A common characteristic of quasi-one-dimensional (q1D) conductors $\beta \text{−}{A}_{0.33}{\mathrm{V}}_2{\mathrm{O}}_5(A$ = Li, Na, and Ag) is that the charge ordering (CO), the ground state (GS) at ambient pressure, and the superconducting (SC) phases, the GS under high pressure, are competing with each other. We have explored high-pressure properties of divalent $\beta$-vanadium bronzes, $\beta \text{−}{A}_{0.33}{\mathrm{V}}_2{\mathrm{O}}_5(A$ = Ca, Sr, and Pb), which are $A$-cation stoichiometry finely controlled single-crystal/powder samples, and found the absence of the SC phase. In these observations, however, we observed enormous and novel phase transitions, a kind of “devil's staircase”-type phase transitions in the charge ordering (CO) phases. The most surprising discovery in this devil's staircase, which was found mainly in $\beta \text{−}{\mathrm{Sr}}_{0.33}{\mathrm{V}}_2{\mathrm{O}}_5$, is that all the charge modulation vectors of many kinds of CO phases can be represented as a primitive lattice translation vector along the $b$ axis multiplied by several odd numbers. This discovery surely demonstrates interplay between the charge degree freedom and the crystallographic symmetry. We propose two possible mechanisms to explain this phenomenon: “self-charge transfer (carrier redistribution)” between the two subsystems in these compounds and “sequential symmetry reduction” that was discussed in Landau theory of phase transitions. In $\beta \text{−}{\mathrm{Ca}}_{0.33}{\mathrm{V}}_2{\mathrm{O}}_5$ we also found a $P\text{−}T$ phase diagram similar in outlook but different in detail. The devil's staircase was also observed but it is an incomplete one. Furthermore, the charge modulation vectors in it are shorter than those in $\beta \text{−}{\mathrm{Sr}}_{0.33}{\mathrm{V}}_2{\mathrm{O}}_5$. In $\beta \text{−}{\mathrm{Pb}}_{0.33}{\mathrm{V}}_2{\mathrm{O}}_5$, which has no CO phase at ambient pressure, the pressure-induced antiferromagnetic ordering was observed at around 50 K above 0.5 GPa. Using these two kinds of mechanisms, we also explain the global high-pressure properties in all the stoichiometric divalent $\beta$-vanadium bronzes, which were observed as a wide variety of electromagnetic states. In addition, we also discuss a possible key for the presence/absence of the SC phase under pressure.

中文翻译：

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二价β-钒青铜在压力下的奇数电荷阶数调制的魔鬼阶梯

准一维（q1D）导体的共同特征 $\beta \text{-}{\mathrm{一个}}_{0.33}{\mathrm{伏特}}_{\mathrm{2个}}{\mathrm{Ø}}_5（\mathrm{一个}$= Li，Na和Ag）表示电荷排序（CO），环境压力下的基态（GS）和超导（SC）相，高压下的GS相互竞争。我们探索了二价的高压特性$\beta$-钒青铜， $\beta \text{-}{\mathrm{一个}}_{0.33}{\mathrm{伏特}}_{\mathrm{2个}}{\mathrm{Ø}}_5（\mathrm{一个}$ = Ca，Sr和Pb），分别是 $\mathrm{一个}$阳离子化学计量法可精确控制单晶/粉末样品，并发现不存在SC相。但是，在这些观察中，我们观察到了巨大且新颖的相变，即电荷排序（CO）相中的一种“魔鬼阶梯”型相变。在这个魔鬼的楼梯上最令人惊讶的发现，主要是在$\beta \text{-}{r}_{0.33}{\mathrm{伏特}}_{\mathrm{2个}}{\mathrm{Ø}}_5$，是可以将多种CO相的所有电荷调制矢量表示为沿C的原始晶格平移矢量 $b$轴乘以几个奇数。该发现肯定证明了电荷度自由度和晶体对称性之间的相互作用。我们提出了两种可能的机制来解释此现象：这些化合物中两个子系统之间的“自电荷转移（载流子重新分布）”和在Landau相变理论中讨论的“顺序对称性降低”。在$\beta \text{-}{钙}_{0.33}{\mathrm{伏特}}_{\mathrm{2个}}{\mathrm{Ø}}_5$ 我们还发现了 $P\text{-}Ť$相图外观相似，但细节不同。还观察到了魔鬼的楼梯，但它是不完整的。此外，其中的电荷调制矢量比$\beta \text{-}{r}_{0.33}{\mathrm{伏特}}_{\mathrm{2个}}{\mathrm{Ø}}_5$。在$\beta \text{-}{\mathrm{铅含量}}_{0.33}{\mathrm{伏特}}_{\mathrm{2个}}{\mathrm{Ø}}_5$，在环境压力下没有CO相，在高于0.5 GPa的50 K处观察到压力引起的反铁磁有序化。使用这两种机制，我们还解释了所有化学计量的二价态的整体高压特性$\beta$-钒青铜，被发现具有多种电磁状态。此外，我们还讨论了在压力下是否存在SC相的可能关键。