Isotropic Energy Gap Research Articles

Effect of polarization on superfluidity in low density neutron matter

It is shown that, contrary to an earlier estimate, the polarizability of the neutron medium tends to suppress rather than enhance the isotropic energy gap in low-density neutron-star matter.

Perturbation Theory of Covalent Crystals. I. Calculation of Cohesive Energy and Compressibility

An extended perturbation theory of IV and III-V covalent semiconductors based on a model pseudopotential method is presented. In the theory, in addition to the usual second order perturbation, higher order terms with respect to pseudopotential corresponding to the covalent bonding effect are taken into account under the so-called isotropic energy gap model. The theory is applied to calculation of cohesive energies and compressibilities of these crystals. A good agreement between the theory and experiment is obtained.

Band-Structure Effects in Superconductivity. I. Formalism

Dyson equations are derived for the interacting electrons and phonons of a perfect crystal. A separation of the electron and phonon fields which is exact within either the Hartree or the Migdal approximation is effected. All umklapp processes and local-field corrections are included, but the hybridization of electronic bands and of phonon modes is given only implicitly. Our equations reduce to previously obtained forms in the jellium approximation and to lowest order in ${r}_{s}$. The Nambu-Gor'kov formalism is used to derive equations for the superconducting energy gap. Since the Migdal approximation is not applicable to the treatment of the Coulomb interaction, we develop other approximations which yield either three-dimensional integral equations for an anisotropic energy gap $\mathbf{\ensuremath{\Delta}}(\mathbf{k},{k}_{0})$ or one-dimensional integral equations for an isotropic energy gap $\ensuremath{\Delta}({k}_{0})$. An easy method for the calculation of the anisotropy of the energy gap $\mathbf{\ensuremath{\Delta}}(\mathbf{k},{k}_{0})$ in the simple metals is presented. The validity of these approximations is discussed and our equations are compared with those of previous authors. The strongly nonlinear homogeneous integral equation for $\ensuremath{\Delta}({k}_{0})$ is transformed into a quasilinear, inhomogeneous integral equation. This transformation immediately displays several interesting properties of the solution $\ensuremath{\Delta}({k}_{0})$ and yields a method for the rapid numerical calculation of $\ensuremath{\Delta}({k}_{0})$.

On the collective excitations of super-conductors with the P-pairing

In this paper the theory of collective excitations of superconductors with the P-pairing is developed. We start from the ground state of the Balian and Wethamer type, with the isotropic energy gap. The collective excitations we get by use of the self-consistent field method, applied by Bogolubov to S-superconductors. In contradistinction to the S-superconductors in our case we have only one spin branch of excitations. We obtain two-quasiparticle excitations with the continuous energy spectrum, separated by a gap. If Coulomb interaction disappears we get the quasi-acoustic excitations with discrete energy spectrum. If the interaction strength multiplied by leveldensity at Fermi surface tends to zero, the dispersion law is the same as for S-superconductors. Applying the same limit in presence of Coulomb interaction we obtain for sufficiently small pairs momenta the Langmuir frequency. In the last section we obtain the electrodynamics of a state with P-pairing. Among other results the gauge-invariance of the Meissner-effect is proved. All results are obtained without any special choice of the form of interaction. Some formulae in the paper are satisfied also for superposition of S- and P-pairing.

On the energy gap in superconducting tin

The surface resistance of specimens of superconducting tin and of tin-indium alloys has been measured at a frequency of 140 kmc/s and at temperatures near to the superconducting transition. In both single crystal and polycrystalline alloy specimens, the onset of quantum absorption was well defined and corresponded to an isotropic energy gap with a value at absolute zero of about 3·6 kT c . With pure tin, however, the absorption edge was not well defined in specimens oriented away from the tetrad axis; but near to the tetrad axis, there seems to be a considerable region in which the gap varies com paratively slowly, taking a value of about 3·6 kT c . Assuming that the absence of a clearly defined absorption edge for other orientations is the result of gap anisotropy, it is shown that regions in which the gap takes values very different from 3·6 kT c must lie well away from the tetrad axis. The analysis also shows that such regions are comparatively unimportant, and that the 3·6 kT c gap predominates strongly.