High-order harmonic generation in hexagonal nanoribbons

Abstract

The generation of high-order harmonics in finite, hexagonal nanoribbons is simulated. Ribbons with armchair and zig-zag edges are investigated by using a tight-binding approach with only nearest-neighbor hopping. By turning an alternating on-site potential off or on, the system describes for example graphene or hexagonal boron nitride, respectively. The incoming laser pulse is linearly polarized along with the ribbons. The emitted light has a polarization component parallel to the polarization of the incoming field. The presence or absence of a polarization component perpendicular to the polarization of the incoming field can be explained by the symmetry of the ribbons. Characteristic features in the harmonic spectra for the finite ribbons are analyzed with the help of the band structure for the corresponding periodic systems.

High-harmonic spectra of hexagonal nanoribbons from real-space time-dependent Schrödinger calculations

“…The results of this paper provide valuable verification of simpler tight-binding models [25]. Our approach is not limited to a fixed number of states (grouped in bands), and our results account for transitions to even higher bands or the continuum.…”

“…In that way, we can reveal differences and similarities in HHG spectra as compared to corresponding tight-binding studies, e.g., in Ref. [25]. The non-interacting electronic orbitals in our Schrödinger solver are defined on a two-dimensional grid of spacing Δx = Δy = 0.2, which encompasses all lattice sites plus a border of 8 on each side.…”

“…In tight-binding calculations (such as in Ref. [25]), hopping takes place along these lines. However, in our simulation based on the time-dependent Schrödinger equation, electronic wavefunctions are not restricted to move along these lines but may propagate in the entire plane.…”

“…These can not be described in tight-binding approximation with one atomic orbital per site, because then the energy difference between states is bound from above by ΔE max (see Ref. [25]).…”

“…The on-site potential causes a top-bottom asymmetry but no left-right asymmetry. Reference [25] investigates the influence of the ribbon's length using a computationally less demanding tightbinding approach. Full time-dependent Schrödinger calculation results for a ribbon of 30 sites (seven hexagons) agree with those for 26 sites (six hexagons).…”