草部 浩一

Electron correlation effects caused by the topological zero mode of a<br /> hydrogenated graphene vacancy, $V_{111}$, with three adsorbed hydrogen atoms is<br /> discussed theoretically. A Kondo model is derived from the multi-reference<br /> representation of the density functional theory, where exchange scattering<br /> processes between the zero mode and low-energy modes in the Dirac cones are<br /> estimated. Even when the Dirac cone is slightly off from the charge neutral<br /> point, a finite on-site correlation energy, $U_0$, for the zero mode of an<br /> isolated $V_{111}$ allows the half-filling of the localized level giving a spin<br /> $s=1/2$. The anti-ferromagnetic Kondo screening mediated by higher order<br /> scattering processes becomes dominant in the dilute limit of the vacancies. Our<br /> estimation of relevant two body interactions certifies appearance of the Kondo<br /> effect at low temperatures.

By constructing $d_{x^2-y^2}-d_{z^2}$ two-orbital models from first<br /> principles, we have obtained a systematic correlation between the Fermi surface<br /> warping and the evaluated $T_c$ for various bilayer as well as single-layer<br /> cuprates. This reveals that smaller mixture of the $d_{z^2}$ orbital component<br /> on the Fermi surface leads to both of larger Fermi surface warping and higher<br /> $T_c$. The theoretical correlation strikingly resembles a systematic plot for<br /> the experimentally observed $T_c$ against the Fermi surface warping due to<br /> Pavarini {\it et al.} [Phys. Rev. Lett. {\bf 87}, 047003 (2001)], and the<br /> present result unambiguously indicates that the $d_{z^2}$ mixture is a key<br /> factor that determines $T_c$ in the cuprates.

To show an optimization method of element substitution for cuprate<br /> superconductors, we investigate Fermi surface shape of TlR2A2Cu3O9 with R=La,<br /> Y, and A=Li, Na, K, Rb, Cs. We adopt the generalized gradient approximation in<br /> the density-functional theory (DFT-GGA) for the study of over-doped phases of<br /> these unknown cuprates. The electronic structures of crystals optimized by<br /> DFT-GGA show systematic element dependence in a Fermi surface shape controlling<br /> parameter, r, of Cu dx2-y2 bands, where nearly absent dz2 component at the<br /> Fermi level and smaller r keeping t1 suggest enhancement of the superconducting<br /> transition temperature within the spin-fluctuation mechanism. For TlYRb2Cu3O9,<br /> smaller r by a reduction factor larger than 10% compared to a reference system<br /> of TlBa2Ca2Cu3O9 (TBCCO) appears in the outer CuO2 plane, but with 12 %<br /> reduction in t1. For TlR2Li2Cu3O9, (R=Y, La), smaller r by a factor larger than<br /> 1% appears keeping t1 as large as TBCCO in the inner plane. Our method may be<br /> used to predict an optimized material structure referencing known cuprate<br /> superconductors.