Eur. Phys. J. B (2018) 91: 132
https://doi.org/10.1140/epjb/e2018-90070-4

Regular Article

Ballistic transport in aperiodic Labyrinth tiling proven through a new convolution theorem

¹ Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, 04510 Ciudad de México, Mexico
² Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, 04510 Ciudad de México, Mexico

^a e-mail: chumin@unam.mx

Received: 11 February 2018
Received in final form: 18 April 2018
Published online: 27 June 2018

Abstract

In this article, we report a distinct convolution theorem developed for the Kubo-Greenwood formula in Labyrinth tiling by transforming the two-dimensional lattice into a set of independent chains with rescaled Hamiltonians. Such transformation leads to an analytical solution of the direct-current conductance spectra, where quantized steps with height of 2g₀ are found in Labyrinth tiling with periodic order along the applied electric field direction, in contrast to the step height of g₀ observed in the corresponding square lattices, being g₀ the conductance quantum. When this convolution theorem is combined with the real-space renormalization method, we are able to address in non-perturbative way the electronic transport in macroscopic aperiodic Labyrinth tiling based on generalized Fibonacci chains. Furthermore, we analytically demonstrate the existence of ballistic transport states in aperiodic Labyrinth tiling. This finding suggests that the periodicity should not be a necessary condition for the single-electron ballistic transport even in multidimensional fully non-periodic lattices.