Hiroshi Namaizawa

Collective modes and a theory of response ofd-wave superconductors

We present a theory of the response ofd-wave superconductors to weak applied fields, by taking account of the Coulomb interaction and all the collective degrees of freedom as well as crystal symmetry. We choose two representative phases: the dγ phase, which has point nodes in the energy gap, and theY2−1 phase, which has line as well as point nodes. The former is a self-consistent solution for cubic as well as spherical symmetries and the latter is one for spherical, cubic, and hexagonal symmetries. We obtain obviously gauge-invariant expressions for the order-parameter fluctuations and the currents, having forms common not only to thed-wave states, but also to thep-wave states studied earlier. We also investigate the collective excitations; in the long-wavelength limit for spherically symmetric systems, there are, on the frequency-temperature plane, seven branches for eachd-wave phase considered, in addition to the common plasma mode and orbital Goldstone modes resulting from the spontaneous breakdown of the rotational invariance. In theY2−1-phase two eigenmodes are found to become gapless at a finite temperature, below which they are purely imaginary. This implies instability of the phase. The effect of crystal anisotropy on the collective spectra is also studied.

On the roton-roton interaction at finite total momentum

Abstract To explain the strong momentum dependence of the roton-roton scattering cross-section observed by Forbes and Wyatt we propose, for the roton-roton interaction at finite total momentum, a simple power law expression in the energy. To match the experiment the allowed values for the power and the coupling constant are found rather limited.

Theory of quasi-two-dimensional quantum solids. II. An anisotropic reaction-matrix approach

A self-consistent theory is proposed for anisotropic quantum solids such as dense helium monolayers adsorbed onto graphite, based upon the reactionmatrix formalism. The effect of the excitations normal to the adsorption plane is fully included in the ground-state as well as in the vibrational properties. Dispersion relations are derived both for the “in-plane” and “out-of-plane” vibrational modes, and the coupling of the two modes is studied as well.

Influence of Spin Fluctuations Upon Heat Capacity of 2D Fermi Liquid Formed on Hectorite

We measured low-temperature heat capacities of two-dimensional Fermi liquid (2D FL) formed on Hectorite down to 15mK. At a coverage where mean atomic distance is comparable to that of bulk3He liquid, we found that the temperature dependence deviates considerably from the expected linearity. To account for the deviation we carried through integrals including RPA spin susceptibility for the Stoner-Hubbard(SH) or the Landaus Fermi liquid (LFL) models over the effectively entire, energy-momentum space without imposing the paramagnon approximation or the like. We found numerically that the spin fluctuation develops a T2correction at TT*, is taken over by a Tlog T term where T* is some hundredths of TF. With these corrections we are able to interprete the data and have determined the parameters for each model consistently at the densities observed.

Raman scattering from He-II near the two-roton threshold

Abstract A new formalism will be proposed for the Raman scattering from He-II near the two-roton threshold by noting that the processes including long wave-length photons dominate the intermediate states, thus being automatically free from the difficulty of the hard-core problem with which the conventional theories were unable to cope. The resulted expression for the intensity is proportional to the multi-phonon part of the structure factor. By expanding the atomic density fluctuation in terms of phonon-roton operators, Hamiltonian for the elementary excitations is constructed and the structure factor is shown to be proportional to the generalized density of states of interacting rotons: It contains the form-factor of a roton-pair creation from the atomic density at every vertex of the ladder processes as well as at the places where the pair is created and annihilated by light quanta. Assuming a power-law in energy for the form-factor the Raman spectra at various pressures are analysed by taking the coupling constant, g, and the roton minimum energy, Δ, as fitting parameters. The allowed margin for the power of the form-factor, α, is found to be 0≤α≲9/16, including both the conventional case (α=0) and the margin set by the direct roton-roton scattering (α≈1/2), thereby solving the long withstanding puzzle why the theories in error are so successful in explaining the Raman feature. The present theory revived the robust concept of roton bound states at low pressures as well as opened the way to determine Δ, the fundamental quantity of the elementary excitations by Raman data alone.

Raman scattering from He II near the two-roton threshold. I. A new formulation

A new formalism will be proposed for the Raman scattering from He II near the two-roton threshold. By showing that the processes including long wavelength photons in the intermediate states are enhanced it is found that the Raman intensity is proportional to the multi-phonon part of the structure factor. To study the structure factor the atomic density fluctuation is expanded in terms of the phonon-roton operators. Based on it the Hamiltonian for the elementary excitations is constructed. Then the structure factor is shown proportional to the generalized density of states of interacting rotons (GDOSIR): It contains the form-factor of a roton-pair creation from the atomic density at every vertex of ladder processes as well as at the places where the pair is created and annihilated by light quanta. Thanks to the commitment of long wave-length photons the proposed formalism is automatically free from the hard-core problem, with which the conventional ones should inevitably confront but were unable to cope.

Theory of quasi-two-dimensional quantum solids. I. Two dimensional correlation and the application to 4He monolayers adsorbed upon graphite

The self-consistent reaction-matrix theory developed for bulk quantum solids is extended to quasi-two-dimensional quantum solids realized by 4He adsorbed upon graphite. The cohesive energy, chemical potential, spreading pressure, and inverse compressibility at 0 K are calculated for 4He in the areal density range 0.076–0.120 »−2. Sound velocities and phonon spectra are also calculated and the characteristic temperatures of the simple twodimensional Debye model are derived. The theoretical results agree well with empirical values.

Rotonology on neutron scattering from He-II at low temperatures

By applying the roton-roton interaction with energy-dependent form-factor, which is proposed [1] to explain anomalous behavior of roton-roton cross section near the two-roton threshold [2] and is also successfully applied [3] to the Raman scattering experiment close to the threshold, we shall study the dynamical structure factor in the region where rotons play vital role to obtain the results which naturally explain neuton experiments, thereby constructing a unified picture for the dynamical feature of He-II, a rotonology.

Superconductivity of Carriers Doped into the Static Charge Density Wave State in 2-Dimensional Square Lattice

On the purpose of studying the effect of long-range Coulomb-interaction in strongly correlated electronic systems we bring in as its representative the nearest-neighbor repulsion (v) in addition to the on-site repulsion (u) and shall investigate the possibility of the superconducting transition .of carriers doped into the charge-density wave (CDW) state expected for v > u/4 in 2-dimensional square lattice. We shall see that strongly correlated hopping processes of doped carriers make the systems superconducting. The favored superconducting phase is of extended s-wave symmetry, and Tc-100 K is shown to easily be attained near the half-filling.

Raman scattering from He II near the two-roton threshold. II: Comparison with experiments

Based on the new formalism which is developed in the preceding paper and is free from the difficulty with which the conventional theories could not cope, we shall examine experimental Roman spectra of He II near the two-roton threshold. The intensity spectrum is determined by the generalized density of states of interacting rotons (GDOSIR). For the form factor of a roton-pair creation from the atomic density fluctuation which appears in GDOSIR, a power law in total energy is assumed. After investigating what types of characteristic structures and how they appear in GDOSIR as α, the power of the form factor, and g, the coupling constant, change, we shall perform line shape analysis between theory and experiment by varying g and ΔR, the roton-minimum energy, by including the instrumental width. It is found that α in the margin 0⩽α ≲1/2 well reproduces experiments at SVP, 5, 10, 15 and 20 kg/cm2, the margin including that set by the direct roton-roton scattering experiment, namely α ≈ 1/2. Further it also includes the conventional theories as a special case (α = 0), thereby solving the puzzle that the theories in error could have predicted the Roman feature so successfully. In addition the values of the coupling constant obtained by the Roman data here are in remarkable correspondence with those determined by the roton-roton scattering, thereby suggesting a possibility for the form of the interaction with α ≈ 1/2 to lead to a unified understanding of roton dynamics. Further the results for ΔR are not only in close agreement with each other for α in the Roman margin but also with the neutron results, from SVP to 20 kg/cm2. Therefore the Roman data alone can afford reliable information on the fundamental parameter of elementary excitations in He II. The results will also be presented for the bound-state energy and the relative peak intensity as functions of pressure and suggestions for experiment are given both for Raman and direct roton-roton scattering which may help narrowing the margin for α further.