准一维导体 LiMo$_{6}$O$_{17}$ 的 Wannier 轨道理论与 ARPES 研究
Wannier-Orbital theory and ARPES for the quasi-1D conductor LiMo$_{6}$O$_{17}$
AI总结：
本文结合 LDA 能带理论与 ARPES 技术研究了锂紫青铜，发现其准一维费米面形状强烈依赖于费米能级位置和 Li 化学计量比，并利用 ARPES 选择定则验证了六能带紧束缚模型。
摘要：
在这三篇系列论文中，我们展示了结合密度泛函（LDA）能带理论（NMTO）与角分辨光电子能谱（ARPES）对锂紫青铜 Li$_{1x}$Mo$_{6}$O$_{17}$ 的联合研究结果。该材料因其异常稳健的准一维（quasi-1D）行为而尤为引人注目。在费米能级附近的一个大能量窗口内，其能带结构基本上是二维的，由每个晶胞中的三个 Mo $t_{2g}$ 类型的扩展 Wannier 轨道（WOs）形成，每个轨道产生一个一维能带，并与另外两个能带呈 120$^{\circ}$ 角延伸。从 $\mathbf{c}/2$ 到 $\mathbf{c}$ 的结构“二聚化”使 $xz$ 和 $yz$ 能带打开能隙，同时使 $xy$ 能带在能隙中保持金属性，但与能隙边缘产生共振耦合，进而与另外两个方向耦合。由此产生的复杂准一维费米面（FS）形状（已被我们的 ARPES 证实）强烈依赖于费米能级在能隙中的位置，这意味着依赖于费米面的性质（如费米面嵌套或超导性）对 Li 化学计量比具有极大的敏感性。该能带结构被表示为六能带解析紧束缚（TB）哈密顿量，并通过识别和应用 ARPES 选择定则得到了详细验证，该定则首次实现了在 ARPES 谱中分离两个微小劈裂的 $xy$ 能带，并观察到了它们复杂的劈裂费米面。强烈的共振作用使得两能带 TB 模型或相关的实空间梯子图像均无法有效描述其低能电子结构。在低至 6$\,$K 的温度下，我们没有发现理论上预期的由准一维链中 LL 波动引起的垂直单粒子跃迁向下重整化的证据。
英文摘要：
In this set of three papers, we present the results of a combined study by density-functional (LDA) band theory (NMTO) and angle-resolved photoemission spectroscopy (ARPES) of lithium purple bronze, 2(Li$_{1x}$Mo$_{6}$O$_{17}$). This material is particularly notable for its unusually robust quasi-one-dimensional (quasi-1D) behavior. The band structure, in a large energy window around the Fermi energy, is basically 2D and formed by three Mo $t_{2g}$-like extended Wannier orbitals (WOs) per cell, each one giving rise to a 1D band running at a 120$^{\circ }$ angle to the two others. A structural "dimerization" from $\mathbf{c}/2$ to $\mathbf{c}$ gaps the $xz$ and $yz$ bands while leaving the $xy$ bands metallic in the gap but resonantly coupled to the gap edges and, hence, to the two other directions. The resulting complex shape of the quasi-1D Fermi surface (FS), verified by our ARPES, thus depends strongly on the Fermi energy position in the gap, implying a great sensitivity to Li stoichiometry of properties dependent on the FS, such as FS nesting or superconductivity. The band structure, expressed as a six-band, analytical tight-binding (TB) Hamiltonian, is verified in detail by the recognition and application of an ARPES selection rule that enables, for the first time, the separation in ARPES spectra of the two barely split $xy$ bands and the observation of their complex split FS. The strong resonances prevent either a two-band TB model or a related real-space ladder picture from giving a valid description of the low-energy electronic structure. Down to a temperature of 6$\,$K we find no evidence for a theoretically expected downward renormalization of perpendicular single particle hopping due to LL fluctuations in the quasi-1D chains.
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