Abstract:

  The transmission as a function of the energy of an incoming electron, T(E), is of central importance in obtaining the electrical conductivity G of a nanodevice via the application of the Landauer equation.  Ballistic transport, when there is no scattering of the electrons, has total transmission for all energies, T(E)=1.  For the ballistic case, or for any case with T(E)=1, in a four probe measurement G=∞ while in a two-probe measurement G=2e2/h with h Planck’s constant and e the electron charge.  A large class of disordered systems (within the single-band tight-binding model) are shown to have T(E)=1, which are called quantum dragons [1,2].  Quantum dragons are found by obtaining exact solutions of the time-independent Schrödinger equation for T(E) for a nanodevice coupled to two semi-infinite leads.  Examples of quantum dragons based on rectangular nanotubes, truncated Bethe lattices (also with extra hopping terms), armchair single-walled carbon nanotubes, zigzag hexagonal nanotubes, disordered systems with cylindrical symmetry, systems with disorder only perpendicular to the direction of electron motion (such as in the figure), and completely disordered systems will be presented.  The dimension in parameter space where the ménagerie of quantum dragons reside is obtained from use of the Perron-Frobenius theorem (or its equivalent for rectangular non-negative matrices).