Basic Cells Special Features and Their Influence on Global Transport Properties of Long Periodic Structures

In this contribution, we address quantum transport in long periodic arrays whose basic cells, localized potentials U(x), display certain particular features. We investigate under which conditions these "local" special characteristics can influence the tunneling behavior through the full structure. As the building blocks, we consider two types of U(x)s: combinations of either Pöschl-Teller, U0/cosh2[αx], potentials (for which the reflection and transmission coefficients are known analytically) or Gaussian-shaped potentials. For the latter, we employ an improved potential slicing procedure using basic barriers, like rectangular, triangular and trapezoidal, to approximate U(x) and thus obtain its scattering amplitudes. By means of a recently derived method, we discuss scattering along lattices composed of a number, N, of these U(x)s. We find that near-resonance energies of an isolated U(x) do impact the corresponding energy bands in the limit of very large Ns, but only when the cell is spatially asymmetric. Then, there is a very narrow opening (defect or rip) in the system conduction quasi-band, corresponding to the energy of the U(x) quasi-state. Also, for specific U0's of a single Pöschl-Teller well, one has 100% transmission for any incident E>0. For the U(x) parameters rather close to such a condition, the associated array leads to a kind of "reflection comb" for large Ns; |TN(k)|2 is not close to one only at very specific values of k, when |TN|2≈0. Finally, the examples here-illustrating how the anomalous transport comportment in finite but long lattices can be inherited from certain singular aspects of the U(x)s-are briefly discussed in the context of known effects in the literature, notably for lattices with asymmetric cells.