calculation of Seebeck coefficient of transition-metal elements*

Ab-initio calculation of the Seebeck coefficient S of transition metal elements are performed within the framework of Kubo–Greenwood formula. The difficult points of calculating S are that, firstly, at T = 0K, the conductivity of pure metal diverges. Second, the Fermi surfaces of transition metals composed of many different states where the constant relaxation time approximation breaks down. To overcome the difficulties, we included the effects of electron-phonon scattering in the calculation of S. We exploited the Korringa–Kohn–Rostoker (KKR) Green's function method combined with the Kubo–Greenwood formula. The electron-phonon scattering was taken into account through ab-initio phonon calculations and an alloy analogy applied to the local static phonons. The KKR coherent potential approximation (KKR–CPA) was used for the latter. The calculated Cu resistivity and the Seebeck coefficients for various transition-metal elements at finite temperature show reasonable overall agreements with experiments. The present approach provides us with a framework applicable to a wide range of materials, including pure metals, compounds, ordered and disordered alloys.