Fermi Liquid Theory for Heavy Fermion Superconductors without Inversion Symmetry: Magnetism and Transport Coefficients

Abstract

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 CePt3Si [Yogi et al.: J. Phys. Soc. Jpn.75 (2006) 013709], which indicates no change of the Knight shift below the superconducting transition temperature for any directions of a magnetic field.

Non-Centrosymmetric Superconductors with Topological Transition of Fermi Surfaces

“…The normalized spin susceptibility χ s /χ n is increased by the TTFS of type (C), as investigated by Fujimoto [8]. Our calculation reproduces his result, but the enhancement of normalized spin susceptibility is much smaller than that due to the TTFS of type (A).…”

“…On the other hand, the Knight shift measurement of Li 2 Pt 3 B did not show such a decrease in spin susceptibility [4,5]. Although the electron correlation effect may enhance the spin susceptibility in the superconducting state [8], such enhancement is unlikely to occur in Li 2 Pd 3 B and Li 2 Pt 3 B in which the correlation effect is negligible [6,7]. The influence of magnetic order has been pointed out for the heavy fermion superconductor CePt 3 Si [10,11]; however, the magnetic order does not occur in Li 2 Pt 3 B.…”

“…The order parameters ∆ ss (k) involve both spin singlet and triplet components due to the ASOC. We here ignore the spin triplet component and assume the s-wave spin singlet order parameter [∆ ↑↓ (k) = −∆ ↓↑ (k) = ψ], since the spin susceptibility at T = 0 is independent of the symmetry of order parameters for a large ASOC |∆ ss (k)| α [8,9,14]. Although the p-wave superconducting state of Li 2 Pt 3 B has been indicated by several experimental results [4,5], we do not touch this possibility since our analysis of the spin susceptibility cannot distinguish the p-wave superconducting state from the s-wave one.…”

“…2(a). In Figs. 3(a) and 3(c), the horizontal thin dashed line shows the normalized spin susceptibility χ s /χ n = 2/3 of conventional cubic non-centrosymmetric superconductors [8,9]. (b) Density of states in the normal state at α = 0.92 in Fig.…”

“…According to the weak coupling theory neglecting the correlation effects, the spin susceptibility in the cubic non-centrosymmetric superconductor should be reduced to 2/3 of the normal state value at T = 0 [8,9]. On the other hand, the Knight shift measurement of Li 2 Pt 3 B did not show such a decrease in spin susceptibility [4,5].…”