电荷区紫青铜$Li_{0.9}Mo_6O_{17}$的Luttinger液体理论
Luttinger liquid theory of purple bronze $Li_{0.9}Mo_6O_{17}$ in the charge regime
摘要：
钼紫青铜Li $_{0.9}$ Mo $_{6}$ O $_{17}$是一种特殊的材料，已知在低至几meV的能量下表现出一维（1D）特性。这一事实似乎在实验和能带结构理论中都得到了很好的证实。我们使用不寻常的，非常一维的带色散\emph{ab-initio} DFT-LMTO带计算作为我们的出发点，研究300 meV以下出现的物理。获得了与主色散方向垂直的色散，并进行了详细的研究。在此基础上，我们推导出一个有效的低能理论内的Tomonaga Luttinger液体（TLL）的框架。我们估计可能的相互作用的强度，并由此推导出的TLL参数的值的电荷模式。最后，我们通过推导重整化群（RG）方程来研究TLL可能的不稳定性，该方程使我们能够预测光谱中潜在能隙的大小。虽然$2k_F$不稳定性强烈地相互抑制，但$4k_F$不稳定性相互协作，这为在最低能量下可能的CDW铺平了道路。这项工作的目的是了解实验结果，特别是那些肯定是躺在1D政权。我们讨论了我们的1D方法的有效性和进一步的前景较低的能量阶段。
英文摘要：
Molybdenum purple bronze Li$_{0.9}$Mo$_{6}$O$_{17}$ is an exceptional material known to exhibit one dimensional (1D) properties for energies down to a few meV. This fact seems to be well established both in experiments and in band structure theory. We use the unusual, very 1-dimensional band dispersion obtained in \emph{ab-initio} DFT-LMTO band calculations as our starting point to study the physics emerging below 300meV. A dispersion perpendicular to the main dispersive direction is obtained and investigated in detail. Based on this, we derive an effective low energy theory within the Tomonaga Luttinger liquid (TLL) framework. We estimate the strength of the possible interactions and from this deduce the values of the TLL parameters for charge modes. Finally we investigate possible instabilities of TLL by deriving renormalization group (RG) equations which allow us to predict the size of potential gaps in the spectrum. While $2k_F$ instabilities strongly suppress each other, the $4k_F$ instabilities cooperate, which paves the way for a possible CDW at the lowest energies. The aim of this work is to understand the experimental findings, in particular the ones which are certainly lying within the 1D regime. We discuss the validity of our 1D approach and further perspectives for the lower energy phases.
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