Renormalization–convolution approach to the electronic transport in two-dimensional aperiodic lattices

A novel method combining the renormalization and convolution techniques is developed for the Kubo–Greenwood formula. Using this method, the dc and ac conductance at zero temperature in two-dimensional (2D) quasiperiodic systems are studied. The results show that the ac conductance of quasiperiodic systems could be significantly modified by the presence of periodic leads, which are usually employed as the measurement connections. Furthermore, when the system is periodic along the applied electrical field, a quantized dc conductance spectrum is observed at zero temperature and this quantized spectrum is destroyed when an oscillating electrical field is introduced. However, when the electric field is applied along a quasiperiodic direction of the system, the ac conductance spectrum shows a non-Drude behaviour, in good agreement with experiment results.