Optimization variational Monte Carlo studies of pairing symmetry in cobaltate superconductors

在上一个财政年度，我们使用优化变分蒙特卡罗（VMC）方法，研究了各向异性三角晶格上的单带Hubbard模型及其强关联版本t-J模型的基态和低能性质，这些模型被认为是新发现的超导钴酸盐的合理模型。作为单带模型研究的延续，在本年度，我们主要研究了两带Hubbard模型的基态性质，特别是超导性的稳定条件及其对对称性，因为d轨道的简并可能在钴酸盐中很重要。假设一个简单的单电子结构，它大致符合费米面附近的钴酸盐的能带结构，我们进行VMC计算与改变的电子相关和电子密度的强度。结果发现，只有当孤立的口袋型费米面与半填充附近的van-Hove奇点重叠时，具有s波、d波和p波以及一些混合波（如d + id波）的超导态才变得稳定。在这些对称中，d + id是最稳定的。这种超导态的稳定化起源于相互作用能的增加，这是由反铁磁（AF）关联的增强引起的，如在铜氧化物超导体中.作为另一个主题，我们还研究了具有对角跳跃的受抑正方晶格上的Hubbard模型中的Mott转变和转变附近的超导电性的存在.我们得到的主要结果是，对于掺杂的情况，对角跳跃的符号是至关重要的;对于实际的关联强度，对于正号（对应于电子掺杂的情况），出现金属AF序，而AF态失去了本征稳定性，并且相分离到具有半填充密度的AF态和具有高掺杂比的d波超导态的区域。

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.