Weyl Semimetals (WSM) for Electronics Applications

The major factor determining transport properties of solids is the number of electron states in a vicinity of Fermi level. In equilibrium, no macroscopic flow of electrons exists and, therefore, in order to create such flow, electrons must be excited over their equilibrium distribution. However, electrons with energies well below the Fermi level (compared to the characteristic energy scale k_BT, where k_B is the Boltzmann constant and T is the temperature), cannot acquire small excitation energy. Indeed, in this case, they would have energy corresponding to already occupied states, which is prohibited by the Pauli principle. In turn, well above the Fermi level, where excitation of electrons is not constrained by the Pauli principle, the electron states are not populated, thus making their contribution to the response negligible.

An elementary classification of materials as conductors and insulators is, therefore, based on the relation between the Fermi level and the energy bands characterizing electron states in the solid. In metals, such as copper or silver, the Fermi level is inside the band and, therefore, metals have high electric and thermal conductivities. In insulators, for instance, silicon dioxide (SiO₂) or crystal sodium chloride (NaCl), the Fermi level is inside the wide, conventionally more than 4 eV, bandgap separating valence and conduction (below and above the Fermi level, respectively) bands, for example, Δ ≈ 8.9 eV in SiO₂ and Δ ≈ 8.5 eV in NaCl.