Fermi liquid theory for heavy fermion superconductors without inversion symmetry : Magnetism and transport coefficients

We present the microscopic Fermi liquid theory for magnetic properties and transport phenomena in interacting electron systems without inversion symmetry both in the normal state and in the superconducting state. Our argument is mainly focused on the application to noncentrosymmetric heavy fermion superconductors. The transport coefficients for the anomalous Hall effect, the thermal anomalous Hall effect, the spin Hall effect, and magnetoelectric effects, of which the existence is a remarkable feature of parity violation, are obtained by taking into account electron correlation effects in a formally exact way. Moreover, we demonstrate that the temperature dependence of the spin susceptibility which consists of the Pauli term and van-Vleck-like term seriously depends on the details of the electronic structure. We give a possible explanation for the recent experimental result obtained by the NMR measurement of CePt$_3$Si [Yogi et al., J. Phys. Soc. Jpn.{\bf 75}, 013709 (2006)], which indicates no change of the Knight shift below the superconducting transition temperature for any directions of a magnetic field.