The fluctuation conductivity of a moderately clean type II superconductor with strong Pauli paramagnetic pair breaking (PPB) is studied by focusing on the quantum regime at low temperatures and in high magnetic fields. First, it is pointed out that, as the PPB effect becomes stronger, the quantum superconducting fluctuation is generally enhanced so that the renormalized Aslamasov-Larkin (AL) fluctuation conductivity tends to vanish upon cooling above the irreversibility line. Furthermore, by examining other [the DOS and the Maki-Thompson (MT)] terms of the fluctuation conductivity, the field dependence of the resulting total conductivity is found to depend significantly on the type of the vortex lattice (or, glass) ordered state at low temperatures where the strong PPB plays important roles. By comparing the present results on the fluctuation conductivity with insulating and negative magnetoresistance behaviors seen upon entering a PPB-induced novel SC phase of iron selenide (FeSe), it is argued that the vortex matter states of the superconducting order parameter in the second lowest (n = 1) Landau level are realized in FeSe in the parallel field configuration in high fields and at low temperatures.

Recent experiments on the iron-based superconductor FeSe in a high magnetic field have suggested the presence of both the fluctuation-induced vortex liquid regime and a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) vortex lattice. To get a general picture of the magnetic phase diagram in type II superconductors with strong superconducting (SC) fluctuation and strong paramagnetic pair breaking (PPB) such as FeSe, the vortex lattice melting curve H m (T ) is theoretically investigated in situations where a FFLO state is expected to occur. In general, PPB tends to narrow the vortex liquid regime intervening between H c2 (T ) and H m (T ). In particular, the vortex liquid regime is found to rapidly shrink upon entering; by cooling, the temperature range in which the FFLO state with a periodic modulation parallel to the magnetic field is stable in mean-field theory. Based on the present results, the high-field SC phase diagrams of FeSe in the parallel and perpendicular field configurations are discussed.

In the novel superfluid polar phase realized in liquid 3 He in highly anisotropic aerogels, a quantum transition to the polar-distorted A (PdA) phase may occur at low but finite pressure P c (0). It is shown that the nontrivial quantum dynamics of the critical fluctuation of PdA order is induced by the presence of both columnar impurity scattering leading to Anderson's theorem for the polar phase and the line node of the quasiparticle gap in the state, and that, in contrast to the situation of the normal to B-phase transition in isotropic aerogels, a weakly divergent behavior of the compressibility appears in the quantum critical region close to P c (0).