Kubo conductivity of macroscopic systems with Fano defects for periodic and quasiperiodic cases by means of renormalization methods in real space

Abstract

In this paper, we investigate the effects on the electrical conductivity originated by the inclusion of Fano defects (FDs) for periodic and quasiperiodic systems of macroscopic size. This study is developed using the extension of the methods of renormalization for the Kubo-Greenwood formula in real space within the tight-binding formalism. Within this formalism, the conductivity is determined in an exact form, without any other approximation. For periodic systems, we find the zeros of conductivity located at the eigenenergies of the coupled chain of N F atoms, and transparent states at the eigenenergies of a chain of N F À 1 atoms. These results are shown in both numerical and analytical way. Moreover, the position of the FD in the system does not alter the conductivity spectrum. On the other hand, for quasiperiodic systems, only some coupled chains preserve the transparent state; this was found both numerically and analytically. The case of two FDs attached to the system is also analyzed, founding a high dependence of the electrical conductivity on the distance between the FDs. Finally, this study is extended to two dimensions.

Real Space Theory for Electron and Phonon Transport in Aperiodic Lattices via Renormalization

“…Orellana, et al in 2003 [97], while engineering Fano resonances in discrete arrays were proposed by A. E. Miroshnichenko and Y. S. Kivshar in 2005 [98]. During the next decade, more detailed studies using RSRM were carried out for the transmission coefficient [99][100][101][102][103][104][105], Landauer resistance [106], Lyapunov exponent [100], local DOS [101][102][103], and Kubo conductivity [107]. Moreover, the ballistic AC conductivity of periodic lattices has been surpassed through quasiperiodicity [108] or Fano resonances [109].…”

Ballistic conduction in macroscopic non‐periodic lattices

“…For periodic chains with an attached periodic Fano impurity chain of N F atoms, both formed by hopping integrals t , there are transparent states at the eigenvalues of a ( N F −1)‐atom periodic chain . In general, the Landauer conductivity of a periodic chain with a coupled Fano impurity chain of arbitrary hopping integrals is shown in Appendix C to be which becomes σ P when , where …”

Taylor series of Landauer conductance

“…In general, it would be convenient to obtain ( ) TE analytically. Remarkably, this has been achieved in some systems, such as atomic chains with impurities [4,7,8], atomic chains with Fano defects [9], atomic chains with attached Aharonov-Bohm loops [10][11][12][13],…”

“…armchair-type carbon nanotubes with site defects [14], armchair graphene nanoconstrictions (GNC) [15], zigzag phosphorene nanoribbons with site defects [16], molecular wires [17,18], graphene nanobubbles [19], graphene heterojunctions [20], graphene nanoribbons with defects [21], and parallel armchair nanotubes [22]. Transparent states have also been analytically demonstrated in atomic chains with impurities following Fibonacci orderings [4], atomic chains with Fano defects [9], and disordered nanotapes with Fano defects [8].…”