With proper care on the boundary conditions, the total orbital angular momentum L z at finite temperatures is microscopically calculated for the Anderson-Brinkman-Morel state in a cylinder with axial symmetry about the z axis, i.e. the textures considered by McClure and Takagi at T =0. The pairing in this geometry occurs between m and 1- m one-particle states, where m denotes the axial quantum number. It is found that L z decreases from its zero temperature value
2ℏN, with N the total particle number, in the same way as the components of the superfluid density tensor. Responsible for this reduction is identified to be the phase shift between m and 1- m quasiparticle states caused by the difference in the centrifugal potentials. This fact implies that the plane-wave representation is not suitable for the problem.
We analyze the evolution of superfluidity for nonzero orbital angular momentum channels from the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein condensation (BEC) limit in three dimensions. First, we analyze the low-energy scattering properties of finite range interactions for all possible angular momentum channels. Second, we discuss ground-state
(T=0) superfluid properties including the order parameter, chemical potential, quasiparticle excitation spectrum, momentum distribution, atomic compressibility, ground-state energy, and low-energy collective excitations. We show that a quantum phase transition occurs for nonzero angular momentum pairing, unlike the
s-wave case where the BCS to BEC evolution is just a crossover. Third, we present a Gaussian fluctuation theory near the critical temperature
(T=Tc), and we analyze the number of bound, scattering, and unbound fermions as well as the chemical potential. Finally, we derive the time-dependent Ginzburg-Landau functional near
Tc, and compare the Ginzburg-Landau coherence length with the zero-temperature average Cooper pair size.
Cooper pairs in chiral superfluids carry quantized units of relative orbital angular momentum (OAM). Various predictions of the intrinsic OAM density or the macroscopic OAM of a two-dimensional chiral superfluid differ by several orders of magnitude, which constitute the so-called angular momentum paradox. Following several previous studies, we substantiate the semiclassical Bogoliubov--de Gennes theory of the single-particle edge current and OAM in two-dimensional chiral superfluids in the BCS limit. The analysis provides a simple intuitive understanding for the vanishing of OAM for a non-
p-wave chiral superfluid (such as
d+id) confined in a rigid potential. When generalized to anisotropic chiral superconductors and three-dimensional chiral superfluids, the theory similarly returns an accurate description. We also present a detailed numerical study of the chiral phases in the BEC limit. Our study suggests that, in both BCS and BEC phases, the relative OAM of the individual Cooper pairs contribute to the total OAM additively, and that in both phases the corresponding macroscopic OAM density distribution is localized at the boundary.
An investigation was conducted within the limits of the Bardeen-Cooper- Schrieffer (BCS) theory of the properties of the l = 1, 2, 3,... states of condensed fermions. The study is confined to states only of zero-total momentum. The results indicated that the most unusual properties were connected with the angular momentum. Less spectacular were the superfluidity or superconductivity properties. Unlike the case for l = 0, the states for all higher l's are sensitive to impurity scattering effects. (B.O.G.)
We present a new calculation of the current $\stackrel{\ensuremath{\rightarrow}}{\mathrm{g}}$ flowing in a ground state of the Bardeen-Cooper-Schrieffer (BCS) form for a weakly inhomogeneous superfluid with the symmetry of
3He-
A. When the structure of the order parameter not determined by symmetry is appropriate to
3He-
A and when the mass density $\ensuremath{\rho}$ of the helium is essentially uniform, our current reduces to that calculated by Cross. If the mass density is allowed to vary, we find a generalization of the Cross current which shows that when ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}_{s}=0$ and the anisotropy axis $\stackrel{\ensuremath{\rightarrow}}{\mathrm{l}}$ is uniform, then the current is simply $(\frac{\ensuremath{\hbar}}{4M}){\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\nabla}}}_{\ensuremath{\rho}}\ifmmode\times\else\texttimes\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{l}}$. We show that this property of the BCS ground state, which taken with the Cross definition leads to an "intrinsic angular momentum density" of $\frac{\ensuremath{\rho}\ensuremath{\hbar}}{2M}$ at zero temperature, also follows directly from the Gor'kov equations. If the range of the order parameter is taken to be small compared with the interatomic separation, then the ground state does not describe
3He-
A, but a Bose-Einstein condensate of tightly bound diatomic molecules. In this limit our current reduces to the form calculated by Ishikawa et al. We indicate why their analysis is only valid in this limit, and offer some rather more general remarks on the differences between Cooper pairing and the Bose-Einstein condensation of diatomic molecules.