Theoretical assessment on the validity of the Wiedemann-Franz law for icosahedral quasicrystals

The validity of the Wiedemann-Franz law (WFL) for icosahedral quasicrystals belonging to the families AlCu(Fe,Ru) and AlPd(Mn,Re) is discussed. We exploit some characteristic features in the electronic structure in order to obtain closed analytical expressions for the transport coefficients in terms of the Hurwitz zeta function. Depending on the Fermi-level position, a systematic deviation from the ideal WFL is observed. The role of self-similar features in the electronic structure on the WFL is discussed. The obtained expression for the Lorenz function may be used in order to refine previous experimental results on the charge-carrier contribution to the thermal conductivity in these materials.

Figure 1

Temperature variation of the normalized Lorenz function for (a) $i\text{−}\mathrm{Al}\mathrm{Cu}\mathrm{Fe}$ phases with the model parameters set respectively labeled 1 (solid line) and 2 (dashed line) in Table , (b) AlCuRu phases with the model parameters set respectively labeled 3 (solid line) and 4 (dashed line) in Table , and (c) AlPdRe phases with the model parameters set respectively labeled 5 (solid line) and 6 (dashed line) in Table . In (d), we illustrate the high-temperature asymptotic limit for samples 1–6.

Figure 2

(Color online) Temperature variation of the normalized Lorenz function for two samples of the icosahedral quasicrystal AlCuFe, with $q_1=0\mathrm{eV}$ (solid line) and $q_1=0.015\mathrm{eV}$ (dashed line), along with the approximant phase AlMnSi with $q_1=-0.025\mathrm{eV}$ (dot-dashed line).

Figure 3

Temperature variation of the normalized Lorenz function for an ideal QC characterized by a self-similar electronic structure model given by ${\delta }_1\equiv -{\tau }^3\delta$, ${\delta }_2\equiv \delta$, ${\gamma }_1\equiv \delta$, ${\gamma }_2\equiv {\tau }^3\delta$, and $\alpha ={\tau }^{-6}$, with $\delta =0.12\mathrm{eV}$.