Sadao Nakajima

On the Electron-Phonon Interaction in Normal Metals. I

By the use of Frohlichs Hamil!onian and the method of Greens functions, the electronxad phonon interaction in a normal metal under a steady magnetic field is studied. It is shown that the period of the de Haas-van Alphen effect is not modified by the interaction. The resonance frequency of the Azbel-Kaner effect, on the other hand, is modified and the cyclotron mass of the electron takes essentially the same value as the thermal mass which is also modified by the interaction as shown previously. The conclusion is in accord with the recent experimental results obtained by Kip and Grimes on Na and K. The same conclusion, however, is obtained also by applying Landaus theory of Fermi liquids to the inter-electronic Coulomb correlation without introducing the electron-phonon interaction, though the mass shift caused by the former seems too small. § I. Introduction In a previous paper> we examined how the electron-phonon interaction modifies the density of one-electron states (i.e. the thermal mass of the electron) and electric conductivity of a normal metal. As emphasized there, the physical point is the dynamical character of the interaction. This character is already evident in the lowest order process in the perturbation theory of the electron self-energy. Thus, between emission and reabsorption of a phonon by an elec-. tron, there exists retardation which makes the time dependence of the selfxad energy essential. Indeed, as we have shown, this dynamical part of the selfxad energy becomes singular when the velocity of sound v. is much less than the electron velocity Vp at the Fermi surface and appreciably modifies the thermal mass. It results also in some anomalous dispersion of the one~electron excitaxad tion spectrum when excitation energies are comparable to the Debye temperature. On the other hand, in the case of electric conductivity, the renormalization of the wave function explicitly comes into play in addition to the mass renormalixad zation mentioned above. These two effects are cancelled by each other both in static and anomalous limits and there appears the bare (band theoretical) electron mass in the expression for conductivity. The aim of the present paper is to extend the theory so as to include a steady magnetic field. We thus deal with de Haas-van Alphen effect and Azbelxad Kaner effect, taking into consideration the electron-phonon interaction. As for the de Haas-van Alphen effect, Luttinger 2> and Gorkov and Bychkov3> have already

Solitary waves in saturated films of superfluid 4He

It is shown that there should exist in saturated films of superfluid 4He at low temperature a nonlinear surface wave described by the Korteweg-de Vries equation. The effect of surface tension makes the solitary wave cold, in contrast to very thin films discussed in a preceding paper. An electrostatic method is proposed to generate cold solitary waves. The asymptotic behavior can be found theoretically by the inverse scattering method. Estimates of parameters imply the possibility of observing each solitary wave separately.

A Model for Elastic Anomalies in K2Pt(CN)4Br0.3·3H2O

A “spin-lattice” model is proposed for K 2 Pt(CN) 4 Br 0.3 ·3H 2 O (KCP) to solve the puzzling problem of the apparent complete softening of shear modulus C 66 without any structural phase transition at low temperatures. Our model emphasizes the importance of the site II water molecules lying between bromine ions and Pt(CN) 4 complexes. Each water molecule is assumed to have three configurations, which are represented by an S =1 Ising spin. An almost complete agreement is obtained between calculation and experimental data. A marked “hardening” of C 66 at low temperatures ( T <90 K) is predicted. A structural phase transition is possible if the spin-lattice coupling can be enhanced by e.g. external pressure. Ultrasonic attenuation coefficient α 66 , and also C 44 , α 44 , are calculated.

Elementary Quantum Theory of Light Scattering in Liquid Helium

The usual formalism of second quantization is generalized to include the case in which liquid helium contains atoms in electronic excited states. The formalism is applied to sccatterxad ing of the photon, where the dipolar coupling between excited and normal atoms is included as perturbation. The resulting cross sections for Brillouin and Raman scattering agree with those obtained by the semi-phenomenological theory of Stephen. The relation with the recent theory of Iwamoto is also discussed in terms of Green functions.

On Superconductivity of the Falicov-Cohen Model

and the thermodynamical critical field nearly quadratic in temperature. The model shows neither nonlinear nor Josephson tunneling. Yet the coefficient b in Cohens gap parameter L1 (E) =bE obeys Ginzburg-Landau equations, so that the model does show the Meissner effect and infinite d.c. conductivity. The shift of the transition point caused by non-magnetic impurities is also obtained to the first order of the impurity concentration.

On the Method of Anomalous Green Functions in the Kondo Problem at Zero Temperature

The method of anomalous Green functions introduced by Takano and Ogawa into the Kondo problem of sod interaction is reformulated more carefully. It is found that the selfxad consistency equation should contain the energy shift caused by the sod interaction as a paraxad meter and therefore can have a non-trivial solution even in the limit of vanishing anomalous Green functions. The equation in this limit has precisely the same form as Yoshimoris secular equation, provided that the most divergent corrections are included into the vertex part. Abrikosov formulation,5) in which the localized spin is described in terms of dexad struction and creation operators of quasifermions. We introduce the Green function which describes the propagation of the pair of an extra electron and a quasifermion injected into the Fermi sea of the free electron gas. The bound state is represented by an isolated pole of the Green function on the complex energy plane. The standard perturbation expansion has been applied. When the most divergent vertex corrections are included, our secular equation to deterxad mine the isolated pole takes exactly the same form as the Yoshimori equation. 4 ) Therefore, Yoshimoris conclusion that only the singlet bound state is possible and his expression for the binding energy apply also to our secular equation. Now, by use. of the same Abrikosov formulation, Takano and Ogawa 6 ) pro- posed a non-perturbational approach. In analogy to the Gorkov 7 ) formulation of BCS theory, they· assumed that anomalous amplitudes such as <claa,e), <a,et Clva) do not vanish, where c, c t are destruction and creation operators of conduction electrons and a, at are those of quasifermions. Takano and Ogawa. made the Hartree-Fock-Gorkov approximation and obtained non-trivial solutions both for singlet and triplet states which have essentially the same binding energies as those obtained by the lowest order Yosida theory.S) Abrikosov 8 ) extended the Takano-Ogawa theory by including anomalous amplitudes such as <at c t ), <ca) and also. by including the most divergent correc-

ELECTRON-PHONON INTERACTION AND CYCLOTRON RESONANCE IN METALS

The theory of electron-phonon interaction shifting of the cyclotron and thermal masses is extended to include a d-c magnetic field in Frohlichs Hamiltonian, obtaining the h-f conductivity. Landaus theory of Fermi liquids was applied to see the effect of the Coulomb interaction of electrons. (R.E.U.)

Effect of Coulomb Interaction on Anomalous Skin Effect

Many-body correlation effects on transport phenomena result from the self-energy effect described by the quasiparticle picture and from the two-body (electron-electron, hole-hole, or electron-hole) correlation effect that cannot be included in the one-particle picture. There is no correction in the extreme anomalous limit; ambiguity exists in the choice of the boundary condition. It is shown tha this ambiguity can be removed by calculating the frequency and wave number dependent conductivity sigma /sub omega / (q) (S. Nakajima, Progr. Theoret. Phys., 23: 694(1960)). The boundary condition is considered when the Maxwell equation coupled with the generalized Ohm law is solved. The general formula of conductivity and the method of Green functions are used. (L.N.N.)

A New Research Project in Japan on Superconducting Materials

Presently I am organizing a group of about forty senior Japanese scientists in universities and some other institutions to work on new superconducting materials towards higher transition temperatures. The three-year research project, which we believe to be the first step of a longer term research activity, will start from April 1984 with financial support of about

Superfluid and excitonic states

2.4 × 106 from the Ministry of Education, Science, and Culture, Japan.