Breaking of the overall permutation symmetry in nonlinear optical susceptibilities of one-dimensional periodic dimerized Huckel model

Based on infinite one-dimensional single-electron periodic models of trans-polyacetylene, we show analytically that the overall permutation symmetry of nonlinear optical susceptibilities is, albeit preserved in the molecular systems with only bound states, no longer generally held for the periodic systems. The overall permutation symmetry breakdown provides a fairly natural explanation to the widely observed large deviations of Kleinman symmetry for periodic systems in off-resonant regions. Physical conditions to experimentally test the overall permutation symmetry break are discussed.Comment: 7 pages, 1 figur

A priori Wannier functions from modified Hartree-Fock and Kohn-Sham equations

The Hartree-Fock equations are modified to directly yield Wannier functions following a proposal of Shukla et al. [Chem. Phys. Lett. 262, 213-218 (1996)]. This approach circumvents the a posteriori application of the Wannier transformation to Bloch functions. I give a novel and rigorous derivation of the relevant equations by introducing an orthogonalizing potential to ensure the orthogonality among the resulting functions. The properties of these, so-called a priori Wannier functions, are analyzed and the relation of the modified Hartree-Fock equations to the conventional, Bloch-function-based equations is elucidated. It is pointed out that the modified equations offer a different route to maximally localized Wannier functions. Their computational solution is found to involve an effort that is comparable to the effort for the solution of the conventional equations. Above all, I show how a priori Wannier functions can be obtained by a modification of the Kohn-Sham equations of density-functional theory.Comment: 7 pages, RevTeX4, revise

Polar type density of states in non-unitary odd-parity superconducting states of gap with point nodes

It is shown that the density of states (DOS) proportional to the excitation energy, the so-called polar like DOS, can arise in the odd-parity states with the superconducting gap vanishing at points even if the spin-orbit interaction for Cooper pairing is strong enough. Such gap stuructures are realized in the non-unitary states, F_{1u}(1,i,0), F_{1u}(1,varepsilon,varepsilon^{2}), and F_{2u}(1,i,0), classified by Volovik and Gorkov, Sov. Phys.-JETP Vol.61 (1985) 843. This is due to the fact that the gap vanishes in quadratic manner around the point on the Fermi surface. It is also shown that the region of quadratic energy dependence of DOS, in the state F_{2u}(1,varepsilon,varepsilon^{2}), is restricted in very small energy region making it difficult to distinguish from the polar-like DOS.Comment: 5 pages, 3 figures, submitted to J. Phys.: Condens. Matter Lette

Exponential decay properties of Wannier functions and related quantities

The spatial decay properties of Wannier functions and related quantities have been investigated using analytical and numerical methods. We find that the form of the decay is a power law times an exponential, with a particular power-law exponent that is universal for each kind of quantity. In one dimension we find an exponent of -3/4 for Wannier functions, -1/2 for the density matrix and for energy matrix elements, and -1/2 or -3/2 for different constructions of non-orthonormal Wannier-like functions.Comment: 4 pages, with 3 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/lh_wann/index.htm

Odd Parity and Line Nodes in Heavy Fermion Superconductors

Group theory arguments have demonstrated that a general odd parity order parameter cannot have line nodes in the presence of spin-orbit coupling. In this paper, it is shown that these arguments do not hold on the $k_z = \pi/c$ zone face of a hexagonal close packed lattice. In particular, three of the six odd parity representations vanish identically on this face. This has potential relevance to the heavy fermion superconductor $UPt_3$.Comment: 5 pages, revte

Nonlinear Magneto-Optical Response of ss- and dd-Wave Superconductors

The nonlinear magneto-optical response of $s$- and $d$-wave superconductors is discussed. We carry out the symmetry analysis of the nonlinear magneto-optical susceptibility in the superconducting state. Due to the surface sensitivity of the nonlinear optical response for systems with bulk inversion symmetry, we perform a group theoretical classification of the superconducting order parameter close to a surface. For the first time, the mixing of singlet and triplet pairing states induced by spin-orbit coupling is systematically taken into account. We show that the interference of singlet and triplet pairing states leads to an observable contribution of the nonlinear magneto-optical Kerr effect. This effect is not only sensitive to the anisotropy of the gap function but also to the symmetry itself. In view of the current discussion of the order parameter symmetry of High-T$_c$ superconductors, results for a tetragonal system with bulk singlet pairing for various pairing symmetries are discussed.Comment: 21 pages (REVTeX) with 8 figures (Postscript

Transport and the Order Parameter of Superconducting UPt3

We calculate the ultrasonic absorption and the thermal conductivity in the superconducting state of UPt$_{3}$ as functions of temperature and direction of propagation and polarization. Two leading candidates for the superconducting order parameter are considered: the $E_{1g}$ and $E_{2u}$ representations. Both can fit the data except for the ultrasonic absorption in the $A$ phase. To do that, it is necessary to suppose that the system has only a single domain, and that must be chosen as the most favorable one. However, the $E_{2u}$ theory requires fine-tuning of parameters to fit the low temperature thermal conductivity. Thus, transport data favor the $E_{1g}$ theory. Measurements of the thermal conductivity as a function of pressure at low temperature could help to further distinguish the two theories.Comment: 7 pages, 4 figure

Magnetic susceptibility of insulators from first principles

We present an {\it ab initio} approach for the computation of the magnetic susceptibility $\chi$ of insulators. The approach is applied to compute $\chi$ in diamond and in solid neon using density functional theory in the local density approximation, obtaining good agreement with experimental data. In solid neon, we predict an observable dependence of $\chi$ upon pressure.Comment: Revtex, to appear in Physical Review Lette

Odd Frequency Pairing in the Kondo Lattice

We discuss the possibility that heavy fermion superconductors involve odd-frequency pairing of the kind first considered by Berezinskii. Using a toy model for odd frequency triplet pairing in the Kondo lattice we are able to examine key properties of this new type of paired state. To make progress treating the strong $n_f=1$ constraint in the Kondo lattice model we use the technical trick of a Majorana representation of the local moments, which permits variational treatments of the model without a Gutzwiller approximation. The simplest mean field theory involves the development of bound states between the local moments and conduction electrons, characterized by a spinor order parameter. We show that this state is a stable realization of odd frequency triplet superconductivity with surfaces of gapless excitations whose spin and charge coherence factors vanish linearly in the quasiparticle energy. A $T^3$ NMR relaxation rate coexists with a linear specific heat. We discuss possible extensions of our toy model to describe heavy fermion superconductivity.Comment: 67 page