Three-dimensional effects on extended states in disordered models of polymers

Abstract

We study electronic transport properties of disordered polymers in a quasi-one-dimensional model with fully three-dimensional interaction potentials. We consider such quasi-one-dimensionallattices in the presence of both uncorrelated and short-range correlated impurities. In our procedure, the actual physical potential acting upon the electrons is replaced by a set of nonlocal separable potentials, leading to a Schrodinger equation that is exactly solvable in the momentum representation. By choosing an appropriate potential with the same spectral structure as the physical one, we obtain a discrete set of algebraic equations that can be mapped onto a tight-binding-like equation. We then show that the reflection coefficient of a pair of impurities placed at neighboring sites (dimer defect) vanishes for a particular resonant energy. When there is a finite number of such defects randomly distributed over the whole lattice, we find that the transmission coefficient is almost unity for states close to the resonant energy, and that those states present a very large localization length. Multifractal analysis techniques applied to very long systems demonstrate that these states are truly extended in the thermodynamic limit. These results are obtained with parameters taken from actual physical systems such as polyacetylene, and thus reinforce the possibility of verifying experimentally theoretical predictions about the absence of localization in quasi-one-dimensional disordered systems.

Persistence of symmetry-protected Dirac points at the surface of the topological crystalline insulator SnTe upon impurity doping

“…42 In spite of its seemingly more complicated form, eqn (7) is amenable to analytical solution for any arbitrary shape function. 43–48…”

Persistence of symmetry-protected Dirac points at the surface of the topological crystalline insulator SnTe

“…Therefore, one can test different shape functions until the desired accuracy of the results is obtained. Typically naive functions with very few adjustable parameters are good candidates [37][38][39][40][41][42].…”

Many-impurity scattering on the surface of a topological insulator

“…The analysis and conclusions can be trivially extended to any 2D material where electron dynamics can be described by the massless Dirac equation. The interaction of the electron with the scatterers is accounted for by a separable pseudo-potential model [24][25][26][27][28][29][30][31] . In spite of its seemingly more complicated form, the separable pseudo-potential model is amenable to analytical solution and allows us to obtain closed expressions for the average Green's function within the SCBA and CPA frameworks.…”

“…Dotted lines correspond to Eqs (27). and(28) while solid lines show the results from self-consistent calculations. Energy is expressed in units of v/a and E c = 15. https://doi.org/10.1038/s41598-021-84801-w…”