Full Point Group Research Articles

A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy

The phase diagram of cuprate high-temperature superconductors features an enigmatic pseudogap region that is characterized by a partial suppression of low energy electronic excitations. Polarized neutron diffraction, Nernst effect, THz polarimetery and ultrasound measurements on YBa$_2$Cu$_3$O$_y$ suggest that the pseudogap onset below a temperature T* coincides with a bona fide thermodynamic phase transition that breaks time-reversal, four-fold rotation and mirror symmetries respectively. However, the full point group above and below T* has not been resolved and the fate of this transition as T* approaches the superconducting critical temperature T$_c$ is poorly understood. Here we reveal the point group of YBa$_2$Cu$_3$O$_y$ inside its pseudogap and neighboring regions using high sensitivity linear and second harmonic optical anisotropy measurements. We show that spatial inversion and two-fold rotational symmetries are broken below T* while mirror symmetries perpendicular to the Cu-O plane are absent at all temperatures. This transition occurs over a wide doping range and persists inside the superconducting dome, with no detectable coupling to either charge ordering or superconductivity. These results suggest that the pseudogap region coincides with an odd-parity order that does not arise from a competing Fermi surface instability and exhibits a quantum phase transition inside the superconducting dome.

Evidence for Time-Reversal Symmetry Breaking in the Noncentrosymmetric SuperconductorLaNiC2

Muon spin relaxation experiments on the noncentrosymmetric intermetallic superconductor LaNiC2 are reported. We find that the onset of superconductivity coincides with the appearance of spontaneous magnetic fields, implying that in the superconducting state time-reversal symmetry is broken. An analysis of the possible pairing symmetries suggests only four triplet states compatible with this observation, all of them nonunitary. They include the intriguing possibility of triplet pairing with the full point group symmetry of the crystal, which is possible only in a noncentrosymmetric superconductor.

Exciton-spin dephasing and relaxation due to symmetry breaking in two-band bulk semiconductors

The full point group symmetry of a crystal can be broken due to internal or external effective fields. In the study of excitons, such symmetry breaking can lead to a coupling of different exciton states and if a system is prepared in an exciton state with a defined total angular momentum (pseudospin), spin beating is obtained. Looking at the fluctuations of these fields, we use the invariant expansion of an effective Hamiltonian to investigate exciton-spin-relaxation dynamics in a model two-band bulk semiconductor and discuss the respective importance of the different spin-flip processes. We find that interaction terms leading to an electron or hole spin flip give rise to a pure transverse dephasing. Terms where the electron and hole spins are simultaneously reversed lead to transitions between the spin states, which are characterized by the longitudinal relaxation time. Similar to motional narrowing in the case of free carriers, the latter process can lead to an increase in the exciton-spin-relaxation times if extrinsic electric, magnetic, or strain fields rapidly fluctuate in the sample. This effect is shown to be due to the electron-hole exchange interaction.

Ab initio cluster model study of polymer–metal interactions

The interactions of hydrocarbon clusters representing polyethylene with Al, Cu and Zn are studied using an ab initio atomic cluster model. Relativistic effective core potentials and full point-group symmetry were employed. A single polyethylene chain is taken to be represented by two hydrocarbon clusters, one cluster is comprised of 3 carbon and 8 hydrogen atoms, the other hydrocarbon cluster is comprised of 5 carbon and 12 hydrogen atoms. The nature of the interactions are investigated by computing potential energy surfaces, electron populations and orbital energies of systems of interest. It is found that the interaction of hydrocarbon cluster with Al is stronger than that with Cu and Zn. This study suggests the feasibility of carrying-out relativistic effective core potential calculation to numerically characterize the comparative adhesion properties of polymers with different types of metal surfaces.

Effective cluster interactions at alloy surfaces and charge self-consistency: Surface segregation in Ni-10 at. % Al and Cu-Ni.

First-principles results are presented for the effective cluster interactions at the surface of a random Ni\char21{}10 at. % Al alloy. The derivation is based on an extension of the generalized perturbation method to semi-infinite inhomogeneous binary alloys, using a layer version of the Korringa-Kohn-Rostocker multiple-scattering approach in conjunction with the single-site coherent potential approximation to compute the self-consistent electronic structure of the system. When applied to the bulk, the method yields effective pair interactions that have the full point-group symmetry of the lattice to a very high level of numerical accuracy, despite the fact that intra- and interlayer couplings (scattering-path operators) are treated differently, and which are in perfect agreement with those of a recent three-dimensional treatment. Besides the pair terms, a selected class of triplet and quadruplet interactions are calculated, as well as the point interactions induced by the presence of the surface. The value of the latter in the first lattice plane is strongly exaggerated in our approach, leading to a complete segregation of the minority species to the surface. Using a value corresponding to the difference in the surface energies of the pure components for this term leads to the observed Al concentration of \ensuremath{\approxeq}25% at the surface. Possible reasons for the shortcomings of the theory are analyzed, and test calculations for the well studied Cu-Ni system show that the free energy of the semi-infinite alloy cannot be approximated by the sum over the single-particle band energies, once charge self-consistency is enforced at the surface.

VALENCE-FLUCTUATION MECHANISM FOR CUPRATE SUPERCONDUCTIVITY

We explore the concept that the above-T c state is a normal Fermi liquid with strong correlations of the type found in valence-fluctuation and heavy-fermion materials. Experimental evidence and theoretical arguments for this phase are presented. Using an Anderson lattice model Hamiltonian, and a variational many-body formalism, the finite-U mechanism for s-like (full point-group symmetry) pairing is examined in detail. At the mean field or (1/N)0 level of approximation, the pairing tendency is strongly opposed by a magnetic tendency arising from a Gutzwiller version of hybridization renormalization. Pairing does not seem possible for realistic Hamiltonian parameters. This finite-U treatment has, however, now been extended to the (1/N)1 level of approximation. The lattice aspect is found to play a major and unexpected role here, leading to strong suppression of the magnetic tendency. This refined treatment is now found to provide adequate pairing attraction, for reasonable Hamiltonian parameters. Superconductivity is found only when the charge transfer energy Δ CT is quite large, Δ CT ≳ U, but there is evidence that Δ CT is indeed of this magnitude in the cuprate materials. Adequate band narrowing (mass enhancement or heaviness) and a very short coherence length are also obtained, in reasonable agreement with experiment. The quasiparticle interaction at the Fermi surface is strongly repulsive. This provides a reasonable source for the large and linear resistivity, as well as for other aspects of marginal-Fermi-liquid phenomenology. Evidence is found for a strong reduction of T c due to pair-breaking by the quasiparticle scattering. The main (fully self-consistent) calculations assume in-plane isotropy. However, a simplified calculation with a more realistic (anisotropic) band structure for the CuO 2 plane is found to provide a highly anisotropic gap, which may or may not have nodes. There is considerable evidence for such types of gap structure. Because a connection is found here between anomalously short coherence length and anomalously high resistivity, we suggest that this mechanism is also operating within other families of "exotic" superconductors.

Anisotropic s-wave gap and nuclear magnetic resonance in high-temperature superconductors.

The Knight shift and the nuclear magnetic relaxation rates ${\mathit{W}}_{\mathrm{\ensuremath{\perp}}}^{63}$, ${\mathit{W}}_{\mathrm{\ensuremath{\parallel}}}^{63}$, and ${\mathit{W}}_{\mathrm{\ensuremath{\parallel}}}^{17}$ are calculated for temperatures below the superconducting transition temperature of the high-temperature cuprate superconductors; the superscripts refer to the $^{63}\mathrm{Cu}$ and the $^{17}\mathrm{O}$ nuclei while the subscripts refer to the direction of the magnetic field with respect to the CuO layers. The calculations are based on a recently proposed interlayer tunneling mechanism of superconductivity in these materials. In general, the results are consistent with experiments even though the superconducting gap respects the full point-group symmetry of the lattice (anisotropic s wave); the anisotropy of the magnitude of the gap is an essential element.

Hole localization and broken symmetry: A theoretical study of core electron ionization in the Li2 molecule

AbstractAb initio SCF, CI, CEPA, and MCSCF techniques are compared and contrasted in a theoretical study of the 1s core ionized Li2 molecule from the point of view of core hole localization. In agreement with earlier studies of symmetric core ionized molecules, SCF theory is found to give a physically reasonable description of core ionization only when symmetry breaking is allowed. This results in a dramatic lowering of the energy of the core ionized state and hence of the ionization potential. By extension, CI wave functions that are developed in terms of a broken symmetry SCF reference plus its single and double excitations are found to perform significantly better than those constructed from symmetry adapted SCF orbitals. Alternatively, if the full point group symmetry is to be retained, a multiconfigurational treatment is called for and, in agreement with the conclusions of an analogous study on O2 [H. Ågren, P.S. Bagus, and B.O. Roos, Chem. Phys. Letters 82, 505(1981)], it is found that a modestly sized MCSCF wave function is capable of accounting for the energetic effects of symmetry breaking. Potential energy curves for Li2 and several states of core ionized Li2 have been calculated, allowing predictions of the adiabatic ionization potential and vibrational, satellite, and Auger structures in the photoelectron spectrum of Li2 to be made.

Atomic transport via point defects in crystals. IV. Anelastic relaxation

The previously formulated kinetic theory of isothermal atomic transport via point defects is here applied to the description of anelastic relaxation in crystals containing defect pairs. Defect reactions leading to the dissociation and reformation of these pairs are included, but the symmetry and elastic strengths of the relaxation modes are unaffected, with the exception of modes having the full point-group symmetry of the crystal. In this respect anelastic relaxation is different from dielectric relaxation, the strength of which can be substantially affected by these reactions for reasons connected with the contributions which the dissociated defects make to the total measured electric current. The characteristic relaxation times associated with the elastically active modes are, however, shortened by these reactions.

An algorithm for the construction of fully symmetry adapted Fock matrices for molecular Hartree-Fock calculations

Algorithms which permit the construction of fully symmetry adapted Fock matrices are presented for cases where the basis functions and integrals are obtained using only the symmetry of a subgroup of the full point group of the system. In this way fully symmetry-adapted SCF MOs may be obtained even for open shell systems. Computationally, the algorithms are practical and fast. The symmetry information about the full point group is contained implicitly in the one-electron parts of the Fock matrices: no specific symmetry data need be provided. The use of these algorithms has been found to be of considerable help in obtaining convergence for excited state SCF wave functions. An algorithm, due to P. O. Löwdin, for removing near linear dependence from basis sets is reviewed. This method used the same matrix transformation techniques which are required for the symmetrization of the Fock matrices. The application of this algorithm to obtain a set of virtual orbitals suitable for configuration interaction calculations is discussed.

Analysis of the rotational spectrum of C3 v molecules by using factorization and diagonalization of the energy matrix : Application to CH 3C 15N

A method is given for the analysis of the rotational spectrum in the ground and excited states of C 3 v molecules; it consists in a direct diagonalization of the energy matrix including all elements whose contribution can become significant for the analysis up to the sixth order of approximation. The method of factoring the energy matrix into four submatrices A 1, A 2, E, E, according to the symmetry species of the full point group C 3 v , is given. The programm enables the calculation of the rotational frequencies and also carries out by a least-squares method the fitting of the molecular constants for vibrational states v = 0 (ground state) and v E = 1, 2, 3, and 4, separately or simultaneously over several of these states. The analysis of the rotational spectrum of CH 3C 15N in the v 8 = 0, 1, 2 states is given as an example.

Details of first order Coriolis resonance in C 3 v molecules

Reinvestigation of first order Coriolis resonance in molecules belongring to the group C 3 v in a very general manner has shown that two apparently different formulations are equivalent. Complete correlation is established between upper state wave functions, the corresponding transitions to these states, and the symmetry of the states under the full point group C 3 v for any arbitrary choice of phases for the rotation and vibration basis functions.