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

García, Carlos Ramírez

doi:10.1002/andp.201700170

Cited by 4 publications

(7 citation statements)

References 36 publications

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“…The RSMM allows us to calculate the S-matrix of a tight-binding system in terms of the Smatrices of its subsystems [5,6]. Examples of these systems are shown in Fig.…”

Section: Recursive Scattering Matrix Methods (Rsmm)mentioning

confidence: 99%

“…with null site energies and hopping integrals 2 c tE  . Recently, Ramírez proposed a general method to find the S-matrix of an arbitrary lead structure ( ) L S [6]. In the following, we describe briefly this method.…”

Section: The Leadsmentioning

confidence: 99%

“…This occurs when the chosen unit structure has the minimum Q [6]. In this case, we may alternatively solve…”

Section: The Leadsmentioning

confidence: 99%

“…T E E E  =  tt. In tight-binding Hamiltonians, S-matrices can be efficiently computed using the recursive scattering matrix method (RSMM) [5,6]. In any case, the conductance is usually solved numerically by evaluating (1) at discrete values of energies.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Taylor series of Landauer conductance

García¹,

Rodríguez²,

Gomez³

2020

Physica E: Low-dimensional Systems and Nanostructures

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“…The RSMM allows us to calculate the S-matrix of a tight-binding system in terms of the Smatrices of its subsystems [5,6]. Examples of these systems are shown in Fig.…”

Section: Recursive Scattering Matrix Methods (Rsmm)mentioning

confidence: 99%

Section: The Leadsmentioning

confidence: 99%

“…This occurs when the chosen unit structure has the minimum Q [6]. In this case, we may alternatively solve…”

Section: The Leadsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Taylor series of Landauer conductance

García¹,

Rodríguez²,

Gomez³

2020

Physica E: Low-dimensional Systems and Nanostructures

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“…On the other hand, the S-matrix for the semi-infinite periodic potential can be calculated from the S-matrix of its unit cell. 24)…”

Section: Phase Factorsmentioning

confidence: 99%

Solving Schrödinger Equation with Scattering Matrices. Bound States of Lennard-Jones Potential

2019

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

Cited by 4 publications

References 36 publications

Taylor series of Landauer conductance

Taylor series of Landauer conductance

Solving Schrödinger Equation with Scattering Matrices. Bound States of Lennard-Jones Potential

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

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