A theoretical description of the new phases of liquid ^{3}He
Abstract
This paper reviews the theory of anisotropic superfluid phases and its application to the new A and B phases of liquid ^{3}He. It is tutorial in nature and advanced formal techniques are avoided; even the formalism of second quantization is not required. After an initial discussion of the Fermiliquid theory of Landau and its application to the normal phase of liquid ^{3}He, the idea of instability against formation of Cooper pairs is introduced. The effective interaction in liquid ^{3}He is considered, with emphasis on the spindependent interaction arising from virtual spin polarization of the medium ("spin fluctuation exchange"). Next, a selfcontained discussion of the "weakcoupling" BCS theory as applied to anisotropic superfluids is given, with special attention to the "GinzburgLandau" region close to the transition temperature. Formulas are derived for the specific heat, spin susceptibility, normal density tensor, and static spindependent correlation properties of superfluids with both singlet and triplet pairing: In the triplet case the ideas of "spin superfluid velocity" and "spin superfluid density" are also introduced. After a preliminary comparison of the weakcoupling theory with experiment, it is shown that feedback effects due to the modification, by formation of Cooper pairs, of the effective interaction connected with spin fluctuation exchange can produce results which are qualitatively different from those of the weakcoupling theory. An attempt is made to reformulate recent graphtheoretical treatments of this phenomenon in a more elementary language, and considerations based on possible invariant forms of the free energy are also introduced. The properties of the socalled AndersonBrinkmanMorel and BalianWerthamer states, which are commonly identified with ^{3}HeA and B, respectively, are studied in detail. Next, the effects which tend to orient the Cooper pair wave function in a given experimental situation are discussed; in this context the form of the free energy terms arising from spatial variation of the wave function is explored. A semiphenomenological theory of the nuclear magnetic resonance properties is developed and applied in particular to the case of unsaturated cw resonance; the analogy with the Josephson effect is emphasized. The question of relaxation and linewidths is also briefly discussed. A partial account is given of the theory of finitewavelength collective oscillations, with particular reference to first, second, and fourth sound and spin waves. The splitting of the Anormal transition in a magnetic field is considered, with special attention to the possibility it offers of testing theories of the "spin fluctuation" type. Finally, a brief assessment is made of the extent to which the current experimental data support the conventional identification of ^{3}HeA and B and the spin fluctuation theory, and some outstanding problems and possibilities are outlined. Subjects not discussed include "firstprinciples" theories of the effective interaction in ^{3}He collective excitations in the "collisionless" regime, and the problem of ultrasonic absorption, "orbit waves," and the theory of the kinetic coefficients.
 Publication:

Reviews of Modern Physics
 Pub Date:
 April 1975
 DOI:
 10.1103/RevModPhys.47.331
 Bibcode:
 1975RvMP...47..331L