Abstract
We study high-order harmonic generation (HHG) in armchair-type single-wall carbon nanotubes (SWNTs) driven by ultrashort, mid-infrared laser pulses. For a SWNT with chiral indices (n, n), we demonstrate that HHG is dominated by bands |m| = n - 1 and that the cut-off frequency saturates with intensity, as it occurs in the case of single layer graphene. As a consequence, HHG in SWNTs can be described effectively as a one-dimensional periodic system, whose high-frequency emission can be modified through the proper control of the structural parameters. Additionally, we show that the HHG mechanism in nanotubes has some similarities to that previously reported in single layer graphene. However, as a main difference, the electron-hole pair excitation in SWNTs is connected to the non-adiabatic crossing through the first van Hove singularity of the |m| = n - 1 bands, instead of the crossing through the Dirac point that takes place in graphene.
Highlights
Structure of A-type single-wall carbon nanotubesFor diameters above one nanometer, the effects of curvature can be neglected and the SWNT’s electronic structure can be derived from that of single-layer graphene [21,22]
Carbon nanotubes are carbon allotropes with quasi-one dimensional periodic structure
We have studied the non-perturbative emission of armchair (n, n) carbon nanotubes irradiated by intense few-cycle infrared laser pulses, both from the numerical integration of the time-dependent Schrödinger equation (TDSE) and using a semiclassical model
Summary
For diameters above one nanometer, the effects of curvature can be neglected and the SWNT’s electronic structure can be derived from that of single-layer graphene [21,22]. A-type —armchair— nanotubes correspond to chiral indices (n, n) and |θ| = 30◦, while (n, 0) denotes Z-type —zigzag— tubes, with |θ| = 0◦. Both zigzag and armchair tubes are achiral species, unlike C —chiral— nanotubes, where n2 n1. Bands are labelled according to the value of |m| and the parities upon the vertical and horizontal mirror symmetries, A/B and +/− respectively. A-type (n, n) nanotubes are semimetals, as both valence and conduction bands are degenerated at the point a0k = ±2π/3 of the band m = n, corresponding to the Dirac points K and K’ of the graphene’s Brillouin zone, see Fig. 1(b). The pink-filled profile in the background shows the density of states, dominated by the van Hove singularities
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