Anomalous Quantum Diffusion and Conductivity of Quasicrystals

TL;DR

This paper investigates how anomalous quantum diffusion in perfect quasicrystals influences their electrical conductivity, revealing unique behaviors such as non-zero low-frequency dissipation and increased d.c. conductivity with disorder, differing from periodic metals.

Contribution

It introduces a phenomenological diffusion law for quasicrystals and analyzes its impact on conductivity, highlighting novel effects absent in periodic metals.

Findings

Non-zero dissipative conductivity at low frequencies in perfect quasicrystals.

D.c. conductivity increases with disorder when diffusion exponent is less than 1/2.

The Drude peak is replaced by a dip in the conductivity spectrum.

Abstract

A phenomenological diffusion law $L(t)\propto t^{\beta}$, where L(t) measures the spreading of a wave-packet in a time t, is assumed for perfect quasicrystals. We show that it affects their conductivity with striking differences compared to the case of periodic metals. In the absence of defects the dissipative part of conductivity is non zero even at low frequencies contrary to the case of crystals. Also if $\beta<1/2$ the d.c. conductivity increases when disorder increases and the so-called Drude peak, characteristic of metals, is replaced by a dip . Experimental results are briefly discussed.