Multi-channel quantum dragons from rectangular nanotubes with even-odd structure

Recently, a large class of nanostructures called quantum dragons have been discovered theoretically [1]. Quantum dragons are nanostuctures with correlated disorder but have an electron transmission probability $\mathcal{T}(E)$$=$$1$ for all energies $ E $ when connected to idealized leads. Hence for a single channel, the electrical conductance for a two-probe measurement should give the quantum of conductance $ G_{o}=\frac{2e^{2}}{h}$. The time independent Schr\"odinger equation for the single band tight binding model is solved exactly to obtain $ \mathcal{T}(E) $. We have generalized the matrix method and the mapping methods of [1] in order to study multi-channel quantum dragons for rectangular nanotubes with even-odd structure. The studies may be relevant for experimental rectangular nanotubes, such as MgO, copper phthalocyanine or some types of graphyne. [1] M.A. Novotny, Phys. Rev. B {\bf 90} 165103 [14 pages] (2014).