Symmetry of boundary conditions of the Dirac equation for electrons in carbon nanotubes.

We consider the effective mass model of spinless electrons in single wall carbon nanotubes that is equivalent to the Dirac equation for massless fermions. Within this framework we derive all possible energy independent hard wall boundary conditions that are applicable to metallic tubes. The boundary conditions are classified in terms of their symmetry properties and we demonstrate that the use of different boundary conditions will result in varying degrees of valley degeneracy breaking of the single particle energy spectrum

Tunneling of correlated electrons in ultra high magnetic field

Effects of the electron-electron interaction on tunneling into a metal in ultra-high magnetic field (ultra-quantum limit) are studied. The range of the interaction is found to have a decisive effect both on the nature of the field-induced instability of the ground state and on the properties of the system at energies above the corresponding gap. For a short-range repulsive interaction, tunneling is dominated by the renormalization of the coupling constant, which leads eventually to the charge-density wave instability. For a long-range interaction, there exists an intermediate energy range in which the conductance obeys a power-law scaling form, similar to that of a 1D Luttinger liquid. The exponent is magnetic-field dependent, and more surprisingly, may be positive or negative, i. e., interactions may either suppress or enhance the tunneling conductance compared to its non-interacting value. At energies near the gap, scaling breaks down and tunneling is again dominated by the instability, which in this case is an (anisotropic) Wigner crystal instability.Comment: 4 pages, 2 .eps 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

Gap Structure of the Spin-Triplet Superconductor Sr2RuO4 Determined from the Field-Orientation Dependence of Specific Heat

We report the field-orientation dependent specific heat of the spin-triplet superconductor Sr2RuO4 under the magnetic field aligned parallel to the RuO2 planes with high accuracy. Below about 0.3 K, striking 4-fold oscillations of the density of states reflecting the superconducting gap structure have been resolved for the first time. We also obtained strong evidence of multi-band superconductivity and concluded that the superconducting gap in the active band, responsible for the superconducting instability, is modulated with a minimum along the [100] direction.Comment: 4 pages, 4 figure

Interface superconductivity in the eutectic Sr2RuO4-Ru: 3-K phase of Sr2RuO4

The eutectic system Sr2RuO4-Ru is referred to as the 3-K phase of the spin-triplet supeconductor Sr2RuO4 because of its enhanced superconducting transition temperature Tc of ~3 K. We have investigated the field-temperature (H-T) phase diagram of the 3-K phase for fields parallel and perpendicular to the ab-plane of Sr2RuO4, using out-of-plane resistivity measurements. We have found an upturn curvature in the Hc2(T) curve for H // c, and a rather gradual temperature dependence of Hc2 close to Tc for both H // ab and H // c. We have also investigated the dependence of Hc2 on the angle between the field and the ab-plane at several temperatures. Fitting the Ginzburg-Landau effective-mass model apparently fails to reproduce the angle dependence, particularly near H // c and at low temperatures. We propose that all of these charecteric features can be explained, at least in a qualitative fashion, on the basis of a theory by Sigrist and Monien that assumes surface superconductivity with a two-component order parameter occurring at the interface between Sr2RuO4 and Ru inclusions. This provides evidence of the chiral state postulated for the 1.5-K phase by several experiments.Comment: 7 pages and 5 figs; accepted for publication in Phys. Rev.

Upper Critical Field of the 3 Kelvin Phase in Sr2RuO4

The inhomogeneous 3 Kelvin phase is most likely a superconducting state nucleating at the interface between micrometer-sized Ru-metal inclusions and Sr2RuO4 above the bulk onset of superconductivity. This filamentary superconducting state yields a characteristic temperature dependence of the upper critical field which is sublinear, i.e., H_{c2} (T) \propto (T^* - T)^{\gamma} with 0.5 \leq \gamma < 1 (T^*: nucleation temperature). The Ginzburg-Landau theory is used to analyze the behavior of the nucleated spin-triplet phase in a field and the characteristic features of H_{c2} observed in the experiment are explained based on a two-component order parameter in the presence of a filament of enhanced superconductivity with a finite width.Comment: 4 pages, 3 figure

Field-Orientation Dependent Heat Capacity Measurements at Low Temperatures with a Vector Magnet System

We describe a heat capacity measurement system for the study of the field-orientation dependence for temperatures down to 50 mK. A "Vector Magnet" combined with a mechanical rotator for the dewar enables the rotation of the magnetic field without mechanical heating in the cryostat by friction. High reproducibility of the field direction, as well as an angular resolution of better than 0.01 degree, is obtained. This system is applicable to other kinds of measurements which require a large sample space or an adiabatic sample environment, and can also be used with multiple refrigerator inserts interchangeably.Comment: 7 pages, 8 figure

Influence of gap structures to specific heat in oriented magnetic fields: Application to the orbital dependent superconductor, Sr2_2RuO4_4

We discuss influence of modulation of gap function and anisotropy of Fermi velocity to field angle dependences of upper critical field, $H_{c2}$, and specific heat, $C$, on the basis of the approximate analytic solution in the quasiclassical formalism. Using 4-fold modulation of the gap function and the Fermi velocity in the single-band model, we demonstrate field and temperature dependence of oscillatory amplitude of $H_{c2}$ and $C$. We apply the method to the effective two-band model to discuss the gap structure of Sr$_2$RuO$_4$, focusing on recent field angle-resolved experiments. It is shown that the gap structures with the intermediate magnitude of minima in $[100]$ direction for $\gamma$ band, and tiny minima of gaps in $[110]$ directions for $\alpha$ and $\beta$ bands give consistent behaviors with experiments. The interplay of the above two gaps also explains the anomalous temperature dependence of in-plane $H_{c2}$ anisotropy, where the opposite contribution from the passive $\alpha\beta$ band is pronounced near $T_c$.Comment: 7 pages, 11 figures in JPSJ forma

Early asymmetric cues triggering the Dorsal/Ventral Gene Regulatory Network of the sea urchin embryo

Dorsal/ventral (DV) patterning of the sea urchin embryo relies on a ventrally-localized organizer expressing Nodal, a pivotal regulator of the DV gene regulatory network. However, the inceptive mechanisms imposing the symmetry-breaking are incompletely understood. In Paracentrotus lividus, the Hbox12 homeodomain-containing repressor is expressed by prospective dorsal cells, spatially facing and preceding the onset of nodal transcription. We report that Hbox12 misexpression provokes DV abnormalities, attenuating nodal and nodal-dependent transcription. Reciprocally, impairing hbox12 function disrupts DV polarity by allowing ectopic expression of nodal. Clonal loss-of-function, inflicted by blastomere transplantation or gene-transfer assays, highlights that DV polarization requires Hbox12 action in dorsal cells. Remarkably, the localized knock-down of nodal restores DV polarity of embryos lacking hbox12 function. Finally, we show that hbox12 is a dorsal-specific negative modulator of the p38-MAPK activity, which is required for nodal expression. Altogether, our results suggest that Hbox12 function is essential for proper positioning of the DV organizer.

Detailed study of the ac susceptibility of Sr2RuO4 in oriented magnetic fields

We have investigated the ac susceptibility of the spin triplet superconductor Sr$_2$RuO$_4$ as a function of magnetic field in various directions at temperatures down to 60 mK. We have focused on the in-plane field configuration (polar angle $\theta \simeq 90^{\circ}$), which is a prerequisite for inducing multiple superconducting phases in Sr$_2$RuO$_4$. We have found that the previous attribution of a pronounced feature in the ac susceptibility to the second superconducting transition itself is not in accord with recent measurements of the thermal conductivity or of the specific heat. We propose that the pronounced feature is a consequence of additional involvement of vortex pinning originating from the second superconducting transition.Comment: Accepted for publication in Phys. Rev.