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arXiv 1510.02496cond-mat.str-el
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欠掺杂铜氧化物中单向和双向电荷密度波序的相互作用

Interplay between uni-directional and bi-directional charge-density-wave orders in underdoped cuprates

Yuxuan Wang, Andrey V. Chubukov

摘要:

我们分析了电荷密度波(CDW)顺序与轴向动量$(Q, 0)$和$(0,Q)$(分别为$Δ_x$和$Δ_y$)之间的相互作用,在欠掺杂的铜酸盐中检测到。实空间中的CDW阶可以是单向的($Δ_x$或$Δ_y$非零)或双向的($Δ_x$和$Δ_y$都非零)。为了理解这两个订单的发展,我们采用磁的情况下,CDW秩序出现由于自旋涨落交换,并推导出Ginzburg-Landau行动的六阶$Δ_x$和$Δ_y$。我们认为,在平均场水平,CDW顺序是双向的,在发病,具有相等的幅度的$Δ_x$和$Δ_y$,但改变到单向内的CDW阶段。这意味着,在一个给定的温度下,CDW秩序是单向的在较小的掺杂,但成为双向的在较大的掺杂。这与最近的X射线数据YBCO,其中检测到的倾向,在较大的掺杂双向秩序。我们讨论了在较高的温度下的双向和单向CDW订单之间的相互作用的离散对称性破缺的作用,也讨论了对密度波(PDW)秩序,这可能会出现随着CDW的作用。我们认为,PDW与CDW相同的动量改变了结构的双向电荷顺序完全取代$Δ_x$或$Δ_y$ CDW组件的PDW。然而,如果一个“安培”的PDW序,即费米子与近似相同的动量配对,也存在,$Δ_x$和$Δ_y$在双向相位中保持非零,尽管幅度不相等。这再次与X射线实验一致,其在较大掺杂下发现在每个域中不相等的$Δ_x$和$Δ_y$。

英文摘要:

We analyze the interplay between charge-density-wave (CDW) orders with axial momenta $(Q, 0)$ and $(0,Q)$ ($Δ_x$ and $Δ_y$ respectively), detected in the underdoped cuprates. The CDW order in real space can be uni-directional (either $Δ_x$ or $Δ_y$ is non-zero) or bi-directional (both $Δ_x$ and $Δ_y$ are non-zero). To understand which of the two orders develop, we adopt the magnetic scenario, in which the CDW order appears due to spin-fluctuation exchange, and derive the Ginzburg-Landau action to the sixth order in $Δ_x$ and $Δ_y$. We argue that, at the mean-field level, the CDW order is bi-directional at the onset, with equal amplitudes of $Δ_x$ and $Δ_y$, but changes to uni-directional inside the CDW phase. This implies that, at a given temperature, CDW order is uni-directional at smaller dopings, but becomes bi-directional at larger dopings. This is consistent with recent x-ray data on YBCO, which detected tendency towards bi-directional order at larger dopings. We discuss the role of discrete symmetry breaking at a higher temperature for the interplay between bi-directional and uni-directional CDW orders and also discuss the role of pair-density-wave (PDW) order, which may appear along with CDW. We argue that PDW with the same momentum as CDW changes the structure of the bi-directional charge order by completely replacing either $Δ_x$ or $Δ_y$ CDW components by PDW. However, if an "Amperean" PDW order, which pairs fermions with approximately the same momenta, is also present, both $Δ_x$ and $Δ_y$ remain non-zero in the bi-directional phase, albeit with non-equal amplitudes. This is again consistent with x-ray experiments, which at larger doping found non-equal $Δ_x$ and $Δ_y$ in every domain.

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