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Title: Strong coupling corrections to the Ginzburg-Landau theory of superfluid {sup 3}He

Abstract

In the Ginzburg-Landau theory of superfluid {sup 3}He, the free energy is expressed as an expansion of invariants of a complex order parameter. Strong coupling effects, which increase with increasing pressure, are embodied in the set of coefficients of these order-parameter invariants [A. J. Leggett, Rev. Mod. Phys. 47, 331 (1975); E. V. Thuneberg, Phys. Rev. B 36, 3583 (1987); J. Low Temp. Phys. 122, 657 (2001)]. Experiments can be used to determine four independent combinations of the coefficients of the five fourth-order invariants. This leaves the phenomenological description of the thermodynamics near T{sub c} incomplete. Theoretical understanding of these coefficients is also quite limited. We analyze our measurements of the magnetic susceptibility and the NMR frequency shift in the B phase which refine the four experimental inputs to the phenomenological theory. We propose a model based on existing experiments, combined with calculations by Sauls and Serene [Phys. Rev. B 24, 183 (1981)] of the pressure dependence of these coefficients, in order to determine all five fourth-order terms. This model leads us to a better understanding of the thermodynamics of superfluid {sup 3}He in its various states. We discuss the surface tension of bulk superfluid {sup 3}He and predictions formore » novel states of the superfluid such as those that are stabilized by elastic scattering of quasiparticles from a highly porous silica aerogel.« less

Authors:
; ; ; ;  [1]
  1. Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208 (United States)
Publication Date:
OSTI Identifier:
20957837
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. B, Condensed Matter and Materials Physics; Journal Volume: 75; Journal Issue: 17; Other Information: DOI: 10.1103/PhysRevB.75.174503; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; CORRECTIONS; ELASTIC SCATTERING; FREE ENERGY; GINZBURG-LANDAU THEORY; HELIUM 3; MAGNETIC SUSCEPTIBILITY; NUCLEAR MAGNETIC RESONANCE; ORDER PARAMETERS; POROUS MATERIALS; PRESSURE DEPENDENCE; QUASI PARTICLES; SILICA; STRONG-COUPLING MODEL; SUPERFLUIDITY; SURFACE TENSION; THERMODYNAMICS

Citation Formats

Choi, H., Davis, J. P., Pollanen, J., Haard, T. M., and Halperin, W. P.. Strong coupling corrections to the Ginzburg-Landau theory of superfluid {sup 3}He. United States: N. p., 2007. Web. doi:10.1103/PHYSREVB.75.174503.
Choi, H., Davis, J. P., Pollanen, J., Haard, T. M., & Halperin, W. P.. Strong coupling corrections to the Ginzburg-Landau theory of superfluid {sup 3}He. United States. doi:10.1103/PHYSREVB.75.174503.
Choi, H., Davis, J. P., Pollanen, J., Haard, T. M., and Halperin, W. P.. Tue . "Strong coupling corrections to the Ginzburg-Landau theory of superfluid {sup 3}He". United States. doi:10.1103/PHYSREVB.75.174503.
@article{osti_20957837,
title = {Strong coupling corrections to the Ginzburg-Landau theory of superfluid {sup 3}He},
author = {Choi, H. and Davis, J. P. and Pollanen, J. and Haard, T. M. and Halperin, W. P.},
abstractNote = {In the Ginzburg-Landau theory of superfluid {sup 3}He, the free energy is expressed as an expansion of invariants of a complex order parameter. Strong coupling effects, which increase with increasing pressure, are embodied in the set of coefficients of these order-parameter invariants [A. J. Leggett, Rev. Mod. Phys. 47, 331 (1975); E. V. Thuneberg, Phys. Rev. B 36, 3583 (1987); J. Low Temp. Phys. 122, 657 (2001)]. Experiments can be used to determine four independent combinations of the coefficients of the five fourth-order invariants. This leaves the phenomenological description of the thermodynamics near T{sub c} incomplete. Theoretical understanding of these coefficients is also quite limited. We analyze our measurements of the magnetic susceptibility and the NMR frequency shift in the B phase which refine the four experimental inputs to the phenomenological theory. We propose a model based on existing experiments, combined with calculations by Sauls and Serene [Phys. Rev. B 24, 183 (1981)] of the pressure dependence of these coefficients, in order to determine all five fourth-order terms. This model leads us to a better understanding of the thermodynamics of superfluid {sup 3}He in its various states. We discuss the surface tension of bulk superfluid {sup 3}He and predictions for novel states of the superfluid such as those that are stabilized by elastic scattering of quasiparticles from a highly porous silica aerogel.},
doi = {10.1103/PHYSREVB.75.174503},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 17,
volume = 75,
place = {United States},
year = {Tue May 01 00:00:00 EDT 2007},
month = {Tue May 01 00:00:00 EDT 2007}
}
  • We first discuss the generalized Eilenberger equations for superfluid /sup 3/He in the presence of a magnetic field and for uniform rotation of the system. These equations determine the space-dependent Green's function, the free energy density, and the supercurrent density at all temperatures. From these equations we derive the generalized Ginzburg-Landau series expansions in powers of spatial derivatives and the order parameter. This is in contrast to Cross' generalized Ginzburg-Landau approach, which takes into account only spatial derivatives up to second order. Explicit expressions are given for the corrections of order (1-T/T/sub c/) to the well-known expressions for the bendingmore » energy, magnetic anisotropy energy, and superfluid current. With the help of these expressions we calculate the stability regions of uniform and helical textures in the superflow-field phase diagram. For decreasing temperature these regions are found to become smaller. The stability region of the uniform texture vanishes at T/sup 0//sub h/approx.0.88T/sub c/, in agreement with Fetter's result.« less
  • Previous spin-fluctuation theories yielding the strong coupling corrections ..delta..beta-bar/sub i/ to the five coefficients of the fourth-order invariants in the free energy functional are extended. First, the superfluid part of the susceptibility is calculated up to order ..delta../sup 4/for all momenta and frequencies and the contribution arising from p-wave fluctuations of the order parameter is included. Then the frequency sums yielding the ..delta..beta-bar/sub i/ are calculated by taking into account the full momentum and frequency dependence of the superfluid susceptibility and the spin fluctuation propagator. The results for the ..delta..beta-bar/sub i/ are plotted vs. a cutoff q/sub c/ on themore » momentum integration for spin-fluctuation parameters IequivalentN(0)I=0.75 and I=0.95. The cutoff takes into account in a rough way the effect of additional terms in the free energy functional which were neglected in previous theories. These additional terms are due to the implicit dependence of the superfluid susceptibility on the spin-fluctuation parameter I via the gap parameter ..delta... The gap equation providing the relation between ..delta.. and I is derived in the weak coupling approximation. The cutoffs obtained by fitting the experimental values of the three combinations of ..delta..beta-bar/sub i/(arising from the measured specific heat discontinuities on the melting curve) are comparable to the cutoff obtained from the spin-fluctuation contribution to the weak coupling free energy (q/sub c/=0.3(2k/sub F/) for I=0.75). The corrections due to the momentum and frequency dependence of the superfluid susceptibility and the spinfluctuation propagator are large and point in the direction of better agreement with experiment: The ratio R/sub 1/ =..delta..beta-bar/sub 5//(..delta..beta-bar/sub 2/+..delta..beta-bar/sub 4/) decreases from 2 to about 1.2. It is concluded that spin-fluctuation theory in its present form cannot account quantitatively for the measured specific heat discontinuities on the melting curve.« less
  • Vortices in superfluid /sup 3/He differ qualitatively from all other vortices. In conventional quantized vortices (/sup 4/He, superconductors) the order parameter is a scalar function with cylindrical symmetry that vanishes on its axis, but in superfluid /sup 3/He the order parameter has nine complex components. More interestingly, the symmetries of the differential equation describing the vortices can be broken by its solutions. In the pressure-temperature phase diagram of /sup 3/He-B, there is a first-order transition (observed in the shift of the NMR line) between two different vortices that, as recent theory has shown, have different broken symmetries. The vortex observedmore » at high pressures has broken parity with either left- or right-handed vortices. The low-pressure vortex (which is the vortex obtained in the weak-coupling Bardeen-Cooper-Schrieffer theory) has, in addition, broken rotational symmetry around its axis, resulting in a novel double-core structure. The Ginzburg-Landau theory of vortices reproduces the properties of the transition, accounts well for the measured susceptibility and magnetization, and gives detailed predictions about properties not yet measured, such as the jump of the magnetization in the transition, the shift of the transition line in magnetic field, and the orientation of the double-core vortex. The lack of helical instability in the double-core vortex implies that the identification of the vortices is unique. The transition between vortices is interpreted in simple physical terms. A qualitative explanation is given to the metastable state of the low-pressure vortex observed at low temperatures. The numerical method for solving the Ginzburg-Landau equation is discussed.« less
  • The scattering amplitude of Bedell and Pines is used to calculate the strong-coupling corrections and specific-heat jumps in superfluid /sup 3/He. Excellent agreement between theory and experiment was found for the specific-heat jumps and the polycritical point below which the B phase becomes more stable than the A phase.
  • A mass superflow in A{sub 1} phase carries both fully polarized nuclear spin flow and zero entropy simultaneously. The second sound in A{sub 1} is then a hybrid spin/entropy wave propagation. The authors have studied the spin/entropy wave propagation in fields up to 5 T between 10 and 30 bar. When A{sub 1} makes transition into the superfluid A{sub 2} phase, the spin/entropy wave is expected to disappear abruptly. Unexpectedly the authors observe that there is a {open_quotes}critical{close_quotes} region within A{sub 1} phase over which the attenuation gradually increases. The observation might be an evidence for presence of minority spinmore » pairs in A{sub 1}. From the measured velocity of spin/entropy wave, the authors determinde the superfluid to normal component density ratio. In the Ginzburg-Landau region of their measurement close to the transition temperature, the superfluid fraction can be simply related to the expansion coefficients, {beta}{sub i}, of free energy in terms of order parameter. Using their results and the phase diagram, the authors have extracted {beta}{sub 24}=({beta}{sub 2}+{beta}{sub 4}) and {beta}{sub 5}. The strong coupling corrections so obtained to the expansion coefficients are in agreement with theory.« less