Account of helical and rotational symmetries in the linear augmented cylindrical wave method for calculating the electronic structure of nanotubes: Towards the<i>ab initio</i>determination of the band structure of a (100, 99) tubule

D’yachkov, P. N.; Makaev, D. V.

doi:10.1103/physrevb.76.195411

“…The linearized augmented cylindrical wave (LACW) technique is an extension of the linearized augmented plane-wave (LAPW) method to the specific case of one-dimensional cylindrical or tubular polyatomic systems such as the WS 2 nanotubes studied here (Figure ). The main foundations and applications of the LACW method have been described in detail elsewhere − and are compiled in a recent review . Similar to the simple version of the original LAPW theory for bulk materials, the LACW method is based on the muffin-tin (MT) and the local density exchange approximation for the electronic potential.…”

Section: Computational Detailsmentioning

confidence: 99%

First-Principles Evaluation of the Morphology of WS₂ Nanotubes for Application as Visible-Light-Driven Water-Splitting Photocatalysts

Piskunov

¹

,

Lisovski

²

,

Zhukovskii

³

et al. 2019

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One-dimensional tungsten disulfide (WS 2 ) single-walled nanotubes (NTs) with either achiral, i.e., armchair ( n , n ) and zigzag-type ( n , 0), or chiral (2 n , n ) configuration with diameters d NT > 1.9 nm have been found to be suitable for photocatalytic applications, since their band gaps correspond to the frequency range of visible light between red and violet (1.5 eV < Δε gap < 2.6 eV). We have simulated the electronic structure of nanotubes with diameters up to 12.0 nm. The calculated top of the valence band and the bottom of the conduction band (ε VB and ε CB , respectively) have been properly aligned relatively to the oxidation (ε O 2 /H 2 O ) and reduction (ε H 2 /H 2 O ) potentials of water. Very narrow nanotubes (0.5 < d NT < 1.9 nm) are unsuitable for water splitting because the condition ε VB < ε O 2 /H 2 O < ε H 2 /H 2 O < ε CB does not hold. For nanotubes with d NT > 1.9 nm, the condition ε VB < ε O 2 /H 2 O < ε H 2 /H 2 O < ε CB is fulfilled. The values of ε VB and ε CB have been found to depend only on the diameter and not on the chirality index of the nanotube. The reported structural and electronic properties have been obtained from either hybrid density functional theory and Hartree–Fock linear combination of atomic orbitals calculations (using the HSE06 functional) or the linear augmented cylindrical waves density functional theory method. In addition to single-walled NTs, we have investigated a number of achiral double-walled ( m , m )@( n , n ) and ( m , 0)@( n , 0) as well as triple-walled ( l , l )@( m , m )@( n , n ) and ( l , 0)@( m , 0)@( n , 0) nanotubes. All multiwalled nanotubes show a common dependence of their band gap on the diameter of the inner nanotube, independent of chirality index and number of walls. This behavior of WS ...

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“…As in the previous calculation of the band structure of infinite AuNTs, the energy levels of the finite-length tubules were calculated by the linearized augmented cylindrical waves (LACW) method. ,, The Born–von Karman cyclic boundary conditions and helical symmetry of the AuNTs were used, which allows one to determine the monatomic unit cell and describe the geometry of finite tubes as a result of helical translations of only one Au atom. The LACW method described in detail elsewhere is just a reformulation of the linear augmented plane-wave (LAPW) technique well-known in the theory of solids for the case of tubular multiatomic systems.…”

Section: Methods Of Calculationmentioning

confidence: 99%

Modeling of Nanoscale Electromagnets Based on Gold Finite Nanosolenoids

D’yachkov

¹

,

D’yachkov

²

2020

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Magnetic fields generated by the nanosolenoids based on the (5, 3) and (10,7) gold nanotubes (AuNTs) 12−600 Å long with numbers of Au atoms 20− 2000 are calculated. The electron energy levels of the finite length tubules were determined using the linearized augmented cylindrical waves method with Born−von Karman cyclic boundary conditions and on account of a helical symmetry of the AuNTs. Using these data, the numbers of conducting channels N F and the lowtemperature ballistic electron currents in the finite AuNTs are determined, and finally, the magnetic fields B of the gold nanosolenoids are obtained. Due to the increase in the number of conduction channels with the increase in the length of the tubes, the internal magnetic field gradually increases from 1.6 T/V in a tubule with L = 12 Å up to 12 T/V in a tube with L = 600 Å, slowly approaching the magnetic field of 14 T/V of the infinite (5, 3) AuNT. At a distance of 5 Å from the ends of the tubes (near z = L/2 − 5 Å), this field decreases rapidly, halving at z = L/2 and almost zeroing near z = L/2 + 5 Å. The field from the outside of the tubes is weak but not zero as in the infinite tubule. It is minimal at z = 0 and reaches a maximum at the edge of the AuNTs, where it is about 3−4 times less than the internal field. These results pave the way for a more realistic design of the nanosolenoids.

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“…Finally, the energies and wave functions of the Hamiltonian (3) are determined by the secular matrix diagonalization. The explicit formulas for the basis functions and secular equations for nonrelativistic and relativistic versions of the LACW method are given in our previous papers , as well as in a recent monograph . The method applied here does not depend on the number of atoms per translational unit cell and is therefore applicable to any AuNT independent of its diameter and chirality, a stable band structure being achieved using about 25 basic functions Ψ λ 0 ( r | kL ).…”

Section: Methods Of Calculationmentioning

confidence: 99%

“…The purpose of this work is to study the electron band structure, electron and spin transport, and the formation of a magnetic field in the chiral AuNTs using the symmetrized relativistic linearized augmented cylindrical wave (LACW) method described in detail elsewhere. − In previous computational studies of the AuNTs, only their translational symmetry was taken into account, and, therefore, calculations were restricted by the compounds with small numbers of atoms per unit cells. In this work, a symmetrized version of the LACW method will be used, in which not only translational but all symmetry properties of the compounds are taken into account, and calculations of any chiral tubes are possible despite the enormous numbers of atoms in their translational cells.…”

Section: Introductionmentioning

confidence: 99%

Gold Nanosolenoids Based on Chiral Nanotubes Calculated Using the Relativistic Linearized Augmented Cylindrical Wave Method

D’yachkov

¹

,

D’yachkov

²

2019

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Spin-dependent band structures, the electron and spin transport, and the formation of magnetic field in the single-walled chiral gold nanotubes (n 1 , n 2 ) are calculated using a relativistic linearized augmented cylindrical wave method. The helical symmetry of tubules was taken into account when constructing the Hamiltonian and basis functions, the unit cells of any tubule being reduced to one atom. This greatly simplifies the calculations and allows us to present the results in a simple form. There are only 10 filled and 2 half-filled spin-dependent dispersion curves in the band structures of any tubule. All of them have the metal-type electronic structures. In the (5, n 2 ) and (10, n 2 ) series calculated, the spin−orbit splitting ΔE S−O values of bands crossing the Fermi level are equal to 0.5 and 0.2 eV, respectively, and the ΔE S−O decreases as one goes to the valence band inner energy states. The numbers N F of crossing points of the bands with the Fermi level coincide almost exactly with the numbers n 1 + n 2 of atomic rows coiling around the tubule's axis, N F ≈ n 1 + n 2 , and a ballistic electron conductivity can be estimated using a simple formula σ ≈ G 0 (n 1 + n 2 ), where G 0 is the conduction quantum. Based on the band structure data for chiral tubes, the cyclic current component and magnetic fields in gold nanosolenoids are calculated. The calculated spin-dependent densities of states for electrons at the Fermi level show that chirality can induce a spin selectivity of electron transport. The spin transport can be controlled by the twisting, stretching, and compression of the tubes. Article pubs.acs.org/JPCC

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Account of helical and rotational symmetries in the linear augmented cylindrical wave method for calculating the electronic structure of nanotubes: Towards theab initiodetermination of the band structure of a (100, 99) tubule

Cited by 56 publications

References 51 publications

First-Principles Evaluation of the Morphology of WS₂ Nanotubes for Application as Visible-Light-Driven Water-Splitting Photocatalysts

First-Principles Evaluation of the Morphology of WS₂ Nanotubes for Application as Visible-Light-Driven Water-Splitting Photocatalysts

Modeling of Nanoscale Electromagnets Based on Gold Finite Nanosolenoids

Gold Nanosolenoids Based on Chiral Nanotubes Calculated Using the Relativistic Linearized Augmented Cylindrical Wave Method

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Account of helical and rotational symmetries in the linear augmented cylindrical wave method for calculating the electronic structure of nanotubes: Towards theab initiodetermination of the band structure of a (100, 99) tubule

Cited by 56 publications

References 51 publications

First-Principles Evaluation of the Morphology of WS2 Nanotubes for Application as Visible-Light-Driven Water-Splitting Photocatalysts

First-Principles Evaluation of the Morphology of WS2 Nanotubes for Application as Visible-Light-Driven Water-Splitting Photocatalysts

Modeling of Nanoscale Electromagnets Based on Gold Finite Nanosolenoids

Gold Nanosolenoids Based on Chiral Nanotubes Calculated Using the Relativistic Linearized Augmented Cylindrical Wave Method

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Product

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First-Principles Evaluation of the Morphology of WS₂ Nanotubes for Application as Visible-Light-Driven Water-Splitting Photocatalysts

First-Principles Evaluation of the Morphology of WS₂ Nanotubes for Application as Visible-Light-Driven Water-Splitting Photocatalysts