Spin ordering and its effect on low-energy quasiparticles in a p-wave superconducting liquid are investigated.We study the properties of a two-dimensional ͑2D͒ p-wave superconducting liquid where the ground state is spin rotation invariant.In quantum spin disordered liquids, the low-energy quasiparticles are bound states of the bare Bogolubov-De Gennes ͑BdeG͒ quasiparticles and zero energy skyrmions, which are charge neutral bosons at the low-energy limit.Further more, spin collective excitations are fractionalized ones carrying a half-spin and obeying fermionic statistics.In thermally spin disordered limits, the quasiparticles are bound states of bare BdeG quasiparticles.The latter situation can be realized in some layered p-wave superconductors where the spin-orbit coupling is weak.
The interplay between bulk properties and boundary conditions in one-dimensional quantum systems, gives rise to many intriguing phenomena. These include the emergence of zero energy modes which are of significant interest to a variety of fields. In this work we investigate the presence of such zero modes in cases where the boundary conditions are dynamical and arise due to the coupling to some quantum degrees of freedom. In particular, we study a one-dimensional spin-singlet superconductor, modeled by the Gross-Neveu field theory, coupled to spin
21 magnetic impurities at its boundaries via a spin-exchange interaction. We solve the model exactly for arbitrary values of the bulk and the impurity coupling strengths using nested coordinate Bethe ansatz and show that the system exhibits a rich boundary phase structure. For a range of couplings, the low energy degrees of freedom form irreducible representations of the supersymmetric
spl(2,1)⊗spl(2,1) algebra which become degenerate at a specific point, indicating the emergence of supersymmetry in the low energy boundary degrees of freedom. We show that at the supersymmetric point there exist exact zero energy modes that map one ground state with the other. We express these in terms of the generators of the algebra.
Three-dimensional (3D) degenerate Fermi gases in the presence of spin-orbit coupling, inducing various kinds of physical findings and phenomena, have attracted tremendous attention in these years. We investigate the 3D spin-orbit coupled degenerate Fermi gases in theory and first present the analytic expression of their ground state. Our study provides an innovative perspective into understanding of the topological properties of 3D unconventional superconductors, and describes the topological phase transitions in trivial and topological phase areas. Further, such a system is provided with a richer set of Cooper pairings than traditional superconductors. The dual Cooper pairs with same spin directions emerge and exhibit peculiar behaviors, leading to topological phase transitions. Our study and discussion can be generalized to some other types of unconventional superconductors and areas of optical lattices.