Single and Multi-channel Quantum Dragons from Rectangular Nanotubes

Recently quantum dragons have been discovered theoretically [1]. Quantum dragons are nanostructures with correlated disorder that permit energy-independent total quantum transmission of electrons. Hence the electrical conductance $G$ in a two-terminal measurement should be the conductance quantum $G_0$$=$$2e^2/h$. The single-band tight banding model is used. An example of a single-channel quantum dragon is a rectangular nanotube with disorder along the direction $z$ of the electron propagation [1]. Quantum dragons are obtained by solving the time-independent Schr{\"o}dinger equation to obtain the electrical transmission ${\cal T}$ as a function of the incoming electron energy $E$. A quantum dragon has ${\cal T}(E)$$=$$1$ for all energies. This work generalizes the solution of the time-independent Schr{\"o}dinger equation to the case of more than one open channel, and applies the method to nanotubes formed from rectangular lattices. One can envision such single-walled rectangular nanotubes for iron starting from free-standing single-atom-thick Fe membranes which have recently been obtained experimentally [2]. \break [1] M.A.\ Novotny, Phys.\ Rev.\ B {\bf 90}, 165103 [14 pages] (2014). \break [2] J.\ Zhao, et al., Science {\bf 343}, 1228 (2014).