Local virial relation and velocity anisotropy for collisionless self-gravitating systems

The collisionless quasi-equilibrium state realized after the cold collapse of self-gravitating systems has two remarkable characters. One of them is the linear temperature-mass (TM) relation, which yields a characteristic non-Gaussian velocity distribution. Another is the local virial (LV) relation, the virial relation which holds even locally in collisionless systems through phase mixing such as cold-collapse. A family of polytropes are examined from a view point of these two characters. The LV relation imposes a strong constraint on these models: only polytropes with index $n \sim 5$ with a flat boundary condition at the center are compatible with the numerical results, except for the outer region. Using the analytic solutions based on the static and spherical Jeans equation, we show that this incompatibility in the outer region implies the important effect of anisotropy of velocity dispersion. Furthermore, the velocity anisotropy is essential in explaining various numerical results under the condition of the local virial relation.Comment: 8 pages, 5 figures, Proceedings of CN-Kyoto International Workshop on Complexity and Nonextensivity; added a reference for section

Magneto-optics induced by the spin chirality in itinerant ferromagnet Nd2_2Mo2_2O7_7

It is demonstrated both theoretically and experimentally that the spin chirality associated with a noncoplanar spin configuration produces a magneto-optical effect. Numerical study of the two-band Hubbard model on a triangle cluster shows that the optical Hall conductivity $\sigma_{xy}(\omega)$ is proportional to the spin chirality. The detailed comparative experiments on pyrochlore-type molybdates $R_2$Mo$_2$O$_7$ with $R=$Nd (Ising-like moments) and $R=$Gd (Heisenberg-like ones) clearly distinguishes the two mechanisms, i.e., spin chirality and spin-orbit interactions. It is concluded that for $R$=Nd, $\sigma_{xy}(\omega)$ is dominated by the spin chirality for the dc ($\omega=0$) and the $d \to d$ incoherent intraband optical transitions between Mo atoms.Comment: 4 pages, 5 figures. submitted to Phys. Rev.

Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems

A criterion to determine the existence of zero-energy edge states is discussed for a class of particle-hole symmetric Hamiltonians. A ``loop'' in a parameter space is assigned for each one-dimensional bulk Hamiltonian, and its topological properties, combined with the chiral symmetry, play an essential role. It provides a unified framework to discuss zero-energy edge modes for several systems such as fully gapped superconductors, two-dimensional d-wave superconductors, and graphite ribbons. A variants of the Peierls instability caused by the presence of edges is also discussed.Comment: Completely rewritten. Discussions on coexistence of is- or id_{xy}-wave order parameter near edges in d_{x^{2}-y^{2}}-wave superconductors are added; 4 pages, 3 figure

Tunnelling spectroscopy of the interface between Sr2RuO4 and a single Ru micro-inclusion in eutectic crystals

The understanding of the zero bias conductance peak (ZBCP) in the tunnelling spectra of S/N junctions involving d-wave cuprate superconductors has been important in the determination of the phase structure of the superconducting order parameter. In this context, the involvement of a p-wave superconductor such as Sr2RuO4 in tunnelling studies is indeed of great importance. We have recently succeeded in fabricating devices that enable S/N junctions forming at interfaces between Sr2RuO4 and Ru micro-inclusions in eutectic crystals to be investigated.3 We have observed a ZBCP and have interpreted it as due to the Andreev bound state, commonly seen in unconventional superconductors. Also we have proposed that the onset of the ZBCP may be used to delineate the phase boundary for the onset of a time reversal symmetry broken (TRSB) state within the superconducting state, which does not always coincide with the onset of the superconducting state. However, these measurements always involved two interfaces between Sr2RuO4 and Ru. In the present study, we have extended the previous measurements to obtain a deeper insight into the properties of a single interface between Sr2RuO4 and Ru.Comment: To appear in J. Phys. Soc. Jpn. Vol. 75 No.12 issu