Pair states in one-dimensional Dirac systems

Hartmann, Richard; Portnoi, M. E.

doi:10.1103/physreva.95.062110

Cited by 15 publications

(9 citation statements)

References 72 publications

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“…71,83,84 In quasimetallic CNTs and ANGRs the exciton binding energy has been shown to never exceed the bandgap for both long-range 53,85 and short-range interaction potentials. 85,86 Therefore, unlike semi-conducting tubes, the electron-hole pairs should be fully ionized at room temperature. Hence, the aforementioned undesirable effects due to dark excitons, should not dominate the optical processes in narrow-gap nanotubes.…”

Section: Excitonic Effectsmentioning

confidence: 99%

“…A possible consequence could be two close THz emission peaks (which will be arguably difficult to resolve given the current state of THz spectroscopy). The very narrow peak at a lower energy will be produced by an optically active excitonic state below the band gap 86 ; whereas, the higher-energy broader peak should occur slightly above the band gap edge -it results from the combination of the band-edge van Hove singularity suppression and the decay of the matrix element with increasing photon energy. The in-depth study of both the van Hove singularity suppression and excitonic transitions in ultra-relativistic quasi-one-dimensional systems remains a subject of current research.…”

Section: Excitonic Effectsmentioning

confidence: 99%

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Interband transitions in narrow-gap carbon nanotubes and graphene nanoribbons

Hartmann

Saroka

Portnoi

2019

Journal of Applied Physics

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Interband transitions in narrow-gap carbon nanotubes and graphene nanoribbons We use the robust nearest-neighbour tight-binding approximation to study on the same footing interband dipole transitions in narrow-bandgap carbon nanotubes and graphene nanoribbons. It is demonstrated that curvature effects in metallic singlewalled carbon nanotubes and edge effects in gapless graphene nanoribbons not only open up bang gaps, which typically correspond to THz frequencies, but also result in a giant enhancement of the probability of optical transitions across these gaps.Moreover, the matrix element of the velocity operator for these transitions has a universal value (equal to the Fermi velocity in graphene) when the photon energy coincides with the band-gap energy. Upon increasing the excitation energy, the transition matrix element first rapidly decreases (for photon energies remaining in the THz range but exceeding two band gap energies it is reduced by three orders of magnitude), and thereafter it starts to increase proportionally to the photon frequency.A similar effect occurs in an armchair carbon nanotube with a band gap opened and controlled by a magnetic field applied along the nanotube axis. There is a direct correspondence between armchair graphene nanoribbons and single-walled zigzag carbon nanotubes. The described sharp photon-energy dependence of the transition matrix element together with the van Hove singularity at the band gap edge of the considered quasi-one-dimensional systems make them promising candidates for active elements of coherent THz radiation emitters. The effect of Pauli blocking of low-energy interband transitions caused by residual doping can be suppressed by creating a population inversion using high-frequency (optical) excitation.

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Section: Excitonic Effectsmentioning

confidence: 99%

Section: Excitonic Effectsmentioning

confidence: 99%

Interband transitions in narrow-gap carbon nanotubes and graphene nanoribbons

Hartmann

Saroka

Portnoi

2019

Journal of Applied Physics

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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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“…However, in narrow gap CNTs and ANGRs the exciton binding energy has been shown to never exceed the bandgap [73,74]. Therefore, at room temperature the electron-hole pairs should be fully ionized.…”

Section: Experimental Detection Of Enhanced Transitionsmentioning

confidence: 99%

Momentum alignment and the optical valley Hall effect in low-dimensional Dirac materials

Saroka¹,

Hartmann²,

Portnoi³

2018

Preprint

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We study the momentum alignment phenomenon and the optical control of valley population in gapless and gapped graphene-like materials. We show that the trigonal warping effect allows for the spatial separation of carriers belonging to different valleys via the application of linearly polarized light. Valley separation in gapped materials can be detected by measuring the degree of circular polarization of band-edge photoluminescence at different sides of the sample or light spot (optical valley Hall effect). We also show that the momentum alignment phenomenon leads to the giant enhancement of near-band-edge interband optical transitions in narrow-gap carbon nanotubes and graphene nanoribbons independent of the mechanism of the gap formation. A detection scheme to observe these giant interband transitions is proposed which opens a route for creating novel terahertz radiation emitters.

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Pair states in one-dimensional Dirac systems

Cited by 15 publications

References 72 publications

Interband transitions in narrow-gap carbon nanotubes and graphene nanoribbons

Interband transitions in narrow-gap carbon nanotubes and graphene nanoribbons

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

Momentum alignment and the optical valley Hall effect in low-dimensional Dirac materials

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