Quantum Dragon Solutions for Electron Transport through Nanostructures based on Rectangular Graphs

Electron transport through nanodevices of atoms in a single-layer rectangular arrangement with free (open) boundary conditions parallel to the direction of the current flow is studied within the single-band tight binding model. The Landauer formula gives the electrical conductance to be a function of the electron transmission probability, ${\cal T}(E)$, as a function of the energy $E$ of the incoming electron. A quantum dragon nanodevice is one which has a perfectly conducting channel, namely ${\cal T}(E)=1$ for all energies which are transmitted by the external leads even though there may be arbitrarily strong electron scattering. The rectangular single-layer systems are shown to be able to be quantum dragon devices, both for uniform leads and for dimerized leads. The quantum dragon condition requires appropriate lead-device connections and correlated randomness in the device.