Paul Brusov

Novel sound phenomena in superfluid helium in aerogel and other impure superfluids

During the last decade new techniques for producing impure superfluids with unique properties have been developed. This new class of systems includes superfluid helium confined to aerogel, HeII with different impurities (D2, N2, Ne, Kr), superfluids in Vycor glasses, and watergel. These systems exhibit very unusual properties including unexpected acoustic features. We discuss the sound properties of these systems and show that sound phenomena in impure superfluids are modified from those in pure superfluids. We calculate the coupling between temperature and pressure oscillations for impure superfluids and for superfluid He in aerogel. We show that the coupling between these two sound modes is governed either by c∂ρ/∂c or σρaρs (for aerogel) rather than thermal expansion coefficient ∂ρ/∂T, which is enormously small in pure superfluids. This replacement plays a fundamental role in all sound phenomena in impure superfluids. It enhances the coupling between the two sound modes that leads to the existence of such phenomena as the slow mode and heat pulse propagation with the velocity of first sound observed in superfluids in aerogel. This means that it is possible to observe in impure superfluids such unusual sound phenomena as slow pressure (density) waves and fast temperature (entropy) waves. The enhancement of the coupling between the two sound modes decreases the threshold values for nonlinear processes as compared to pure superfluids. Sound conversion, which has been observed in pure superfluids only by shock waves should be observed at moderate sound amplitude in impure superfluids. Cerenkov emission of second sound by first sound (which never been observed in pure superfluids) could be observed in impure superfluids.

A method of distinction of a mixed dx2−y2+idxy state of HTSC from the pure d-wave state

Abstract Recent experiments and theoretical considerations show that in HTSC the mixture of different d-wave states is realized. We calculate for the first time the collective mode spectrum in a mixed state d x 2 − y 2 +id xy of HTSC. We use the model of d-pairing for superconductive and superfluid fermi-systems (HTSC, HFSC, etc., developed by P.N. Brusov and N.P. Brusova within path integration technique earlier. There are 10 collective modes in considered state: five of them are high frequency and five others seem to be Goldstone-like ones. In spite of the fact that spectra in both states d x 2 − y 2 and d xy are identical the spectrum in mixture d x 2 − y 2 +id xy state turns out to be quite different from them. Thus the probe of the spectrum in ultrasound and/or microwave absorption experiments could be used to distinguish the mixture — of two d-wave states from pure d-wave state.

Ultrasound attenuation and collective modes in mixed d x2-y2 + id xy state of unconventional superconductors

We discuss two methods used for the study of unconventional superconductors: ultrasound attenuation and collective modes. These two methods, as well as microwave absorption, turn out to be coupled and have become very important now. Within models built by path integration technique we analyze some recent ideas concerning possible realization of the mixture of different d-wave states in high temperature superconductors (HTSC).We specifically consider the mixture of dx2-y2 and dxy states. We study the collective mode spectrum and the ultrasound attenuation in the mixed state, and show that each of the two methods allows us to distinguish a pure d-wave state from a mixed one. They also allow us to identify the type of pairing and order parameter in unconventional superconductors, including the presence and topology of gap nodes, the magnitude of the gap, and degree of admixture in the mixed state.

The collective modes in HTSC and heavy fermion superconductors (HFSC) under d-pairing

Abstract The model of d-pairing for superconductive and superfluid fermi-systems(HTSC, HFSC etc.) created by P.N. Brusov and N.P. Brusova within path integration technique earlier has been applied to investigation of the collective mode spectrum in HTSC and HFSC. We considered 5 states in HTSC (d x 2 −y 2 ,d 3z 2 −r 2, d xy ,d xz ,d yz ) and 3 in HFSC (dγ, Y 2−1 , sin 2 θ). We found 5 high frequency modes in each state as well as 5 Goldstone-like ones. Results could be used to interpret microwave and ultrasonic absorption experiments as well as to identify the superconductive states through these experiments.

The path integral model of d- pairing superconductors

The model of d-pairing for superconductive and superfluid fermi-systems (HTCS, HFSC, etc.) has been developed within path integration technique. The action functional which determines all properties of the model system including collective ones, has been obtained by path integration over “fast” and “slow” fermi-fields. It could be used for determination of different superconductive states, for calculation of the transition temperatures as well as for calculation of collective mode spectrum for HTSC and HFSC.

COLLECTIVE PROPERTIES OF UNCONVENTIONAL SUPERCONDUCTORS

In light of recent experiments, the study of the collective excitations in unconventional superconductors (USC) becomes very important. We build by path integration technique 2D and 3D models of p- and d-pairing for superfluids and superconductors (SC). Within these models we calculate the collective excitations in different USC (high temperature superconductors (HTSC), heavy fermion superconductors (HFSC) etc.) under p- and d-pairing. We considered both bulk and 2D systems. Some recent ideas concerning realization in HTSC of the mixtures of different states are investigated. In particular, we consider the mixture of dx2-y2 and dxy states in HTSC. Obtained results could be used for interpretation of the sound and microwave absorption data as well as for identification of the type of pairing and order parameter in unconventional superconductors.

The collective excitations in heavy-fermion superconductors under d-pairing

Abstract Within path integral model of d-pairing for heavy-fermion superconductors (HFSC) developed recently by Brusov and Brusova-Kulik, the whole collective mode spectrum has been calculated for three states of HFSC. Among them, two states (dγ and Y2−1) have been treated by Hiroshima and Namaizawa before, while the third state is considered for the first time. The number of collective modes in each phase is equal to ten,among which five are high-frequency modes while the five others are Goldstone or Goldstone-like ones. The spectrum can be used to identify the superconducting states through ultrasound and microwave absorption experiments as well as to interpret these experiments.

Nonlinear hydrodynamic equations for superfluid helium in aerogel

Abstract Aerogel in superfluids is studied very intensively during last decade. The importance of these systems is connected to the fact that this allows to investigate the influence of impurities on superfluidity. We have derived for the first time nonlinear hydrodynamic equations for superfluid helium in aerogel. These equations are generalization of McKenna et al. equations for nonlinear hydrodynamics case and could be used to study sound propagation phenomena in aerogel–superfluid system, in particular—to study sound conversion phenomena. We have obtained two alternative sets of equations, one of which is a generalization of a traditional set of nonlinear hydrodynamics equations for the case of an aerogel–superfluid system and, the other one represents a la Putterman equations (equation for v → s is replaced by equation for A → = ρ n ρσ w → , where w → = v → n − v → s ).

Collective excitations in unconventional superconductors

In light of recent experiments study of the collective excitations in unconventional superconductors (USC) becomes very important. We build by path integration technique 2D and 3D models of p- and d- pairing for superfluids and superconductors (SC). Within these models we calculate the collective excitations in different USC [high temperature superconductors (HTSC), heavy fermion superconductors (HFSC) etc.] under p- and d-pairing. We consider both bulk and 2D systems. Some recent ideas concerning realization in HTSC of the mixtures of different states are investigated. In particular, we consider the mixture of d x 2 -y 2 and d xy states in HTSC. Obtained results could be used for interpretation of the sound and microwave absorption data as well as for identification of the type of pairing and order parameter in unconventional superconductors.

Identification of 3He-A by ultrasound experiments

Abstract On the basis of available experimental data Gould [Physica B 178 (1992) 266] has suggested that 3 He-A, conventionally identified as the axial phase, may actually be an axi-planar phase. Some experiments have been done to clarify the situation [see, for example, T.R. Mullins et al., Phys. Rev. Lett. 72 (1994) 4177] but the problem is still open. While we take no position on the interpretation of the data, we note that the collective mode structure of the two phases differ and that appropriate measurements could resolve the issue. We investigate this problem within a simple, time-dependent Ginzburg–Landau (GL) model as well as by studying the second variation of the free energy functional. Both methods show that the spectrum in the axial phase is degenerate, while it is split in the axi-planar phase. This fact may serve as a sensitive test of the existence of the latter.