Optimization variational Monte Carlo studies of pairing symmetry in cobaltate superconductors

在上个财政年度，我们用最优化变分蒙特卡罗(VMC)方法研究了各向异性三角晶格上单带Hubbard模型及其强关联版本t-J模型的基态和低能性质，这被认为是新发现的超导钴的可能模型。作为单带模型的继续，今年我们主要研究了两带Hubbard模型的基态性质，特别是超导的稳定条件和它的配对对称性，因为d轨道的简并在钴酸盐中可能是重要的。假设一个简单的单电子结构与钴的费米表面附近的能带结构基本吻合，我们通过改变电子关联强度和电子密度进行了VMC计算。结果发现，只有当孤立的袖珍费米面与Van-Hove奇点在半填充附近重叠时，含有S波、d波和p波以及d+id波等混合波的超导状态才会变得稳定。在这些对称性中，d+id最稳定。超导态的这种稳定化源于相互作用能的增加，这是由于反铁磁(AF)关联的增强而引起的，就像在铜酸盐超导体中一样。作为另一个主题，我们还研究了对角跳跃受阻正方形晶格上Hubbard模型的Mott相变和相变附近超导电性的存在。我们得到的主要结果是，对于掺杂情况，对角线跃迁的符号是关键的；对于实际关联强度，正符号(对应于电子掺杂情况)出现了金属的AF有序，而AF态失去了固有的稳定性，并且在半填充密度的AF态和高掺杂比的d波超导态的区域失去了本征稳定性和相分离。

In the last fiscal year, using an optimization variational Monte Carlo (VMC) method, we studied ground-state and low-energy properties of single-band Hubbard models and its strongly correlated version t-J models on anisotropic triangular lattices, which is considered to be plausible models of the newly-found superconducting cobaltates.As a continuation of these studies for the single-band models, in this year, we mainly studied ground-state properties of a two-band Hubbard model, in particular, a stable condition of superconductivity and its pairing symmetry, because it is probable that the degeneracy of d orbitals are important in the cobaltate. Assuming a simple one-electron structure which roughly fits the band structure near Fermi surface of the cobaltate, we performed VMC calculations with changing the strength of electron correlation and electron density. As a result, we found that superconducting states with s-, d-and p-waves and some mixed waves like a d+id-wave become stable only when an isolated pocket-type Fermi surface overlaps with van-Hove-singularity points near half filling. Among these symmetries, the d+id is the most stable. This stabilization of the superconducting states originates in the gain in interaction energy, which is induced by the enhancement of antiferromagnetic (AF) correlation, as in the cuprate superconductors.As another topic, we also studied Mott transitions and existence of superconductivity near the transition in a Hubbard model on frustrated square lattices with diagonal hoppings. The main result we obtained is that, for doped cases, the sign of diagonal hopping is crucial; for realistic correlation strength,.a metallic AF order appears for the positive sign (corresponding to electron-doped cases), whereas AF states lose intrinsic stability and phase separate to the regions of an AF state with the half-filled density and of a d-wave superconducting state with a high doping ratio.