Pseudo-SAMOs array in positively charged semiconductor single-walled carbon nanotubes

Super Atom Molecular Orbitals (SAMOs) are electronic excited states found in fullerenes in which an electron is excited to one or, more generally, several virtual orbitals with hydrogen like character. The existence of hydrogen-like metastable SAMO states has previously been demonstrated both experimentally and theoretically in fullerenes. In single-walled carbon nanotubes (SWCNTs), the existence of similar states with a maximum in the center of the hollow structure was theoretically demonstrated. In fullerenes, the SAMOs were classified according to their localization form by the orbital quantum number and named s, p, d-SAMOs. In this paper, we show the existence of different states with a maximum in the center of the SWCNTs, which are called pseudo-SAMOs. For the first time in SWCNTs, high-energy pseudo-SAMOs, which appear under high positive charging of the structure, have been demonstrated. As the positive charge of the SWCNT increases, the number of these states also increases as the depth of the Coulomb potential well increases. In the cross-section of the nanotube, the pseudo-SAMOs resemble the SAMOs in fullerenes, but due to the cylindrical symmetry of the nanotube, their shape along the tube axis z deviates from the shape of spherically symmetric wave functions. It is shown that quantization of pseudo-SAMOs along thez-axis occurs in finite SWCNTs, and the pseudo-z quantum number is used in addition to their characterization. For pseudo-SAMOs, the general set of quantum numbers does not repeat: in the case of invariance of the principal and orbital quantum numbers, the magnetic quantum number (the orientation of the orbital in space) changes. In the case of finite structures for pseudo-SAMOs with the same principal and orbital quantum number, the pseudo-z quantum number increases with increasing state number. The lifetimes of the pseudo-SAMOs in the finite SWCNT were estimated. In this nanotube, the lifetime of the pseudo-SAMOs is 1-2 orders of magnitude longer than the lifetime of the surface-localized states and is generally in the order of 10^-8s.