We found that an Al-Si-Ru cubic quasicrystalline approximant has a semiconducting band structure by performing an orbital analysis based on density functional theory. These semiconducting transport properties have been confirmed in an experimentally synthesized sample. The temperature dependences of the electrical conductivity and the Seebeck coefficient were consistent with the trends of an intrinsic semiconductor with a band gap of 0.15 eV above 350 K. The lattice thermal conductivity had a low value of approximately 1.0 W m −1 K −1 above 400 K, which is close to the theoretical minimum.Since the discovery of the quasicrystal (QC) in 1984 [1], many of the unique properties of QCs have been revealed, including their crystal structures [2] and electrical properties [3]. However, the question of whether or not semiconducting or insulating QCs exist remains one of the fundamental problems to be solved in solid state physics, although the QC concept has been established as one of the categories of solid-state structures.Semiconducting QCs have attracted attention, not only from the perspective of academic interest, but also from the viewpoint of application to thermoelectric (TE) materials to realize a direct conversion between the thermal and electrical energies. The performance of a TE material can be evaluated using the dimensionless figure of merit zT = S 2 σ T /(κ el + κ lat ), where S, σ , T , κ el , and κ lat are the Seebeck coefficient, the electrical conductivity, the absolute temperature, the electronic thermal conductivity, and the lattice thermal conductivity, respectively. The highest zT between QCs achieved to date is 0.26, which is only approximately one quarter of the general target value of unity, at 500 K in an Al-Ga-Pd-Mn QC [4]. The main problem is that the value of S (≈100 μV K −1 ) is only approximately one half of that of typical practical materials. To obtain a sufficiently large S at a target temperature T , a semiconductor with a band gap of 6-10k B T , where k B is the Boltzmann constant, is generally required [5]. Therefore, the discovery of a semiconducting QC is necessary to enable the breakthrough of QCs for use as TE materials.While semiconductorlike properties that were attributed to a combination of the pseudogap in the density of states (DOS) and electronic weak localization were previously reported in some aluminum-transition metal (Al-TM) QCs [6-10] and quasicrystalline approximants (QCAs) [10,11], a finite band gap has yet to be observed experimentally in these materials to date. There have been several theoretical works on semiconducting QCAs based on density functional theory (DFT) that have thus far contributed to the understanding of the problem of complex semiconducting QCs. Krajčí and Hafner investigated the electronic structures of hypothetical QCAs that were constructed using a model of Al-TM icosahedral QCs [12][13][14]. While they predicted the existence of some QCAs with semiconducting electronic structures and indicated the presence of an energy gap in QCs, these typ...