Time-reversal symmetry breaking and gapped surface states due to spontaneous emergence of new order in dd-wave nanoislands

We solve the Bogoliubov-de Gennes equations self-consistently for the $d$-wave order parameter in nanoscale $d$-wave systems with [110] surfaces and show that spontaneous time-reversal symmetry (TRS) breaking occurs at low temperatures due to a spontaneously induced complex order parameter of extended $s$-wave symmetry. The Andreev surface bound states, which are protected by a one-dimensional (1D) topological invariant in the presence of TRS, are gapped by the emergence of this new order parameter. The extended $s$-wave order parameter is localized within a narrow region near the surfaces, which is consistent with the fact that topological protection of the gapless Andreev surface states is characterized by the 1D topological invariant. In this TRS-breaking phase, not only is the complex order parameter induced, but also the $d$-wave order parameter itself becomes complex. Furthermore, the disappearance of topological protection brings about novel vortex phenomena near the surfaces. We show that vortex-antivortex pairs are formed in the extended $s$-wave order parameter along the surfaces if the side length of a nanoisland or the width of an infinitely long nanoribbon is relatively large.Comment: 6 pages, 4 figures + 6 pages (supplemental material), to be published in Phys. Rev. B Rapid communicatio

Two activators of in vitro fertilization in mice from licorice

AbstractSystems for artificial insemination have been established in some animals. However, due to limited availability of sperm and oocytes, more effective treatment methodologies are required. Recently, it was demonstrated that the rate of in vitro fertilization (IVF) in mice was improved by adding a water extract of licorice (Glycyrrhiza uralensis), but not glycyrrhizic acid, to the artificial insemination culture medium. In this study, we examined licorice extract for active compounds using bioassay-guided separation. The results indicated that isoliquiritigenin and formononetin were the active molecules in licorice that contributed to the improved rate of IVF