Singularities In Density Of States Research Articles

Effects of density of states on superconductivity

The effects of the electronic density of states (DOS) on superconductivity are studied within the BCS theory using a one-electron anisotropic tight-binding model for the energy band. By tuning the ratio of the interlayer to intralayer couplings, the model interpolates the two-dimensional and three-dimensional cases. The transition temperature T c and the isotope effect exponent α are studied as a function of the position of the Fermi energy for various degrees of anisotropy. The transition temperature is highest for uncoupled layers with the Fermi energy near to the logarithmic singularity in the 2D DOS, while the corresponding value of α shows a minimum. As the interlayer coupling is increased, the singularity in the DOS is rounded-off. The enhancement in T c is suppressed and α approaches the BCS value of 0.5.

Dependence of the transition temperature on deviations from stoichiometry in the cuprate superconductors

A band of holes moving in an antiferromagnetic plane is used to model the weakly non-stoichiometric cuprate superconductors. We note that a singular density of states at the Brillouin-zone boundary, as is obtained from many different starting points, leads to a maximum in the transition temperature as a function of the deviation from stoichiometry. Numerical calculations of this effect, based on (i) the tight-binding bands that follow from Roth's approximate treatment of the Hubbard model for the Cu${\mathrm{O}}_{2}$ planes, and (ii) the attractive pairing between the oxygen holes that can result from considerations of the extended Hubbard model, are presented.

Narrow band limit of the periodic Anderson model with an interatomic hybridization

We analyze the single-particle part of the periodic Anderson model starting from the atomic representation for band (5 d) and localized (4 f) orbitals. This system with an interatomic hybridization, is transformed into a two-band structure with an intraatomic mixing between the component bands. The resultant hybridized-band structure has narrow lower band with a singular density of states (DOS) at its upper edge. The importance of this singularity for orbitally degenerate 4 f or 5 f systems is briefly discussed.

Excitons in aluminium

A nearly free electron description of the parallel bands responsible for the 1.6 eV absorption edge in aluminium gives rise to an inverse square-root singularity in the joint density of states. The authors have explored the possibility of excitons associated with the corresponding optical transitions. A calculation based on the Bethe-Salpeter equation with a statically screened Coulomb interaction between carriers shows that the singularity in the joint density of states leads to a singlet exciton with a binding energy of only 5 meV. For the case of a triplet exciton they estimate a binding energy of 20 meV. These results are discussed in relation to experiments.

Electron correlations and logarithmic singularities in density of states and conductivity of disordered two-dimensional systems

A simple method is developed for obtaining results from the interaction theory proposed by Altshuler and Aronov (1979). This method yields the logarithmic singularities in the density of states and the conductivity of disordered 2D metals, in agreement with the results of those authors. It produces also the T-1/2 behaviour for a disordered long wire. The correlation between the interaction theory, the localisation theory and experiment is discussed. In particular, it is pointed out that, at zero temperature and for materials for which the inverse screening length is much less than the Fermi wavevector KF, both theories yield the same conductivity. Both effects are probably present in inversion layers.

Two-Phonon Optical Absorption in CuCl and CuBr Crystals

Optical absorption spectra of CuCl and CuBr crystals have been measured in the far-infrared region and at low temperatures between 2 and 80 K. Side-bands due to two-phonon summation and difference processes have been observed. Structures in the absorption spectrum are interpreted as van Hove singularities in the two-phonon density of states and some of them are assigned to combinations of zone boundary phonons.

Strong-Coupling Saturation of Superconductivity inNb3Al0.8Ge0.2

The recent suggestion, based on the tunneling experiments, that the superconducting transition temperature ${T}_{c}$ of ${\mathrm{Nb}}_{3}$${\mathrm{Al}}_{0.8}$${\mathrm{Ge}}_{0.2}$ is saturated with respect to the variation of the phonon frequencies, is critically examined. This is first done within the McMillan set of ideas concerning the high ${T}_{c}$, which was used in formulating the suggestion. The suggestion is thus shown to be in contradiction with the known pressure dependence of ${T}_{c}$. The observed weak variation of ${T}_{c}$ in the martensitic transition is not explained by the saturation effect but rather by the inefficiency of the low-frequency phonons in building up the superconductivity. It is further pointed out that the models of ${\mathrm{Nb}}_{3}X$ compounds, based on the singularity in the electron density of states, are not expected to yield a saturation of ${T}_{c}$ with respect to the phonon frequencies.

Infrared absorption due to H− ions in sodium and potassium halides. II. Impurity induced absorption in the far-infrared region

Measurements and calculations of the impurity induced far-infrared absorption due to H− ions in the sodium and potassium halides are presented. The defect model which was previously determined from theoretical fits to experimental local mode and anharmonic side band data is used to predict the absorption spectrum in the far-infrared region below the reststrahlen frequency. The agreement with the observed absorption spectra is good. It is shown that certain features may be interpreted as Van Hove singularities in the unperturbed density of states of the host crystals and that other peaks in the KBr and KI spectra are due to localized resonances.

Magnetoacoustic density of states resonance

A magnetoacoustic resonance in antimony is described. It is due to a singularity in density of states. This resonance suggest that the Fermi surface of antimony deviates from an ellipsoid.

Bound-Electron-Lattice Coupling and Vibronic Spectra

The radial extent of the coupling between the bound electronic states of a defect ion in a crystal and the vibrations of the lattice ions is investigated. An electrostatic-coupling model is used to evaluate the electronlattice interaction. It is found that those electronic transitions which involve a change in configuration are coupled primarily to the vibrations of ions in the immediate vicinity of the defect. Consequently, if there exist local or pseudolocalized vibrations, the resultant vibronic spectra are dominated by transitions to vibrational modes which have high local amplitude. In contrast, it is found that in general, electronic transitions within a configuration are coupled to nonlocalized vibrations as well as to the localized vibrations. In the special case of the transition $^{5}D_{0}\ensuremath{\rightarrow}^{7}F_{0}$ of ${\mathrm{Sm}}^{2+}$, the coupling is primarily to nonlocalized vibrations, so that the vibrations resemble those of ions of the undisturbed lattice. The observed vibronic structure accompanying this transition of ${\mathrm{Sm}}^{2+}$ in the alkali halides is presented. A comparison is made for ${\mathrm{Sm}}^{2+}$: KBr between the singularities in the phonon density of states as observed in the vibronic structure, and those predicted from the published dispersion curves of KBr obtained from neutron-scattering data. The agreement is found to be very good. The vibronic structure accompanying the same transition of ${\mathrm{Sm}}^{2+}$ in the alkaline-earth halides is also discussed.