We derive and analyze an effective Ginzburg-Landau (GL) functional for a charge density wave (CDW) for a model of electrons on a tight binding square lattice with density-density interactions. We show, using realistic electronic dispersions for the cuprates, that for the simplest GL theory, the preferred symmetry is of the uni-directional (stripe) type, but upon inclusion of third-order terms, the CDW may exhibit a transition from a uni-directional to a checkerboard pattern depending on the strength and range of the interaction.
Experiments have shown that the families of cuprate superconductors that have the largest transition temperature at optimal doping also have the largest oxygen hole content at that doping. They have also shown that a large charge-transfer gap, a quantity accessible in the normal state, is detrimental to superconductivity. We solve the three-band Hubbard model with cellular dynamical mean-field theory and show that both of these observations follow from the model. Cuprates play a special role amongst doped charge-transfer insulators of transition metal oxides because copper has the largest cova…
Superconductivity in layered cuprates is induced by doping holes into a parent antiferromagnetic insulator. It is now recognized that another common emergent order involves charge stripes, and our understanding of the relationship between charge stripes and superconductivity has been evolving. Here we review studies of 214 cuprate families obtained by doping La$_2$CuO$_4$. Charge-stripe order tends to compete with bulk superconductivity; nevertheless, there is plentiful evidence that it coexists with two-dimensional superconductivity. This has been interpreted in terms of pair-density-wave sup…
Inhomogeneous slowing down of spin fluctuations induced by charge stripe order in 1/8-doped lanthanum cuprates
我们报告$^{139}$ La核磁共振（NMR）测量的La $_{2-x}$ Sr $_x$ CuO $_4$（$0.07\leq x \leq 0.15$）和La $_{2-x}$ Ba $_x$ CuO $_4$（$x=1/8$）单晶，专注于自旋冻结观察到的1/8掺杂铜酸镧。电荷条纹有序似乎诱导自旋涨落向自旋有序方向的非均匀减慢，并与超导性竞争。
Motivated by the recent resonant x-ray scattering (RXS) and resonant inelastic x-ray scattering (RIXS) experiments in electron-doped cuprates, we study the charge excitation spectrum in a layered t-J model with the long-range Coulomb interaction. We show that the spectrum is not dominated by a specific type of charge excitations, but by different kinds of charge fluctuations, and is characterized by a dual structure in the energy space. Low-energy charge excitations correspond to various types of bond-charge fluctuations driven by the exchange term (J-term) whereas high-energy charge excitatio…
Dynamic charge transfers, or charge fluxes, generated by anharmonic phonon couplings have previously shown some fundamental connections with the pseudogap phase and other important phases in cuprate superconductors. The anharmonicity here suggests the importance of nonadiabatic behaviors of charge fluxes in cuprates. These charge fluxes will result in the dynamic charge transfer that can be directly calculated by the charge difference induced by phonons in density functional theory simulations. However, retrieving the flux field from the calculated charge transfer is nontrivial. In this articl…
Quantum phase transitions play an important role in shaping the phase diagram of high-temperature cuprate superconductors. These cuprates possess intertwined orders which interact strongly with superconductivity. However, the evidence for the quantum critical point associated with the charge order in the superconducting phase remains elusive. Here we show the short-range charge orders and the spectral signature of the quantum fluctuations in La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) near the optimal doping using high-resolution resonant inelastic X-ray scattering. On performing calculations through a dia…
This Reply to preceding Comment of arXiv:1909.09867 shows why the statements in the Comment are misleading. We point out that our physical picture and theirs are fundamentally different, therefore the claim of using their correlation to include ours shows a very limited physical relevance, which instead may impede the precise understanding of either of the two pictures.
Besides the mechanism responsible for high critical temperature superconductivity, the grand unresolved issue of the cuprates is the occurrence of a strange metallic state above the so-called pseudogap temperature $T^*$. Even though such state has been successfully described within a phenomenological scheme, the so-called Marginal Fermi-Liquid theory, a microscopic explanation is still missing. However, recent resonant X-ray scattering experiments identified a new class of charge density fluctuations characterized by low characteristic energies and short correlation lengths, which are related …
Identification of the electronic state that appears upon doping a Mott insulator is important to understand the physics of cuprate high-temperature superconductors. Recent scanning tunneling microscopy of cuprates provides evidence that a charge-ordered state emerges before the superconducting state upon doping the parent compound. We study this phenomenon by computing the charge response function of the Hubbard model including frequency-dependent local vertex corrections that satisfy the compressibility sum-rule. We find that upon approaching the Mott phase from the overdoped side, the charge…
In a recent manuscript Phys. Rev. Lett. 127, 197001 (2021) Puviani et al. claim that the Higgs mode gives an enhancement of the Raman response in the symmetric $A_{1g}$ Raman channel of cuprates. Here we report a series of technical mistakes in their derivation that completely invalidate this conclusion. In particular, the Raman response function contains two renormalized vertices, with a clearly overcounting of diagrams and uncontrolled results for the Higgs-mode contribution.
Recent advances in momentum-resolved electron energy-loss spectroscopy (MEELS) and resonant inelastic X-ray scattering (RIXS) now allow one to access the charge response function with unprecedented versatility and accuracy. This allows for the study of excitations which were inaccessible recently, such as low-energy and finite momentum collective modes. The SU(2) theory of the cuprates is based on a composite order parameter with SU(2) symmetry fluctuating between superconductivity and charge order. The phase where it fluctuates is a candidate for the pseudogap phase of the cuprates. This theo…
Flux phase as possible time-reversal symmetry breaking surface states of high-$T_C$ cuprate superconductors
在$d_{x^2-y-2}$波超导体的（110）面，超导序被强烈抑制。在这种情况下，可能会出现大量禁止的有序状态。本文用Bogoliubov de Gennes方法处理含扩展转移积分的$t-J$模型，研究了高$T_C$铜氧化物超导体的这一问题.结果发现，磁通相位与交错电流沿表面，或反铁磁状态可以发生在表面附近。出射表面态的稳定性随系统费米面形状的不同而不同。可能的关系的实验上的克尔效应，建议时间反演对称性破缺进行了讨论。
Screening of point charge impurities in highly anisotropic metals: application to $μ^+$ spin relaxation in underdoped cuprates
我们计算屏蔽电荷密度分布由于点电荷，如正μ子（$μ^+$），放置在平面之间的高度各向异性的层状金属。在欠掺杂的空穴铜氧化物中，屏蔽电荷将$μ^+$附近的金属平面晶胞中的电荷密度转换为接近其在绝缘状态下的值。极化中子衍射所观察到的电流环有序状态，然后消失在这样的细胞，也在附近的细胞在一个距离的顺序的内在相关长度的环有序状态。这又强烈地抑制了$μ^+$位置处的回路电流场。我们估计了欠掺杂$_2$ Cu $_3$ O $_{6+x}$和La $_{2-x}$ Sr $_x$ CuO $_4$中的抑制场，发现在前一种情况下与观测到的0.2- 0.3 G场一致，在后一种情况下与观测到的$\sim$ 0.2 G上界一致.这解决了中子衍射和$μ$ SR实验之间的争议。筛选计算也有相关的铜酸盐中的其他电荷杂质的影响，如掺杂剂本身。
We present a possible explanation for a recently observed magnetic field induced charge order in cuprate superconductors (Edkins et al.~arXiv:1802.04673 [cond-mat.supr-con]). We argue that it arises from the reorganization of spin-vortex-induced loop current (SVILC) pattern due to supercurrent-flow caused by the magnetic field. The reorganization is from the most stable tiling of $4a times 6a$ spin-vortex quartets ($a$ is the lattice constant in the CuO$_2$ plane, and a spin-vortex quartet is stable of unit of spin-vortices that contains four holes, four spin-vortices, and four SVILCs) to that…
Perspective on S. Mukhopadhyay, et al. Evidence for a vestigial nematic state in the cuprate pseudogap phase, PNAS 116, 13249 (2019); arXiv:1904.00915.
We study competitions between charge uniform and inhomogeneous states in two-dimensional Hubbard models by using a variational Monte Carlo method. At realistic parameters for cuprate superconductors, emergent effective attraction of carriers generated from repulsive Coulomb interaction leads to charge/spin stripe ground states, which severely compete with uniform superconducting excited states in the energy scale of 10 K for the cuprates. Stripe period increases with decreasing hole doping $δ$, which agrees with the experiments for La-based cuprates at $δ$ = 1/8. For lower $δ$, we find a phase…
The recent development of x-ray scattering techniques revealed the charge-excitation spectrum in high-$T_c$ cuprate superconductors. While the presence of a dispersive signal in the high-energy charge-excitation spectrum is well accepted in the electron-doped cuprates, its interpretation and universality are controversial. Since charge fluctuations are observed ubiquitously in cuprate superconductors, the understanding of its origin is a pivotal issue. Here, we employ the layered $t$-$J$ model with the long-range Coulomb interaction and show that an acoustic-like plasmon mode with a gap at in-…
