Structural classification of boron nitride twisted bilayers and ab initio investigation of their stacking-dependent electronic structure

Since the discovery of superconductive twisted bilayer graphene which initiated the field of twistronics, moir\'e systems have not ceased to exhibit fascinating properties. We demonstrate that in boron nitride twisted bilayers, for a given moir\'e periodicity, there are five different stackings which preserve the monolayer hexagonal symmetry (i.e. the invariance upon rotations of 120$^\circ$) and not only two as always discussed in literature. We introduce some definitions and a nomenclature that identify unambiguously the twist angle and the stacking sequence of any hexagonal bilayer with order-3 rotation symmetry. Moreover, we employ density functional theory to study the evolution of the band structure as a function of the twist angle for each of the five stacking sequences of boron nitride bilayers. We show that the gap is indirect at any angle and in any stacking, and identify features that are conserved within the same stacking sequence irrespective of the angle of twist.Comment: 16 pages (6.5 main text); 15 figures (5 in main); 5 tables (3 in main). Appendixes concatenated to main tex

Gap engineering and wave function symmetry in C and BN armchair nanoribbons

Many are the ways of engineering the band gap of nanoribbons including application of stress, electric field and functionalization of the edges. In this article, we investigate separately the effects of these methods on armchair graphene and boron nitride nanoribbons. By means of density functional theory calculations, we show that, despite their similar structure, the two materials respond in opposite ways to these stimuli. By treating them as perturbations of a heteroatomic ladder model based on the tight-binding formalism, we connect the two behaviours to the different symmetries of the top valence and bottom conduction wave functions. These results indicate that opposite and complementary strategies are preferable to engineer the gapwidth of armchair graphene and boron nitride nanoribbons

Excitons in boron nitride single layer

Boron nitride single layer belongs to the family of 2D materials whose optical properties are currently receiving considerable attention. Strong excitonic effects have already been observed in the bulk and still stronger effects are predicted for single layers. We present here a detailed study of these properties by combining \textit{ab initio} calculations and a tight-binding-Wannier analysis in both real and reciprocal space. Due to the simplicity of the band structure with single valence ($\pi$) and conduction ($\pi^*$) bands the tight-binding analysis becomes quasi quantitative with only two adjustable parameters and provides tools for a detailed analysis of the exciton properties. Strong deviations from the usual hydrogenic model are evidenced. The ground state exciton is not a genuine Frenkel exciton, but a very localized "tightly-bound" one. The other ones are similar to those found in transition metal dichalcogenides and, although more localized, can be described within a Wannier-Mott scheme

Two-photon absorption in two-dimensional materials: The case of hexagonal boron nitride

13 pages, 4 figuresInternational audienceWe calculate the two-photon absorption in bulk and single layer hexagonal boron nitride (hBN) both by an ab-initio real-time Bethe-Salpeter approach and by a the real-space solution of the excitonic problem in tight-binding formalism. The two-photon absorption obeys different selection rules from those governing linear optics and therefore provides complementary information on the electronic excitations of hBN. Combining the results from the simulations with a symmetry analysis we show that two-photon absorption is able to probe the lowest energy $1s$ states in the single layer hBN and the lowest dark degenerate dark states of bulk hBN. This deviation from the "usual" selection rules based on the continuous hydrogenic model is explained within a simple model that accounts for the crystalline symmetry. The same model can be applied to other two-dimensional materials with the same point-group symmetry, such as the transition metal chalcogenides. We also discuss the selection rules related to the inversion symmetry of the bulk layer stacking

Persistent currents in carbon nanotubes based rings

Persistent currents in rings constructed from carbon nanotubes are investigated theoretically. After studying the contribution of finite temperature or quenched disorder on covalent rings, the complexity due to the bundle packing is addressed. The case of interacting nanotori and self-interacting coiled nanotubes are analyzed in details in relation with experiments.Comment: 7 sections, 9 figure

Le magnétisme des nanotubes (une approche théorique)

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