Extremely small thermal conductivity of the Al-based Mackay-type 1/1-cubic approximants

We study the hopping conduction in a composite made of straight metallic nanowires randomly and isotropically suspended in an insulator. Uncontrolled donors and acceptors in the insulator lead to random charging of wires and, hence, to a finite bare density of states at the Fermi level. Then the Coulomb interactions between electrons of distant wires result in the soft Coulomb gap. At low temperatures the conductivity sigma is due to variable range hopping of electrons between wires and obeys the Efros-Shklovskii (ES) law ln sigma proportional to-(T-ES/T)(1/2). We show that T-ES proportional to 1/(nL(3))(2), where n is the concentration of wires and L is the wire length. Due to enhanced screening of Coulomb potentials, at large enough nL(3) the ES law is replaced by the Mott law.