In this review, the physics of Pfaffian paired states, in the context of fractional quantum Hall effect, is discussed using field-theoretical approaches. The Pfaffian states are prime examples of topological ([Formula: see text]-wave) Cooper pairing and are characterized by non-Abelian statistics of their quasiparticles. Here we focus on conditions for their realization and competition among them at half-integer filling factors. Using the Dirac composite fermion description, in the presence of a mass term, we study the influence of Landau level mixing in selecting a particular Pfaffian state. While Pfaffian and anti-Pfaffian are selected when Landau level mixing is not strong, and can be taken into account perturbatively, the particle–hole (PH) Pfaffian state requires non-perturbative inclusion of at least two Landau levels. Our findings, for small Landau level mixing, are in accordance with numerical investigations in the literature, and call for a non-perturbative approach in the search for PH Pfaffian correlations. We demonstrated that a method based on the Chern–Simons field-theoretical approach can be used to generate characteristic interaction pseudo-potentials for Pfaffian paired states.
Utilizing a microscopic Bogoliubov-de Gennes approach we study Josephson effect in arbitrarily oriented d-wave superconductors connected through two ferromagnets with noncollinear magnetizations, by solving scattering problem. The critical Josephson current is calculated for various parameters of the junction. Mutual influence of d-wave superconducting electrodes orientation and angle α between magnetization in ferromagnetic bilayer of thickness d is analyzed. For various orientation of superconducting electrodes, we calculate (d,α) phase diagram, and discuss the possibility to achieve except coexistence of two stable states 0 and π, also coexistence of three stable states 0, π and π∕2, by varying the angle between magnetizations. We observe also areas of coexistence of stable and metastable states.
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