How does a gap at the Fermi surface reduce electrical conductivity in quasicrystals?

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quasicrystal Figure 1: Hexagonal lattice of atomic sites.

In quasicrystals, electrical conductivity is reduced because of the appearance of a gap in the electronic density of states at the Fermi surface.

The Fermi surface acts as the boundary that separates filled electronic states from empty ones. In a solid, it is specifically these electrons at or near the Fermi surface that are responsible for carrying electrical current. When a gap forms in the density of states at this energy level, the number of available electrons capable of participating in conduction is significantly diminished. Consequently, this scarcity of charge carriers leads to low electrical conductivity, a characteristic that distinguishes quasicrystals from their constituent elements, which are typically good conductors.12