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It is shown theoretically that ferromagnetic superconductors, UGe$_2$, URhGe, and UCoGe can be described in terms of the A-phase like triplet pairing similar to superfluid $^3$He in a unified way, including peculiar reentrant, S-shape, or L-shape $H_{rm c2}$ curves. The associated double transition inevitable between the A$_1$ and A$_2$-phases in the $H$-$T$ plane is predicted, both of which are characterized by non-unitary state with broken time reversal symmetry and the half-gap. UTe$_2$, which has been discovered quite recently to be a spin-polarized superconductor, is analyzed successively in the same view point, pointing out that the expected A$_1$-A$_2$ transition is indeed emerging experimentally. Thus the four heavy Fermion compounds all together are entitled to be topologically rich solid state materials worth further investigating together with superfluid $^3$He A-phase.
The specific heat of superfluid $^{3}$He, disordered by a silica aerogel, is found to have a sharp discontinuity marking the thermodynamic transition to superfluidity at a temperature reduced from that of bulk $^{3}$He. The magnitude of the discontin
Recently the influence of antisymmetric spin-orbit coupling has been studied in novel topological superconductors such as half-Heuslers and artificial hetero-structures. We investigate the effect of Rashba and/or Dresselhaus spin-orbit couplings on t
We study the effect of dissipation on quantum phase fluctuations in d-wave superconductors. Dissipation, arising from a nonzero low frequency optical conductivity which has been measured in experiments below $T_c$, has two effects: (1) a reduction of
In the Ginzburg-Landau theory of superfluid $^{3}$He, the free energy is expressed as an expansion of invariants of a complex order parameter. Strong coupling effects, which increase with increasing pressure, are embodied in the set of coefficients o
The pressure dependence of the order parameter in superfluid $^3$He is amazingly simple. In the Ginzburg-Landau regime, i.e. close to $T_c$, the square of the order parameter can be accurately measured by its proportionality to NMR frequency shifts a