E. Yépez

A simple algorithm for the group theoretical classification of quantum states

Here we present a simple and easily handled algorithm for the group theoretical classification of quantum states that although, it is implicit in a general group theory formulation, it is not presented the way it is discussed here, and which facilitates its application by non-specialists. It consists in finding the minimal set of symmetry operations needed to identify unequivocally the symmetry for each state and a direct calculation of the character of the representation expanded by the vector state. The algorithm allows simple and fast calculations of the symmetry properties, even for large symmetry groups and systems with many degrees of freedom. In particular the occurrence of accidental degeneracy is distinguished clearly using this method. In order to illustrate the application of the method, we discuss the classification of the vibrational states for two different molecular systems.

A THEORETICAL-ANALYSIS OF PHONON-SPECTRA IN HIGH-TC SUPERCONDUCTORS

Abstract The normal modes of vibration of the superconductors Y 1 Ba 2 Cu 3 O 7 and related compounds are calculated using the harmonic aproximation. The conditions for the Jahn-Teller effect and its influence on the phonon density of states are analysed.

Theoretical analysis of the Jahn-Teller effect in the LaBaCuO superconductor

Abstract We just commemorated the 10 years anniversary of the discovery of the high Tc superconductivity of Bednorz and Muller (BM). In their celebrated paper BM mentioned the possible role of the Jahn-Teller (JT) effect in the enhancement of the transition temperature to the superconducting state. In the present work we analize, under the quasi-molecular approximation, the conditions for the existence of the JT effect in the CuO6 cluster belongin to the LaBaCuO superconductor of BM. The electronic part is obtained from self consistent ab initio calculations and the force constants are calculated taking the second derivatives of the energy using the Hartree-Fock approximation for the electronic part. Both, the electronic and vibrational parts are classified accordingly to the irreducible representations of the D4h group in order to establish the JT theorem. The physical consecuences of the presence of the JT effect in CuO6 cluster are discussed.

A theoretical phonon calculation in the Bi2Sr2CaCu2O8 superconductor

Abstract The normal modes of vibration of the Bi 2 Sr 2 CaCu 2 O 8 superconducting material (with Tc near 85 K) are calculated within the harmonic approximation. The theoretical group analysis of the normal modes and the phonon density of states are reported.

Jahn-Teller effect in the LaSrCuO superconductor

The CuO 6 octahedron in the T structure of the La-Sr-Cu-O superconductor is considered within the quasi-molecular approximation in order to calculate the electronic structure and the vibrational modes that could participate in the Jahn-Teller effect. The electronic calculations are made within the extended Huckel model and the vibrations are taken from previously reported results. Once the electronic and vibrational participants are determined using group theory analysis, the intensity of the electron-phonon interaction is calculated to establish the Jahn-Teller deformation

Surface properties for α-cluster nuclear matter

We introduce a new microscopic model for α-cluster matter, which simulates the properties of ordinary nuclear matter and α-clustering in a curved surface of a large but finite nucleus. The model is based on a nested icosahedral fullerene-like multiple-shell structure, where each vertex is occupied by a microscopic α-particle. The novel aspect of this model is that it allows a consistent description of nuclear surface properties from microscopic parameters to be made without using the leptodermous expansion. In particular, we show that the calculated surface energy is in excellent agreement with the corresponding coefficient of the Bethe-Weizacker semi-empirical mass formula. We discuss the properties of the surface α-cluster state, which resembles an ultra cold bosonic quantum gas trapped in an optical lattice. By comparing the surface and interior states we are able to estimate the α preformation probability. Possible extensions of this model to study nuclear dynamics through surface vibrations and departures from approximate sphericity are mentioned.

Density functional electronic spectrum of the CuO6-10 cluster and possible local Jahn-Teller distortions in the La-Ba-Cu-O superconductor

We present a density functional theory (DFT) calculation in the generalized gradient approximation to study the possibility for the existence of Jahn–Teller (JT) or pseudo Jahn–Teller (PJT) type local distortions in the La–Ba–Cu–O superconducting system. We performed the calculation and correspondingly group theory classification of the electronic ground state of the CuO6-10 elongated octahedra cluster, immersed in a background simulating the superconductor. Part of the motivation to do this study is that the origin of the apical deformation of the CuO6-10 cluster is not due to a pure JT effect, having therefore a non a priori condition to remove the degeneracy of the electronic ground state of the parent regular octahedron. We present a comparative analysis of the symmetry classified electron spectrum with previously reported results using unrestricted Hartree–Fock calculations (UHF). Both the DFT and UHF calculations produced a non-degenerate electronic ground state, not having therefore the necessary condition for a pure JT effect. However, the appearance of a degenerate Eg state near to the highest occupied molecular orbital in the DFT calculation, suggests the possibility for a PJT effect responsible for a local distortion of the oxidized cluster.

APICAL OXYGEN MOVEMENT IN YBA2CU3O6+X AS A FUNCTION OF THE OXYGEN CONCENTRATION

Abstract We report the results of an analysis of the vibrational properties of the apical oxygen O(4) in YBa2Cu3O6+δ as a function of the the oxygen concentration O(1) in the chains. The analysis is based on the calculation of the behaviour of the partial phonon density of states for O(4) for different x values. Following the movement of the peaks corresponding to different modes we pay special attention to the discussion of possible anomalous displacement of the apical oxygen in the c direction.

Phonon contibution for th elow temperature specific heat of solid C60 and K3C60

Abstract We present the result of a theoretical analysis of the phonon contribution to the specific heat for both pure C 60 and alkaline doped K 3 C 60 fullerenes. This is based on the construction of the phonon density of states through the solution of the dynamical matrix, using a Born-Mayer type potential, for the different points in the Brillouin zone. Our results show the contribution to the specific heat for the different modes and in particular we study the low-lying modes coming from intramolecular motions appearing at low temperatures.

Dynamic atomic displacements in YBa2Cu3O6+x as a function of temperature

Abstract Mean-square displacements in the superconductor YBa 2 Cu 3 O 6+δ are calculated using the partial phonon density of states through the solution of the dynamical matrix. We make a comparison of the results found and study the consistency of the method for analysing displacement properties. In particular we discuss the movements of chain O (1) and apical O (4) oxygens. From a comparison of the results with data coming from diffraction experiments we look for possible anomalous behaviour of the oxygens as a function of temperature.