Interband transitions in narrow-gap carbon nanotubes and graphene nanoribbons

Abstract

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.

Optical Momentum Alignment Effect in WSe2 Phototransistor

“…Recently, graphene and graphene‐like gapped 2D Dirac materials are theoretically predicted to exhibit similar behavior, owing to the pseudospin. [ 16 ] For WSe 2 , according to Fermi's Golden Rule, the transition rate W ( k ) for an electron with a wave vector k is given, to first‐order time‐dependent perturbation theory by Here, the ψ C and ψ V ( E C and E V ) are the wave functions (energies) of conduction and valence bands, respectively. P is the polarization vector of the incident light, which is parallel to the crystal's surface.…”

“…Theoretical studies show that at the low energy regime the angular generation density g is where defines the degree of momentum alignment, θ is the angle between the momentum of the photo‐excited electron and the polarization direction of the incident light, F 0 (ε 0 ) is the total density of carriers created at energy ε 0 , and subscript 0 means that no relaxation has occurred. [ 16 ] As illustrated in Figure 2b, a linearly polarized incident light is expected to generate an anisotropic distribution of photo‐excited EHPs, where the momentum direction of carriers is preferentially perpendicular to the polarization direction of incident light. Indeed, the pseudospin‐related optical transition selection rules of WSe 2 induce the optical momentum alignment effect.…”

“…Recently, graphene and graphene-like gapped 2D Dirac materials are theoretically predicted to exhibit similar behavior, owing to the pseudospin. [16] For WSe 2 , according to Fermi's Golden Rule, the transition rate W(k) for an electron with a wave vector k is given, to first-order time-dependent perturbation theory by…”

“…[ 15 ] Recently, graphene and graphene‐like gapped 2D Dirac materials are theoretically predicated to have a strongly anisotropic distribution of photo‐excited carriers under linearly polarized excitation due to the pseudospin‐induced optical transition selection rules. [ 16 ] Therefore, it will be important to explore how linearly polarized excitation influences photocurrent generation in TMDs.…”