Abstract
We use an ab-initio approach to design and study a novel two-dimensional material - a planar array of carbon nanotubes separated by an optimal distance defined by the van der Waals interaction. We show that the energy spectrum for an array of quasi-metallic nanotubes is described by a strongly anisotropic hyperbolic dispersion and formulate a model low-energy Hamiltonian for its semi-analytical treatment. Periodic-potential-induced lifting of the valley degeneracy for an array of zigzag narrow-gap nanotubes leads to the band gap collapse. In contrast, the band gap is opened in an array of gapless armchair tubes. These unusual spectra, marked by pronounced van Hove singularities in the low-energy density of states, open the opportunity for interesting physical effects and prospective optoelectronic applications.
Highlights
One of the recent trends in contemporary nanotechnology is the use of van der Waals heterostructures for band-structure engineering [1,2]
For armchair Carbon nanotubes (CNTs), the main effect of introducing periodicity in the direction normal to the nanotube axis should be the opening of a small band gap, whereas degeneracy lifting in zigzag tubes is expected to result in a very complex dispersion stemming from crossings and avoided crossings of various energy levels
Detailed results are presented for an array of (15, 0) CNTs only; our further study shows that the main features of the spectrum, such as the closing of the total band gap, the appearance of tilted Dirac cones, strong anisotropy, and α1 0.039
Summary
One of the recent trends in contemporary nanotechnology is the use of van der Waals heterostructures for band-structure engineering [1,2]. It could be expected that aligning metallic single-walled carbon nanotubes in a regular array may produce an even more interesting dispersion In this respect, zigzag (3p, 0) CNTs should be more promising than armchair tubes. For armchair CNTs, the main effect of introducing periodicity in the direction normal to the nanotube axis should be the opening of a small band gap, whereas degeneracy lifting in zigzag tubes is expected to result in a very complex dispersion stemming from crossings and avoided crossings of various energy levels. Our study will be mostly focused on narrow-gap zigzag CNTs, with only limited results for armchair tubes of similar diameter presented mostly for comparison Our approach to this problem is based on ab initio calculations, which allows us to simultaneously find the optimal distance between nanotubes in the array which minimizes the total energy and the in-plane energy spectrum. For single-tube calculations, we used the QUANTUM ESPRESSO code for a three-dimensional system with widely separated nanotubes and confirmed that the dispersion in any direction normal to the nanotube axis was flat
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