A model in which a gap forms in the renormalized electronic density of state (DOS) with missing states recovered just above the pseudogap $Δ_{pg}$, is able to give a robust description of the striking, triangular like, peak seen in the real part of the optical self-energy of underdoped cuprates. We use this model to explore the effect of the pseudogap on the real part of the optical conductivity and on the partial sum rule associated with it. An important result is that the optical spectral weight redistributes over a much larger frequency window than it does in the DOS.
Evidence for a pseudogap in underdoped $Bi_2Sr_2CaCu_2O_{8+δ}$ and $YBa_2Cu_3O_{6.50}$ from in-plane optical conductivity measurements
欠掺杂Bi $_{2}$ Sr $_{2}$ CaCu $_{2}$ O $_{8+δ}$（Bi-2212）和ortho Ⅱ YBa $_{2}$ Cu $_{3}$ O $_{6.5}$的面内光学自能数据的实部包含了关于赝能隙的新的重要信息。使用理论模型的方法，我们发现，在赝能隙$Δ_{pg}$以下的态密度损失伴随着一个堆积以上的能量。的堆积，随着一个尖锐的模式在玻色子光谱函数导致一个不寻常的快速增加的光散射率和一个典型的倾斜的峰值在实部的光学自能。这些特征在最佳掺杂和过掺杂样品中没有发现，并且代表了迄今为止在面内光学电导率中的赝隙开口的最清晰的签名。
We report on infrared studies of charge dynamics in a prototypical pnictide system: the BaFe2As2 family. Our experiments have identified hallmarks of the pseudogap state in the BaFe2As2 system that mirror the spectroscopic manifestations of the pseudogap in the cuprates. The magnitude of the infrared pseudogap is in accord with that of the spin-density-wave gap of the parent compound. By monitoring the superconducting gap of both P- and Co-doped compounds, we find that the infrared pseudogap is unrelated to superconductivity. The appearance of the pseudogap is found to correlate with the evolu…
The pseudogap state is widely regarded as a precursor to high-temperature superconductivity yet remains poorly understood. Using high field (30 T) NMR, we report two electronically distinct oxygen sites within the copper-oxygen (Cu-O) planes of an underdoped cuprate in the pseudogap state. At temperatures well above the bulk superconducting transition, roughly 25% of the oxygen sites evidence superconducting pair formation, the remaining evidence antiferromagnetic ordering on the nearest neighbor Cu sites. Any superconducting fluctuations are slower than the microsecond timescales of the NMR p…
The characteristic pseudogap temperature T* in Bi2Sr2CaCu2O8 system has been systematically evaluated as a function of doping, especially focusing on its overdoped region, by measuring the out-of-plane resistivity under the magnetic fields. Overdoped samples have been prepared by annealing TSFZ-grown Bi2Sr2CaCu2O8 single crystals under the high oxygen pressures (990 kgf/cm2). At a zero field, the out-of-plane resistivity showed a metallic behavior down to Tc (= 62 K), while under the magnetic fields of over 3 T,it showed typical upturn behavior from around 65 K upon decreasing temperature. Thi…
To investigate the relationship between the pseudogap and superconductivity, we measured both the in-plane ($ρ_{ab}$) and out-of-plane ($ρ_c$) resistivity for oxygen-controlled Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ single crystals subject to magnetic fields (parallel to the $c$ axis) of up to 17.5 T. The onset temperature for the superconductive fluctuation, $T_{scf}$, is determined by the large positive in-plane magnetoresistance (MR) and negative out-of-plane MR observed near $T_c$, whereas the pseudogap opening temperature $T^*$ is determined by the semiconductive upturn of the zero-field $ρ_…
Our knowledge of the ground state of underdoped hole-doped cuprates has evolved considerably over the last few years. There is now compelling evidence that inside the pseudogap phase, charge order breaks translational symmetry leading to a reconstructed Fermi surface made of small pockets. Quantum oscillations, [Doiron-Leyraud N, et al. (2007) Nature 447:564-568], optical conductivity [Mirzaei SI, et al. (2013) Proc Natl Acad Sci USA 110:5774-5778] and the validity of Wiedemann-Franz law [Grissonnache G, et al. (2016) Phys. Rev. B 93:064513] point to a Fermi liquid regime at low temperature in…
The paper analyzes the influence of the hole density, the out-of-plane or in-plane disorder, and the isotopic oxygen mass on the zero temperature energy gap ($2Δ\left(0\right)$) for $\rm{Y}_{1-x}\rm{Ca}_{x}\rm{Ba}_2\left(\rm{Cu}_{1-y}\rm{Zn}_{y}\right)_{3}\rm{O}_{7-δ}$ (YCBCZO) and $\rm{La}_{1.96-x}\rm{Sr}_{x}\rm{Ho}_{0.04}\rm{CuO}_{4}$ (LSHCO) superconductors. It has been found that the energy gap is visibly correlated with the value of the pseudogap temperature ($T^{\star}$). On the other hand, no correlation between $2Δ\left(0\right)$ and the critical temperature ($T_{C}$) has been found. T…
We present in-plane infrared reflectance measurement on two superconducting cuprates with relatively low T$_c$: a nearly optimally-doped Bi$_2$Sr$_{1.6}$La$_{0.4}$CuO$_{6+δ}$ with T$_c$=33 K and an underdoped La$_{1.89}$Sr$_{0.11}$CuO$_4$ with T$_c$=30 K. The measurement clearly reveals that the superconducting energy gap is distinct from the pseudogap. They have different energy scales and appear at different temperatures. The results suggest that the pseudogap is not a precursor to the superconducting state. The data also challenge the longstanding viewpoint that the superconductivity within…
We have found a quantitative connection between the evolution of the inhomogeneous nanoscale electronic gaps (INSEG) state detected in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ by scanning tunneling microscopy/spectroscopy (STM/S) and the two universal, the upper and the lower, pseudogaps in high-temperature cuprate superconductors (HTCS). When the doping and temperature dependent INSEG map were analyzed by using our proposed hole-scale, we find that the two pseudogaps are connected to two specific coverages of the CuO$_2$ plane by INSEG: the 50\% and 100\% coverages of the CuO$_2$ planes by INSEG corresp…
The c-axis optical response of the underdoped cuprates is qualitatively different from its in-plane counterpart. The features of the pseudogap show themselves more prominently in the c-axis than in-plane. We compute both the c-axis and in-plane optical conductivity using the Yang-Rice-Zhang model of the underdoped cuprates. This model combined with coherent interlayer tunnelling is enough to explain the qualitative differences between the in-plane and c-axis data. We show how pseudogap features manifest themselves in the infrared and microwave conductivity within this model.
We report the observation of a pseudogap in the \emph{ab}-plane optical conductivity of underdoped Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ ($x = 0.2$ and 0.12) single crystals. Both samples show prominent gaps opened by a spin density wave (SDW) order and superconductivity at the transition temperatures $T_{\it SDW}$ and $T_c$, respectively. In addition, we observe an evident pseudogap below $T^{\ast} \sim$ 75 K, a temperature much lower than $T_{\it SDW}$ but much higher than $T_{c}$. A spectral weight analysis shows that the pseudogap is closely connected to the superconducting gap, indicating the…
In conventional superconductors the magnitude of the pairing fluctuation is primarily determined by Tc and the superconducting (SC) coherence length, ξ. In systems with strong structural and electronic anisotropies, the interlayer separation, s, plays a significant role. In cuprates, the pseudogap (PG) correlation induces a downturn in the temperature dependent resistivity. As Tc is approached from above, this downturn in the resistivity is supposed to either i) add to or ii) join smoothly to that due to paraconductivity caused by short-lived Cooper pairs. It is important to differentiate betw…
Pairs fluctuation supercurrents and inverse lifetimes were measured on epitaxial c-axis junctions of the cuprates in the pseudogap regime, with a $PrBa_2Cu_3O_{7-δ}$ barrier sandwiched in between two $YBa_2Cu_3O_{7-δ}$ or doped $YBa_2Cu_3O_y$ electrodes, with or without magnetic fields parallel to the a-b planes. All junctions had a $\rm T_c(high)\approx 85-90$ K and a $\rm T_c(low)\approx 50-55$ K electrodes, allowing us to study pairs fluctuation supercurrents and inverse life times in between these two temperatures. In junctions with a pseudogap electrode under zero field, an excesss curren…
A central issue in the quest to understand the superconductivity in cuprates is the nature and origin of the pseudogap state, which harbours anomalous electronic states such as Fermi arc, charge density wave (CDW), and $d$-wave superconductivity. A fundamentally important, but long-standing controversial problem has been whether the pseudogap state is a distinct thermodynamic phase characterized by broken symmetries below the onset temperature $T^*$. Electronic nematicity, a fourfold ($C_4$) rotational symmetry breaking, has emerged as a key feature inside the pseudogap regime, but the presenc…
Evidence for competition between the superconducting and the pseudogap state in (BiPb)_2(SrLa)_2CuO_{6+δ} from muon-spin rotation experiments
用μ子自旋转动方法研究了最佳掺杂的（BiPb）2（SrLa）2 CuO_{6+δ}（OP Bi 2201）的面内磁穿透深度λ ab。λ_{ab}^{-2}（T）的测量结果与费米面周围的d波序参量和均匀准粒子权重的简单模型不一致。假设在ARPES实验[Phys. Rev. Lett { \bf 98}，267004（2007）]中获得的角隙对称性，数据被很好地描述，其中表明OP Bi 2201中的超导能隙仅存在于节点附近的费米表面的片段中。我们发现，费米面的其余部分，这是强烈的赝能隙状态的影响，不显着贡献的超导冷凝。我们的数据提供的证据表明，高温超导和赝能隙行为的铜酸盐是竞争现象。
To elucidate the pseudogap phase diagram including the overdoped state of high transition temperature (high-$T_c$) cuprates, we must understand the origin of the positive out-of-plane magnetoconductivity (MC) observed in these compounds. For this purpose, the out-of-plane resistivity $ρ_c(T,H)$ of an overdoped Bi$_{1.6}$Pb$_{0.4}$Sr$_{2}$CaCu$_{1.96}$Fe$_{0.04}$O$_{8+δ}$ (Bi-2212) single crystal is measured under pulsed magnetic fields up to 60 T. We show that the superconductive density-of-states (DOS) depletion effect, in addition to the pseudogap effect, clearly appears below the supercondu…
We propose a novel chiral order parameter to explain the unusual polar Kerr effect in underdoped cuprates. It is based on the loop-current model by Varma, which is characterized by the in-plane anapole moment N and exhibits the magnetoelectric effect. We propose a helical structure where the vector N^(n) in the layer n is twisted by the angle pi/2 relative to N^(n-1), thus breaking inversion symmetry. We show that coupling between magnetoelectric terms in the neighboring layers for this structure produces optical gyrotropy, which results in circular dichroism and the polar Kerr effect.
By using high magnetic field data to estimate the background conductivity, Rullier-Albenque and coworkers have recently published [Phys.Rev.B 84, 014522 (2011)] experimental evidence that the in-plane paraconductivity in cuprates is almost independent of doping. In this Comment we also show that, in contrast with their claims, these useful data may be explained at a quantitative level in terms of the Gaussian-Ginzburg-Landau approach for layered superconductors, extended by Carballeira and coworkers to high reduced-temperatures by introducing a total-energy cutoff [Phys.Rev.B 63, 144515 (2001)…
Most of 2D superconductors are of type II, i.e., they are penetrated by quantized vortices when exposed to out-of-plane magnetic fields. In presence of a supercurrent, a Lorentz-like force acts on the vortices, leading to drift and dissipation. The current-induced vortex motion is impeded by pinning at defects, enabling the use of superconductors to generate high magnetic fields without dissipation. Usually, the pinning strength decreases upon any type of pair-breaking. Here we show that in Rashba superconductors the application of an in-plane field leads, instead, to an unexpected enhancement…
The real-space localized hole pair is constructed in the Cu-O plane of the hole-doped cuprate superconductors. We prove analytically and numerically that two electrons, due to the nearest-neighbor Coulomb repulsive confinement effect, can be in pairing inside a single plaquette with the d-wave symmetry. The scenario supports the `no glue' pairing picture for the cuprates. Based on the scenarios, the physical origin of the Fermi pocket (or Fermi arc) and the two pseudogap behavior are provided. Our framework leads directly to a unified linear relationship between the pseudogap temperature T* an…
We use ultrafast optical spectroscopy to study the nonequilibrium quasiparticle relaxation dynamics of the iron-based superconductor KCa$_2$Fe$_4$As$_4$F$_2$ with $T_c=33.5$ K. Our results reveal a possible pseudogap ($Δ_{PG}$ = 2.4 $\pm$ 0.1 meV) below $T^*\approx 50$ K but prior to the opening of a superconducting gap ($Δ_{SC}$(0) $\approx$ 4.3 $\pm$ 0.1 meV). Measurements under high pump fluence real two distinct, coherent phonon oscillations with 1.95 and 5.51 THz frequencies, respectively. The high-frequency $A_{1g}$(2) mode corresponds to the $c-$axis polarized vibrations of FeAs planes …
Large pulsed magnetic fields up to 60 Tesla are used to suppress the contribution of superconducting fluctuations (SCF) to the ab-plane conductivity above Tc in a series of YBa2Cu3O(6+x). These experiments allow us to determine the field H'c(T) and the temperature T'c above which the SCFs are fully suppressed. A careful investigation near optimal doping shows that T'c is higher than the pseudogap temperature T*, which is an unambiguous evidence that the pseudogap cannot be assigned to preformed pairs. Accurate determinations of the SCF contribution to the conductivity versus temperature and ma…
The magnetic field and temperature dependence of the in-plane tunneling conductance $dI/dV(V)$ in high-quality nonsuperconducting (down to 10 mK) layered oxycarbonate Bi$_{2+x}$Sr$_{4-x}$Cu$_2$CO$_3$O$_{8+δ}$ single crystals has been investigated using break junctions. Combining measurements of the in-plane magnetoresistivity $ρ_{ab}(T,H)$ and the magnetotunneling, we present evidence for the existence of a small "pseudogap" in a nonsuperconducting cuprate, without local incoherent pairs or any correlation phenomena associated with superconductivity. We are unable to distinguish if such a "pse…
Temperature-dependent inter-plane resistivity, $ρ_c(T)$, was measured systematically as a function of transition metal substitution in the iron-arsenide superconductors Ba(Fe$_{1-x}$T$_x$)$_2$As$_2$, $T$= Ni, Pd, Rh. The data are compared with the behavior found in Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$, revealing resistive signatures of pseudogap. In all compounds we find resistivity crossover at a characteristic pseudogap temperature $T^*$ from non-metallic to metallic temperature dependence on cooling. Suppression of $T^*$ proceeds very similar in cases of Ni and Pd doping and much faster than in s…
We report in-plane resistivity ($ρ$) and transverse magnetoresistance (MR) measurements in underdoped HgBa$_2$CuO$_{4+δ}$ (Hg1201). Contrary to the longstanding view that Kohler's rule is strongly violated in underdoped cuprates, we find that it is in fact satisfied in the pseudogap phase of Hg1201. The transverse MR shows a quadratic field dependence, $δρ/ρ_o=a H^{2}$, with $a(T)\propto T^{-4}$. In combination with the observed $ρ\propto T^2$ dependence, this is consistent with a single Fermi-liquid quasiparticle scattering rate. We show that this behavior is universal, yet typically masked i…
