There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

On the theory of superconductivity

The d1 layer metals TaS2, TaSe2, NbSe2, in all their various polytypic modifications, acquire, below some appropriate temperature, phase conditions that their electromagnetic properties have previously revealed as ‘anomalous’. Our present electron-microscope studies indicate that this anomalous behaviour usually includes the adoption, at some stage, of a superlattice. The size of superlattice adopted often is forecast in the pattern of satellite spotting and strong diffuse scattering found above the transition. Our conclusions are that charge-density waves and their concomitant periodic structural distortions occur in all these 4d1/5d1 dichalcogenides. We have related the observed periodicities of these CDW states to the theoretical form of the parent Fermi surfaces. Particularly for the 1T octahedrally coordinated polytypes the Fermi surface is very simple and markedly two-dimensional in character, with large near-parallel walls. Such a situation is known theoretically to favour the formation of...

Charge-density waves and superlattices in the metallic layered transition metal dichalcogenides

The Fermi gas model of one-dimensional conductors is reviewed. The exact solutions known for particular values of the coupling constants in a single chain problem (Tomonaga model, Luther-Emery model) are discussed. Renormalization group arguments are used to extend these solutions to arbitrary values of the couplings. The instabilities and possible ground states are studied by investigating the behaviour of the response functions. The relationship between this model and others is discussed and is used to obtain further information about the behaviour of the system. The model is generalized to a set of coupled chains to describe quasi-one-dimensional systems. The crossover from one-dimensional to three-dimensional behaviour and the type of ordering are discussed.

/pdf/the-fermi-gas-model-of-one-dimensional-conductors-4zpdg1dd6f.pdf

The Fermi gas model of one-dimensional conductors

A theory of the tetramethyltetraselenafulvalene (TMTSF) salts and their sulfur analogs is developed. It is shown that the phase diagram is controlled by electron-electron umklapp scattering. The theory accounts for differences between the sulfur and selenium series, and the absence of Peierls' transitions. Predictions of the pressure dependence of the spin-density-wave critical temperature and correlations of the dimerization of the organic stacks with critical pressures and temperatures are verified experimentally.

Electron-Electron Umklapp Scattering in Organic Superconductors

The phonon-induced $d\ensuremath{-}d$ coupling, calculated in tight-binding approximation, is shown to account for the order of magnitude of ${T}_{c}$ in transition metals. The model relates the coupling constant to the cohesive energy rather than to the melting temperature as proposed by Matthias.

Tight Binding and Transition-Metal Superconductivity

Strong-Coupling Superconductivity in V 3 X type of Compounds

The intraband electron-phonon coupling, calculated in the tight-binding approximation, is derived from an effective deformation potential. This coupling agrees with expressions obtained by previous authors. The potential reduces to the Bardeen-Shockley deformation potential and to the Longuet-Higgins-Salem result in the long-wavelength and short-wavelength limits, respectively. The phonon-induced $d\ensuremath{-}d$ coupling alone is shown to account for the order of magnitude of the superconducting transition temperature in transition metals. The McMillan procedure for the computation of the superconductive coupling is analyzed in the case when the Fermi level falls close to a pronounced Van Hove singularity in the electron density of states. In this case the behavior of the density of states $n$ may dominate the behavior of the product $\mathrm{nV}$, where $V$ is the electron-electron effective interaction.

Slaven Barišić

Papers

Electron-Electron Umklapp Scattering in Organic Superconductors

Tight Binding and Transition-Metal Superconductivity

Strong-Coupling Superconductivity in V 3 X type of Compounds

Rigid-Atom Electron-Phonon Coupling in the Tight-Binding Approximation.I

Electron mechanism for the structural phase transitions in La2−xBaxCuO4