To investigate the relationship between atomic topology, vibrational and electronic properties and superconductivity of bismuth, a 216-atom amorphous structure (a-Bi216) was computer-generated using our undermelt-quench approach. Its pair distribution function compares well with experiment. The calculated electronic and vibrational densities of states (eDOS and vDOS, respectively) show that the amorphous eDOS is about 4 times the crystalline at the Fermi energy, whereas for the vDOS the energy range of the amorphous is roughly the same as the crystalline but the shapes are quite different. A simple BCS estimate of the possible crystalline superconducting transition temperature gives an upper limit of 1.3 mK. The e-ph coupling is more preponderant in a-Bi than in crystalline bismuth (x-Bi) as indicated by the λ obtained via McMillan’s formula, λc = 0.24 and experiment λa = 2.46. Therefore with respect to x-Bi, superconductivity in a-Bi is enhanced by the higher values of λ and of eDOS at the Fermi energy.
Cooper pairing in two dimensions is analyzed with a set of renormalized equations to determine its binding energy for any fermion number density and all coupling assuming a generic pairwise residual interfermion interaction. Also considered are Cooper pairs ͑CP's͒ with nonzero center-of-mass momentum ͑CMM͒ and their binding energy is expanded analytically in powers of the CMM up to quadratic terms. A Fermi-sea-dependent linear term in the CMM dominates the pair excitation energy in weak coupling ͑also called the BCS regime͒ while the more familiar quadratic term prevails in strong coupling ͑the Bose regime͒. The crossover, though strictly unrelated to BCS theory per se, is studied numerically as it is expected to play a central role in a model of superconductivity as a Bose-Einstein condensation of CPs where the transition temperature vanishes for all dimensionality dр2 for quadratic dispersion, but is nonzero for all dу1 for linear dispersion.The original Cooper pair ͑CP͒ problem 1 in two ͑2D͒ and three ͑3D͒ dimensions possesses ultraviolet divergences in momentum space that are usually removed via interactions regularized with large-momentum cutoffs.2 One such regularized potential is the BCS model interaction which is of great practical use in studying Cooper pairing 1 and superconductivity.3 Although there are controversies over the precise pairing mechanism, and thus over the microscopic Hamiltonian appropriate for high-T c superconductors, some of the properties of these materials have been explained satisfactorily within a BCS-Bose crossover picture 4-7 via a renormalized BCS theory for a short-range interaction. In the weak-coupling limit of the BCS-Bose crossover description one recovers the pure mean-field BCS theory of weakly bound, severely overlapping CPs. For strong coupling ͑and/or low density͒ well separated, nonoverlapping ͑so-called ''local''͒ pairs appear 4 in what is known as the Bose regime. It is of interest to detail how renormalized Cooper pairing itself evolves independently of the BCS-Bose crossover picture in order to then discuss the possible BoseEinstein ͑BE͒ condensation ͑BEC͒ of such pairs. We address this here in a single-CP picture, while considering also the important case ͑generally neglected in BCS theory͒ of nonzero center-of-mass-momentum ͑CMM͒ CPs that are expected to play a significant role in BE condensates at higher temperatures.In this report we derive a renormalized Cooper equation for a pair of fermions interacting via either a zero-or a finiterange interaction. We find an analytic expression for the CP excitation energy up to terms quadratic in the CMM which is valid for any coupling. For weak coupling only the linear term dominates, as it also does for the BCS model interaction. 8 The linear term was mentioned for 3D as far back as 1964 ͑Ref. 9, p. 33͒. For strong coupling we now find that the quadratic term dominates and is just the kinetic energy of the strongly bound composite pair moving in vacuum.The CP dispersion relation enters into each summand in the BE dis...
titleAb Initio studies of the atomic structure and electronic density of states of pure and hydrogenated a-Si We propose a method to simulate a-Si and a-Si:H using an ab initio approach based on the however the radial structures of a-Si:H are in better agreement with experiment indicating that the experimental work was done on defective samples.
The structure, formation, and migration energies of kinks on the 90 ± partial dislocation in silicon have been studied using a first principles method and periodic boundary conditions. Of the possible types of kinks only those that reverse the sense of the reconstruction of the dislocation on either side of them are found to be stable. Values of 0.04 6 0.03 and 1.09 6 0.03 eV for the formation and migration energies of these defects have been obtained and compared to experimental values. The structure and bonding of these defects have been analyzed both in their equilibrium positions and during their migration. [S0031-9007(98)07772-2]
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