Polar type density of states in non-unitary odd-parity superconducting states of gap with point nodes

It is shown that the density of states (DOS) proportional to the excitation energy, the so-called polar like DOS, can arise in the odd-parity states with the superconducting gap vanishing at points even if the spin-orbit interaction for Cooper pairing is strong enough. Such gap stuructures are realized in the non-unitary states, F1u(1, i, 0), F1u(1, ε, ε ), and F2u(1, i, 0), classified by Volovik and Gorkov, Sov. Phys.−JETP 61 (1985) 843. This is due to the fact that the gap vanishes in quadratic manner around the point on the Fermi surface. It is also shown that the region of quadratic energy dependence of DOS, in the state F2u(1, ε, ε ), is restricted in very small energy region making it difficult to distinguish from the polar-like DOS.