Exciton states in narrow-gap carbon nanotubes

Hartmann, Richard; Portnoi, M. E.

doi:10.1063/1.4940294

Cited by 7 publications

(6 citation statements)

References 52 publications

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“…This simplification reduces the problem to the twoparticle Dirac equation, which is well known in the quantum field theory. In recent years, the two-particle Dirac equation with a simplified electron-interaction interaction was adapted to the narrow-gap and gapless electronic systems in graphene and carbon nanotubes [12][13][14][15][16].…”

Section: B a Simplified Modelmentioning

confidence: 99%

“…The studies of excitons in topologically trivial narrow-gap materials revealed a substantial dependence of the exciton properties on the electron dispersion in the bands. Such investigations were carried out in recent years for the quasirelativistic dispersion of electrons and holes in a gapped graphene and carbon nanotubes [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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Two-body problem for two-dimensional electrons in the Bernervig-Hughes-Zhang model

Sablikov

2017

Phys. Rev. B

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We study the two-body problem for two-dimensional electron systems in a symmetrized Bernevig-Hughes-Zhang model which is widely used to describe topological and conventional insulators. The main result is that two interacting electrons can form bound states with the energy in the gap of the band spectrum. The pairing mechanism can be interpreted as the formation of a negative reduced effective mass of two electrons. The problem is complicated because the relative motion of the electrons is coupled to the center-of-mass motion. We consider the case of zero total momentum. Detail calculations are carried out for the repulsive interaction potential of steplike form. The states are classified according to their spin structure and two-particle basis functions that form a given bound state. We analyze the spectra and electronic structure of the bound states in the case of both topological and trivial phases and especially focus on effects originating from the band inversion and the coupling of the electron and hole bands. In the trivial phase and the topological phase with the large coupling parameter a, the bound state spectra are qualitatively similar. However, when a is less a certain value, the situation changes dramatically. In the topological phase, new states arise with a higher binding energy at lower interaction potential, which evidences that the band inversion can favor pairing the electrons. arXiv:1702.02041v2 [cond-mat.mes-hall]

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Section: B a Simplified Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two-body problem for two-dimensional electrons in the Bernervig-Hughes-Zhang model

Sablikov

2017

Phys. Rev. B

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“…which is a linear combination of the symmetric Pöschl-Teller potential with an additional term which enables the introduction of asymmetry 74 . This potential belongs to the class of quantum models, which are quasi-exactly solvable 23,[75][76][77][78][79][80][81] , where only some of the eigenfunctions and eigenvalues are found explicitly. The depth of the well is given by − (a − b) 2 /4a, and the potential width is characterized by the parameter L, which was introduced after Eq.…”

Section: Relativistic One-dimensional P öSchl-teller Problemmentioning

confidence: 99%

Two-dimensional Dirac particles in a Pöschl-Teller waveguide

Hartmann

Portnoi

2017

Sci Rep

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We obtain exact solutions to the two-dimensional (2D) Dirac equation for the one-dimensional Pöschl-Teller potential which contains an asymmetry term. The eigenfunctions are expressed in terms of Heun confluent functions, while the eigenvalues are determined via the solutions of a simple transcendental equation. For the symmetric case, the eigenfunctions of the supercritical states are expressed as spheroidal wave functions, and approximate analytical expressions are obtained for the corresponding eigenvalues. A universal condition for any square integrable symmetric potential is obtained for the minimum strength of the potential required to hold a bound state of zero energy. Applications for smooth electron waveguides in 2D Dirac-Weyl systems are discussed.

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“…This potential, shown in Fig. 2a, belongs to the class of quantum models which are quasi-exactly solvable 2,[86][87][88][89][90][91][92] , where only some of the eigenfunctions and eigenvalues are found explicitly. The depth of the well is given by V 0 , and the potential width is characterized by the parameter L. Here V 0 and L are taken to be positive parameters.…”

Section: Quasi-exact Solution To the Tilted Dirac Equation For The Hyperbolic Secant Potentialmentioning

confidence: 99%

Mapping borophene onto graphene: Quasi-exact solutions for guiding potentials in tilted Dirac cones

Ng¹,

Wild²,

Portnoi³

et al. 2021

Preprint

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We show that if the solutions to the (2+1)-dimensional massless Dirac equation for a given 1D potential are known, then they can be used to obtain the eigenvalues and eigenfunctions for the same potential, orientated at an arbitrary angle, in a tilted anisotropic 2D Dirac material. This simple set of transformations enables all the exact and quasi-exact solutions associated with 1D quantum wells in graphene to be applied to the confinement problem in tilted Dirac materials such as borophene. We also show that smooth electron waveguides in tilted Dirac materials can be used to manipulate the degree of valley polarization of quasiparticles travelling along a particular direction of the channel. We examine the particular case of the hyperbolic secant potential to model realistic top-gated structures for valleytronic applications.

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Exciton states in narrow-gap carbon nanotubes

Cited by 7 publications

References 52 publications

Two-body problem for two-dimensional electrons in the Bernervig-Hughes-Zhang model

Two-body problem for two-dimensional electrons in the Bernervig-Hughes-Zhang model

Two-dimensional Dirac particles in a Pöschl-Teller waveguide

Mapping borophene onto graphene: Quasi-exact solutions for guiding potentials in tilted Dirac cones

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