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Physical review. B, Condensed matter

Order parameter and exchange field of superfluid B3 near magnetically active surfaces

Weiyi Zhang

Published Jun 1, 1994• 0 citations
Publisher

Abstract

The order parameter and exchange field of superfluid $^{3}\mathit{B}$ near magnetically active surfaces with perfect reflection are calculated using the quasiclassical theory and a magnetically scattering surface model. Our results show that an exchange field is usually induced in the vicinity of such surfaces due to the spin rotation of the impending quasiparticles, but for certain magnetic configuration of the surface, the order parameters are not depressed at all. This is in strong contrast to the situation near nonmagnetic surfaces where the perpendicular order parameter always vanishes due to the triplet pairing nature of the Cooper pair. We discuss the possible application of this property to identify the Cooper pair symmetry of other unconventional superconductors.

DOI
10.1103/physrevb.49.15864

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The order parameter and exchange field of superfluid 3B^{3}\mathit{B}3B near magnetically active surfaces with perfect reflection are calculated using the quasiclassical theory and a magnetically scattering surface model. Our results show that an exchange field is usually induced in the vicinity of such surfaces due to the spin rotation of the impending quasiparticles, but for certain magnetic configuration of the surface, the order parameters are not depressed at all. This is in strong contrast to the situation near nonmagnetic surfaces where the perpendicular order parameter always vanishes due to the triplet pairing nature of the Cooper pair. We discuss the possible application of this property to identify the Cooper pair symmetry of other unconventional superconductors.
The field dependence of the magnetic susceptibility and collective mode frequencies of superfluid 3B^{3}\mathit{B}3B are calculated perturbatively in (\ensuremath{\gamma}H/\ensuremath{\Delta}) using the quasiclassical theory. With the aid of this perturbation theory, we interpret the gap distortion, nonlinear susceptibility, and collective excitations of the order parameter in terms of additional correlations between Cooper pairs that are induced by a magnetic field. We also calculate the dispersion splittings of the real squashing modes in a magnetic field. In addition to the nonlinear Zeeman shifts of these modes, which occur in strong magnetic fields (\ensuremath{\gamma}H\ensuremath{\sim}0.10\ensuremath{\Delta}), there are low-field (\ensuremath{\gamma}H\ensuremath{\sim}q2{q}^{2}q2vf2{v}_{f}^{2}vf2​/\ensuremath{\Delta}) nonlinearities of the collective mode frequencies resulting from the field dependence of the quantization axis. Our results for all of these response properties of 3B^{3}\mathit{B}3B depend upon a small number of material parameters; thus measurements of these properties can provide detailed information on the quasiparticle interactions.
The order parameter of superfluid 3B^{3}\mathit{B}3B is calculated near surfaces with the quasiclassical theory and a thin-dirty-layer surface-scattering model. The surface structures depend on the temperature, the surface roughness, the Fermi-liquid parameters, and the mass superflow tangential to the surface. All these are studied with special emphasis on the roughness and the superflow. A numerical technique of solving the quasiclassical equations is discussed.
The order-parameter texture has been studied in rotating 3B^{3}\mathit{B}3B in the vortex-free state with NMR techniques. A sequence of textural phase transitions is observed with increasing rotation speed. It is generated by competing interactions with magnetic field, surfaces, and rotation. Two surface interactions are extracted: the susceptibility anisotropy at the wall and the gyromagnetism due to a magnetic-field-induced surface supercurrent. The results are consistent with an order-parameter structure approaching the planar state with diffuse quasiparticle scattering at the wall.
A supercurrent is well recognized as being of prime importance within mean-field theory, but remains largely unexplored in strongly correlated electron systems (SCES) and the quantum critical region. To clarify the impact of the supercurrent on magnetism and superconductivity near an antiferromagnetic quantum critical point, we study the two-dimensional Hubbard model based on a fluctuation exchange approximation for a current-carrying superconducting state. We show a supercurrent-induced antiferromagnetism and emergence of spin-triplet Cooper pairs. The former results from Bogoliubov Fermi surfaces, suppression in the superconducting gap, and strong correlation effects beyond the mean-field theory. Our results suggest that the supercurrent can bring out rich phenomena of superconductivity in SCES.
We study superfluidity in strongly correlated systems by focusing three features as follows. First, interplay between superfluidity and other order parameters near quantum critical points is studied. The onset positions of the order parameters with or without superconductivity determines how they interact with each other. For the spin density wave (SDW) transition, we find that the quantum critical point shifts by order |∆|, where ∆ is pairing amplitude, so that the region of SDW order is smaller in the superconductor than in the metal. This shift is larger than the |∆|2 shift predicted by theories of competing orders which ignore Fermi surface effects. Second, we study a doped antiferromagnetic Mott insulator motivated by copper based high temperature superconductors. Based on spin and charge fractionalization, the algebraic charge liquid phase whose bosonic spinons have energy gap but fermionic holons form Fermi surfaces and its superconductivity are studied. We show fluctuations of local SDW order orientation lead to d-wave superconductivity, and its quantum critical pairing mechanisms are investigated. Also, a theory of bound states between spinons and holons is studied. We show that the fractionalization induces a doubling electron-like quasiparticles, which naturally induces the fractionalized Fermi liquid. The bound state theory describes exotic properties of the underdoped Cuprates such as “nodal-antinodal dichotomy” at a mean field level description. At last, we study superfluidity of fermions in optical lattices near the Feshbach resonance. Due to divergence of scattering length at the resonance, universality is observed and characteristics of superfluidity has been studied. We extend such universal properties by considering superfluid-insulator transition with an even integer number of fermions per unit cell. The resulting insulator interpolates between a band insulator of fermions and a Mott insulator of fermion pairs.
The Fermi-liquid approach generalized to superfluid systems is used to derive general formulas for the normal and abnormal distribution functions (DF) for quasiparticles of a superfluid Fermi liquid (SFL) consisting of electrically neutral fermions with spin-triplet pairing (the spin of a pair s=1, the orbital angular momentum l of the pair being an arbitrary odd number) in a static uniform magnetic field, taking into account the Landau spin-exchange Fermi-liquid interaction at temperatures 0<T<Tc (Tc is the temperature of phase transition from the normal to the superfluid state). In deriving the DF, the explicit form of the energy functional (EF) for SFL is not used. A system of coupled equations is obtained for the order parameter, energy of quasiparticles, and effective magnetic field for the SFL under investigation in the case of an EF quadratic in DF. The obtained DF and the system of equations are applicable for describing both unitary and nonunitary phases of superfluid He3 in a magnetic field, e.g., for determining the magnetization and magnetic susceptibility of these phases.