We study the incommensurate charge ordered states in the $\mathit{t-t^{\prime}-J}$ model using the Gutzwiller mean field theory on large systems. In particular, we explore the properties of incommensurate charge modulated states referred to as nodal pair density waves (nPDW) in the literature. nPDW states intertwine site and bond charge order with modulated $d$-wave pair order, and are characterized by a nonzero amplitude of uniform pairing; they also manifest a dominant intra-unit cell $d$-density wave form factor. To compare with a recent scanning tunneling microscopy (STM) study [Hamidian \textit{et al.}, Nat. Phys. 3519 (2015)] of the cuprate superconductor BSCCO-2212, we compute the continuum local density of states (LDOS) at a typical STM tip height using the Wannier function based approach. By Fourier transforming Cu and O sub-lattice LDOS we also obtain bias-dependent intra-unit cell form factors and spatial phase difference. We find that in the nPDW state the behavior of form factors and spatial phase difference as a function of energy agrees remarkably well with the experiment. This is in contrast to commensurate charge modulated states, which we show do not agree with experiment. We propose that the nPDW states are good candidates for the charge density wave phase observed in the superconducting state of underdoped cuprates.
Incommensurate Spin Density Wave versus local magnetic inhomogeneities in Ba(Fe1-xNix)2As2: a 57Fe Mossbauer spectroscopy study
本文报道了纯Ba（Fe_（1-x）Ni_x）_2As_2（x=0.01和0.03）的~（57）Fe穆斯堡尔谱。我们表明，所有这些材料呈现一个一阶磁向磁有序状态的转变。在掺杂的化合物中，Fe超精细场的广泛分布存在于磁性相中。我们成功地拟合了Ba（Fe 1-xNix）2As 2中的穆斯堡尔谱数据，在两个不同的模型框架内：1）无公度自旋密度波; 2）掺杂剂引起的Fe极化扰动，最近提出解释Ba（Fe 1-xNix）2As 2中的75 As NMR数据，该模型仅在非常稀的极限x=0.01下有效。此外，我们在这里表明，这些NMR数据也可以成功地分析的“无公度模型”的所有掺杂含量通过使用从穆斯堡尔谱分析得到的参数。因此，不能根据75 As NMR数据排除无公度自旋密度波的存在。
Incommensurate phonon anomaly and the nature of charge density waves in cuprates
虽然电荷密度波（CDW）的不稳定性是普遍存在的超导铜酸盐，不同的有序波矢量在不同的铜酸盐家庭阻碍了统一的描述CDW的形成机制。本文研究了正则CDW有序铜氧化物La $_{1.875}$ Ba $_{0.125}$ CuO $_{4}$中低能声子的温度依赖性。我们发现与CDW关联相关的声子软化波矢在高温前体相中变得依赖于温度，并且从0.238倒易空间单位（r.l.u.）低于有序化转变温度达0.3~r.l.u.在300~K.这种高温行为表明，“214”型铜酸盐可以在与先前报道的非“214”型铜酸盐（如YBa $_{2}$ Cu $_{3}$ O $_{6+δ}$）中的CDW相关性相似的波矢处主持CDW相关性。这表明，铜酸盐CDW可能产生于相同的潜在的不稳定性，尽管它们显然不同的低温有序波矢量。
Distinct Charge Orders in the Planes and Chains of Ortho-III-Ordered YBa$_2$Cu$_3$O$_{6+δ}$ Superconductors Identified by Resonant Elastic X-ray Scattering
最近，电荷密度波（CDW）秩序的CuO $_2$平面欠掺杂的YBa $_2$ Cu $_3$ O $_{6+δ}$检测使用共振软X射线散射。一个重要的问题仍然存在：是链层负责这种电荷排序？在这里，我们探讨的共振散射强度的能量和偏振依赖性的解孪晶样品的YBa $_2$铜$_3$ O $_{6.75}$与邻-III氧在链层中的顺序。我们表明，邻-III CDW秩序的链是不同的CDW秩序的飞机。邻位-III结构产生相称的超晶格反射在$Q$ =[0.33 0 $L$ ]，其能量和偏振依赖性同意与预期的氧有序和空间调制的Cu价在链中。在[0.30 0 $L$ ]和[0 0.30 $L$ ]从在平面中的CDW顺序的不相称的峰被示出是不同的$Q$以及它们的温度，能量和偏振依赖性，因此是无关的链层的结构。此外，在平面中的CDW顺序的能量依赖性被示出从Cu 2 $p$到3 $d_{x^2-y^2}$过渡的能量的空间调制的结果，类似于条纹有序的214铜酸盐。
