Kagome金属KV $_3$ Sb PDMATHAAD、RbV $_3$ Sb PDMATHAAD和CsV $_3$ Sb $_5$中的位阻-基心正交$4Q$电荷密度波序
Hexagonal-to-base-centered-orthorhombic $4Q$ charge density wave order in kagome metals KV$_3$Sb$_5$, RbV$_3$Sb$_5$, and CsV$_3$Sb$_5$
摘要：
我用第一性原理计算寻找可果美金属KV $_3$ Sb $_5$，RbV $_3$ Sb $_5$和CsV $_3$ Sb $_5$的基态结构。群论分析表明，有17个不同的扭曲，是可能的，由于声子不稳定性的$M$ $(\frac{1}{2},0,0)$和$L$ $(\frac{1}{2},0,\frac{1}{2})$点在这些材料的母相$P6/mmm$的Brilouin区。我为这三种化合物生成了这些结构，并进行了完全的结构弛豫，使原子力和晶格应力最小化。我发现，$Fmmm$相位与顺序参数$M_1^+$ $(a,0,0)$ $+$ $L_2^-$ $(0,b,b)$在所有三种化合物中具有最低的能量。然而，$Fmmm$在其$Z$ $(0,0,1)$点处表现出动力学不稳定性，该点对应于父$P6/mmm$相中的$A$ $(0,0,\frac{1}{2})$点。这种不稳定性的凝聚导致了一种以基为中心的正交结构，空间群为$Cmcm$和$4Q$，序参数为$M_1^+$ $(a,0,0)$ $+$ $L_2^-$ $(0,b,b)$ $+$ $A_6^+$ $(\frac{1}{2}c,\frac{-\sqrt{3}}{2}c)$。
英文摘要：
I search for the ground state structures of the kagome metals KV$_3$Sb$_5$, RbV$_3$Sb$_5$, and CsV$_3$Sb$_5$ using first principles calculations. Group-theoretical analysis shows that there are seventeen different distortions that are possible due to the phonon instabilities at the $M$ $(\frac{1}{2},0,0)$ and $L$ $(\frac{1}{2},0,\frac{1}{2})$ points in the Brilouin zone of the parent $P6/mmm$ phase of these materials. I generated these structures for the three compounds and performed full structural relaxations that minimize the atomic forces and lattice stresses. I find that the $Fmmm$ phase with the order parameter $M_1^+$ $(a,0,0)$ $+$ $L_2^-$ $(0,b,b)$ has the lowest energy among these possibilities in all three compounds. However, the $Fmmm$ exhibits a dynamical instability at its $Z$ $(0,0,1)$ point, which corresponds to the $A$ $(0,0,\frac{1}{2})$ point in the parent $P6/mmm$ phase. Condensation of this instability leads to a base-centered orthorhombic structure with the space group $Cmcm$ and $4Q$ order parameter $M_1^+$ $(a,0,0)$ $+$ $L_2^-$ $(0,b,b)$ $+$ $A_6^+$ $(\frac{1}{2}c,\frac{-\sqrt{3}}{2}c)$.
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