arXiv subjects
Publications and source records attributed to I. A. Fomin.
Role of inhomogeneous perturbations of nematic aerogel on the form of the order parameter emerging at the transition of liquid $^3$He in the superfluid state is considered. It is shown that a region of stability of the polar distorted ABM phase can begin right from the transition temperature. The symmetry argument is given, which selects the most favorable aerogel for stabilization of pure polar phase.
It is shown that in the polar phase of superfluid 3 He, stabilized by nematic aerogel, at the condition of specular reflection of quasi-particles from the strands of aerogel the temperature dependence of the gap in the spectrum of quasi-particles coincides with that in the bulk polar phase without impurities. The analogy with the Anderson theorem for conventional superconductors is discussed.
The orbital anisotropy induced in the superfluid 3He by nematic aerogel is, generally speaking, spatially non-uniform. This anisotropy in its turn induces spatial fluctuations of the order parameter. It is shown here that for the polar phase these fluctuations decrease the overall amplitude of the order parameter and the value of the frequency shift of the transverse NMR. Different contributions to this effect are discussed and estimated. Their temperature dependencies are discssed as well.
It is shown that if impurities in superfluid 3He have form of infinitely long non-magnetic strands, which are straight, parallel to each other and reflect quasi-particles specularly, the temperature of transition of liquid 3He from the normal into the polar phase coincides with that for the bulk liquid without impurities. Magnetic scattering lowers transition temperature for the polar phase in analogy with the conventional superconductors. These results are discussed in connection with the recent experimental findings.
Random textures of the orbital part of the order parameter of superfluid 3He-A in aerogel are analyzed theoretically in the Ginzburg and Landau region both in the presence and in the absence of a global anisotropy. Correlation functions of angles, determining orientation of the order parameter are found for relative distances which are small in comparison with the characteristic scale of the random texture. Modifications of the Larkin-Imry-Ma state in limiting cases of a relatively strong uniaxial compression and of a uniaxial stretching are analyzed and characteristic parameters of the emerging states are found.
Spacial variation of the orbital part of the order parameter of $^3$He-A in aerogel is represented as a random walk of the unit vector $\mathbf{l}$ in a field of random anisotropy produced by the strands of aerogel. For a range of distances, where variation of $\mathbf{l}$ is small in comparison with its absolute value correlation function of directions of $\mathbf{l}(\mathbf{r})$ is expressed in terms of the correlation function of the random anisotropy field. With simplifying assumptions about this correlation function a spatial dependence of the average variation $\langleδ\mathbf{l}^2\rangle$ is found analytically for isotropic and axially anisotropic aerogels. Average projections of $\mathbf{l}$ on the axes of anisotropy are expressed in terms of characteristic parameters of the problem. Within the "model of random cylinders" numerical estimations of characteristic length for disruption of the long-range order and of the critical anisotropy for restoration of this order are made and compared with other estimations .
Deformed aerogels induce a global anisotropy in the superfluid 3He and orient the orbital part of its order parameter. Here a phenomenological theory of the orientational effect of elastic deformations of aerogels on the superfluid phases of 3He in the spirit of conventional theory of elasticity is formulated. Phenomenological coefficients, entering basic relations, depend on properties of given aerogel in the non-deformed state. Examples of originally isotropic silica aerogel and axially symmetric "nematically ordered" aerogel are considered. Values of phenomenological coefficients are estimated with the aid of a simple microscopic model. An example of a nonuniform deformation of "nematically ordered" aerogel is discussed.
The conventional theory of superconducting alloys does not take into account a discreet character of impurities. Experimental data for superfluid $^3$He in aerogel and for some of high-$T_c$ superconductors reveal a significant discrepancy between the observed temperatures $T_c$ of their transitions in the superfluid or superconducting state and that predicted by the theory. Here a theoretical scheme is presented for finding corrections to the $T_c$ originating from spatial correlations between impurities. Analysis is limited to the Ginzburg and Landau temperature region. The shift of $T_c$ with respect to the pure material is represented as a series in concentration of the impurities $x$. In the first order on $x$ the conventional mean-field result for the lowering of $T_c$ is recovered. Contribution of correlations enters the second order term. It is expressed via the structure factor of the ensemble of impurities. For superfluid $^3$He in silica aerogel the sign of the correction corresponds to an enhancement of the $T_c$ so that the resulting pairbreaking effect of impurities is weakened. When correlation radius of impurities $R$ exceeds the coherence length of the superfluid $ξ_0$ the contribution of correlations to the shift of $T_c$ acquires a factor $\sim(R/ξ_0)^2$ and the weakening of the pairbreaking effect becomes appreciable. The presented scheme is applied to the superfluid $^3$He in aerogel.
Highly anisotropic "nematically ordered" aerogel induces global uniaxial anisotropy in superfluid 3He. The anisotropy lowers symmetry of 3He in aerogel from spherical to axial. As a result instead of one transition temperature in the state, characterized by the orbital moment l=1 there are two, corresponding to projections l_z=o and l_z=\pm 1. The splitting of transition has a pronounced effect on the phase diagram of superfluid 3He and on a structures of appearing phases. Possible phase diagrams, obtained phenomenologically on a basis of Landau expansion of thermodynamic potential in a vicinity of the transition temperature are presented here. The order parameters, corresponding to each phase and their temperature dependencies are found.
Stimulated by the results of NMR experiments with superfluid $^3$He in "nematically ordered" aerogel [1] we report on the results of phenomenological analysis of stability of different phases of superfluid $^3$He subjected to a strong homogeneous uniaxial anisotropy. On a basis of this analysis we suggest a form of the order parameter for the new ESP2 phase observed in the quoted experiments. In the weak coupling limit the suggested order parameter approaches that of the axi-planar phase. We discuss a possible experimental check of the proposed identification of the new phase.
Motivated by the disparity between the experimentally observed properties of superfluid 3He in aerogel and predictions of the Abrikosov and Gorkov theory of superconducting alloys we consider effect of correlated pair-breaking impurities on the temperature dependence of the square of magnitude of the average order parameter and related thermodynamic properties of a Fermi superfluid. We show that the correlations, increasing the spectral density of the fluctuations with small wave vectors increase the transition temperature and enhance a temperature region below Tc where fluctuations of the order parameter dominate. Outside of this region we treat effect of impurities as a perturbation and express corrections to thermodynamic properties in terms of the structure factor of impurities. Assuming a simple model expression for correlation function of aerogel we find corrections to the temperature dependence of the NMR frequency shifts for A-like and B-like phases of 3He and compare these with experimental data.
It is shown that weak correlations between the pair-breaking impurities in superconductors influence a temperature dependence of the order parameter within the Ginzburg and Landau region if the correlation radius of impurities R is greater than the coherence length of the superconductor $ξ_0$.Dependence of the square of the average order parameter on a temperature difference $T_c-T$ changes its slope in a region $ξ_0\sqrt{T_c/(T_c-T)\sim R $. Influence of correlations on other thermodynamic properties of superconductors is discussed too.
Effect of two-particle correlations between impurities on the temperature of transition of a Fermi liquid in the superfluid or superconducting state is analyzed. It is shown, that correlations with a radius exceeding correlation length of the superconductor can have pronounced effect on the transition temperature. The equation for the transition temperature is corrected for correlations of the impurities. Possible applications of the new equation are discussed.
It is shown that instability of homogeneous precession is caused by combined effect of anisotropy of spin wave velocities and dipole interaction. In the principal order on the ratio of the Leggett frequency to the Larmor frequency the increments of growth of spin wave amplitudes are found. The magnitude of the maximum increment for all deviation angles of spin from its equilibrium orientation is calculated. The estimation is made of the minimum temperature down to which the precession is stable.
Using liquid 3He in aerogel as an example, it is shown that correlations in positions of impurities affect the temperature $T_c$ of transition of Fermi liquid in an unconventional superfluid or superconductive state. The effect is significant if the correlation length for impurities is greater than the coherence length in the superfluid or superconductive state $ξ_0$. For 3He in aerogel the suppression of $T_c$ is expressed in terms of the structure factor of aerogel. With the account of the fractal structure of aerogel a simple expression is obtained for the decrease of $T_c$ from its clean value. This expression is in a satisfactory agreement with experimental data.
A mutual action of the random anisotropy brought in the superfluid 3He by aerogel and of the global anisotropy caused by its deformation is considered. Strong global anisotropy tends to suppress fluctuations of orientation of the order parameter and stabilizes ABM order parameter. In a limit of vanishing anisotropy these fluctuations are getting critical. It is argued that still in a region of small fluctuations the average order parameter can acquire "robust" component. This component maintains a long-range order even in a limit of vanishing global anisotropy.
Theory of Rainer and Vuorio of small objects in superfluid ^3He is applied for calculation of the average orientational effect of a deformed aerogel on the order parameter of 3He. The minimum deformation which stabilizes the ordered state is evaluated both for specular and diffusive scattering of quasiparticles by the threads of aerogel.
Effect of the "random anisotropy" type disorder on orientation of the magnetization in an amorphous magnet is considered. It is shown, that the principal corrections to the free energy of the magnet originate from the fluctuations of the order parameter in the direction of its degeneracy. The types of disorder are found, which lift the continuous degeneracy and suppress the Larkin-Imry-Ma mechanism of disruption of the long-range order in continuously degenerate systems.