer-Büttiker formalism. In addition, a new method to determine extended-state band structures of general infinite periodic wires is presented, which exploits properties of the S-matrix. Finally, these methods are used to obtain band structure of graphene arm-chair and zig-zag nanoribbons and transmission functions in three terminal Z-shaped graphene nanoribbon structures.

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A_{i}^{false(+ false)}

and

A_{i}^{false(- false)}

are respectively the amplitude coefficients of the right incoming and outgoing waves of attached chains, while

B_{i}^{false(+ false)}

and

B_{i}^{false(- false)}

are those of the left‐side, being

i = 1, 2, \dots, Q

. S‐matrix of the unit layer ( S ) relates the coefficients of incoming and outgoing waves of external chains as

(\begin{matrix} A^{(-)} \\ B^{(-)} \end{matrix}) = S (\begin{matrix} A^{(+)} \\ B^{(+)} \end{matrix}) = (\begin{matrix} {boldS}_{11} & {boldS}_{12} \\ {boldS}_{21} & {boldS}_{22} \end{matrix}) (\begin{matrix} A^{(+)} \\ B^{(+)} \end{matrix})

being

{boldA}^{false(\pm false)}

and

{boldB}^{false(\pm false)}

column vectors of Q rows such as

{(A^{(\pm)})}_{i} = A_{i}^{(\pm)}

and

…”

Section: Extended States Of General Infinite Periodic Wiresmentioning

confidence: 99%

Section: Extended States Of General Infinite Periodic Wiresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Determining Transport Properties of Complex Multiterminal Systems: S‐Matrix of General Tight‐Binding Periodic Leads

García¹

2017

Annalen der Physik

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Bound States In and Out of the Continuum in Nanoribbons with Wider Sections: A Novel Algorithm based on the Recursive S‐Matrix Method

Díaz¹,

García²

2022

Annalen der Physik

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A novel method to find bound states in general tight‐binding Hamiltonians with semi‐infinite leads is reported. The method is based on the recursive S‐matrix method, which allows to compute iteratively the S‐matrix of a general system in terms of the S‐matrices of its subsystems. The condition that the S‐matrices of the subsystems must accomplish to have a bound state at energy E is established. Energies that accomplish this relation, can be determined with high accuracy and efficiency by using the Taylor series of the S‐matrices. The method allows to find bound states energies and wavefunctions in (BIC) and out (BOC) of the continuum, including degenerate ones. Bound states in nanoribbons with wider sections are computed for square and honeycomb lattices. Using this method, the bound states in a graphene nanoribbon with two quantum‐dot‐like structures which are reported to have BICs by using another technique are verified. However, this new analysis reveals that such BICs are double, one with even and the other with odd wavefunction, with slightly separated energies. In this way, the new method can be used to efficiently find new BICs and to improve precision in previously reported ones.

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