Generalized β\beta-conformal change and special Finsler spaces

In this paper, we investigate the change of Finslr metrics $$L(x,y) \to\bar{L}(x,y) = f(e^{\sigma(x)}L(x,y),\beta(x,y)),$$ which we refer to as a generalized $\beta$-conformal change. Under this change, we study some special Finsler spaces, namely, quasi C-reducible, semi C-reducible, C-reducible, $C_2$-like, $S_3$-like and $S_4$-like Finsler spaces. We also obtain the transformation of the T-tensor under this change and study some interesting special cases. We then impose a certain condition on the generalized $\beta$-conformal change, which we call the b-condition, and investigate the geometric consequences of such condition. Finally, we give the conditions under which a generalized $\beta$-conformal change is projective and generalize some known results in the literature.Comment: References added, some modifications are performed, LateX file, 24 page

Elasticity-Driven Nanoscale Electronic Structure in Superconductors

The effects of long-range anisotropic elastic deformations on electronic structure in superconductors are analyzed within the framework of the Bogoliubov-de Gennes equations. Cases of twin boundaries and isolated defects are considered as illustrations. We find that the superconducting order parameter is depressed in the regions where pronounced lattice deformation occurs. The calculated local density of states suggests that the electronic structure is strongly modulated in response to lattice deformations, and propagates to longer distances. In particular, this allows the trapping of low-lying quasiparticle states around defects. Some of our predictions can be directly tested by STM experiments.Comment: 5 pages, 5 figures, reference added, accepted to Physical Review Letter

Impurity spin textures across conventional and deconfined quantum critical points of two-dimensional antiferromagnets

We describe the spin distribution in the vicinity of a non-magnetic impurity in a two-dimensional antiferromagnet undergoing a transition from a magnetically ordered Neel state to a paramagnet with a spin gap. The quantum critical ground state in a finite system has total spin S=1/2 (if the system without the impurity had an even number of S=1/2 spins), and recent numerical studies in a double layer antiferromagnet (K. H.Hoglund et al., cond-mat/0611418) have shown that the spin has a universal spatial form delocalized across the entire sample. We present the field theory describing the uniform and staggered magnetizations in this spin texture for two classes of antiferromagnets: (i) the transition from a Neel state to a paramagnet with local spin singlets, in models with an even number of S=1/2 spins per unit cell, which are described by a O(3) Landau-Ginzburg-Wilson field theory; and (ii) the transition from a Neel state to a valence bond solid, in antiferromagnets with a single S=1/2 spin per unit cell, which are described by a deconfined field theory of spinons.Comment: 30 pages, 9 figure

Single Impurity Effects in Multiband Superconductors with Different Sign Order Parameters

A single impurity problem is investigated for multiband s-wave superconductors with different sign order parameters (+-s-wave superconductors) suggested in Fe-pnictide superconductors. Not only intraband but also interband scattering is considered at the impurity. The latter gives rise to impurity-induced local boundstates close to the impurity. We present an exact form of the energy of the local boundstates as a function of strength of the two types of impurity scattering. The essential role of the impurity is unchanged in finite number of impurities. The main conclusions for a single impurity problem help us understand effects of dense impurities in the +-s-wave superconductors. Local density of states around the single impurity is also investigated. We suggest impurity site nuclear magnetic resonance as a suitable experiment to probe the local boundstates that is peculiar to the +-s-wave state. We find that the +-s-wave model is mapped to a chiral dx2-y2+-idxy-wave, reflecting the unconventional nature of the sign reversing order parameter. For a quantum magnetic impurity, interband scattering destabilizes the Kondo singlet.Comment: 23 pages, 7 figures, to be published in J. Phys. Soc. Jpn. (2009) No.

On the Bloch Theorem Concerning Spontaneous Electric Current

We study the Bloch theorem which states absence of the spontaneous current in interacting electron systems. This theorem is shown to be still applicable to the system with the magnetic field induced by the electric current. Application to the spontaneous surface current is also examined in detail. Our result excludes the possibility of the recently proposed $d$-wave superconductivity having the surface flow and finite total current.Comment: 12 pages, LaTeX, 3 Postscript figure

Tunneling spectra for (dx2−y2+isd_{x^2-y^2}+is)-wave superconductors versus tunneling spectra for (dx2−y2+idxyd_{x^2-y^2}+id_{xy})-wave superconductors

The tunneling conductance spectra of a normal metal / insulator / singlet superconductor is calculated from the reflection amplitudes using the Blonder-Tinkham-Klapwijk (BTK) formulation. The pairing symmetry of the superconductor is assumed to be $d_{x^2-y^2}+is$, or $d_{x^2-y^2}+id_{xy}$. It is found that in the ($d_{x^2-y^2}+is$)-wave case there is a well defined conductance peak in the conductance spectra, in the amplitude of the secondary s-wave component. In the ($d_{x^2-y^2}+id_{xy}$)-wave case the tunneling conductance has residual values within the gap, due to the formation of bound states. The bound state energies depend on the angle of the incident quasiparticles, and also on the boundary orientation. On the basis of this observation an electron focusing experiment is proposed to probe the ($d_{x^2-y^2}+id_{xy}$)-wave state.Comment: 17 pages with 9 figure

New Kinetic Equation for Pair-annihilating Particles: Generalization of the Boltzmann Equation

A convenient form of kinetic equation is derived for pair annihilation of heavy stable particles relevant to the dark matter problem in cosmology. The kinetic equation thus derived extends the on-shell Boltzmann equation in a most straightforward way, including the off-shell effect. A detailed balance equation for the equilibrium abundance is further analyzed. Perturbative analysis of this equation supports a previous result for the equilibrium abundance using the thermal field theory, and gives the temperature power dependence of equilibrium value at low temperatures. Estimate of the relic abundance is possible using this new equilibrium abundance in the sudden freeze-out approximation.Comment: 19 pages, LATEX file with 2 PS figure