低维分子轨道晶体中的电子关联效应和奇特量子态

Recent experimental discoveries of quasi-one-dimensional chromium-based superconductors have stimulated intensive research interests in a wide class of molecular-orbital crystals for possible unconventional superconductivity and novel quantum states driven by electron correlations. Such molecular-orbital-based crystals have two or more transitional metal elements in each unit cells, or have non-symmorphic space group symmetries in their crystal structures, thus exhibiting stronger electron correlation effect than those in conventional organic molecular superconductors and more complicated band structures than those in cuprates and iron-based superconductors. Due to both strong electron correlation as in atomic systems and structural complicity as in molecular systems, they provide challenges to the conventional understanding of superconductivity. In this project, we shall study a family of low-dimensional molecular-orbital crystals with C3 and non-symmorphic space group symmetries as represented by quasi-one dimensional alkali CrAs-based superconductors. We shall model such systems by the anisotropic multiorbital Hubbard models based on the 3d atomic orbitals and focus mainly on the possible unconventional superconductivity and novel quantum magnetism. Various powerful analytic or numeric methods including the density matrix renormalization, bosonization as well as quantum Monte Carlo simulation will be utilized. We shall explore the distinct roles played by the Coulomb interaction, Hunds coupling as well as spin-orbit coupling in terms of either atomic orbitals or molecular orbitals. All these will be important in understanding the interesting and novel properties of the alkali chromium pnictides as well as other molecular-orbital crystals with strong electron correlations.

准一维碱金属铬基砷化物超导的发现激发了人们对分子轨道晶体材料中的电子关联、非常规超导及其它新奇量子态的研究兴趣。这类材料中晶格元胞包含两个或更多的过渡金属元素，或具有非点式空间群对称性，比传统有机分子超导体有更强的电子关联效应，比铜基、铁基超导体有更复杂的能带结构，兼具原子轨道的强关联特征和分子轨道的复杂性，从而对现行超导理论提出诸多挑战。本项目针对这类材料的晶格结构，拟研究一类具有三度旋转对称性和非点式对称性的多轨道Hubbard模型及其推广情形，通过d-电子的原子轨道确定该模型的分子轨道特征，发展运用密度矩阵重整化群、玻色化、量子蒙特卡洛等方法深入研究可能的非常规超导电性、量子磁性等新奇量子态，并从理论上澄清库仑作用、洪特耦合、自旋轨道耦合等物理因素对于原子轨道和分子轨道的不同意义。这些研究有助于认识包括碱金属铬基砷化物超导体在内的诸多低维分子轨道晶体材料中的电子关联效应和新奇量子态。

本项目基于碱金属铬基砷化物超导材料结构带来的启示，拟针对具有复杂晶格结构和分子轨道的关联电子体系，以相应的推广的分子轨道Hubbard模型作为基础理论模型，理解和研究这些复杂体系中电子关联效应和可能的新奇量子态。这类体系的晶格结构一般具有多种旋转对称性或非典型对称性，可以呈准一维、准二维结构或层状结构，容易形成非平凡拓扑结构，并伴随半金属、超导等诸多有趣的物理现象。作为代表性的应用，本项目对层状六边形结构半金属材料和铁空位的新型铁磁外尔半金属材料中的复杂晶格产生的能带结构和电子关联效应导致的新奇现象作了研究，发现了拓扑相变、拓扑半金属带来的有趣实验现象， 并在理论上提出了自旋完全极化的理想的关联半金属体系的理论模型。这些结果有一定的学术意义，有望推动相关物理问题的进一步研究。