本文采用平均场反铁磁性和超导电性共存的模型，研究了电子掺杂Pr $_{2-x}$ Ce $_x$ CuO $_{4-δ}$的穿透深度随温度的变化关系。尽管存在一个$d_{x^2-y^2}$配对间隙的基础频谱，我们发现低$T$渗透深度的低掺杂的情况下，与实验结果一致的无节点的行为。随着掺杂的增加，穿透深度的线性$T$行为（d波配对的特征）随着较低的磁性带穿过费米能级并产生节点费米表面袋而出现。
英文摘要：
We have investigated the doping dependence of the penetration depth vs. temperature in electron doped Pr$_{2-x}$Ce$_x$CuO$_{4-δ}$ using a model which assumes the uniform coexistence of (mean-field) antiferromagnetism and superconductivity. Despite the presence of a $d_{x^2-y^2}$ pairing gap in the underlying spectrum, we find nodeless behavior of the low-$T$ penetration depth in underdoped case, in accord with experimental results. As doping increases, a linear-in-$T$ behavior of the penetration depth, characteristic of d-wave pairing, emerges as the lower magnetic band crosses the Fermi level and creates a nodal Fermi surface pocket.
Uniform Mixing of Antiferromagnetism and High-Tc Superconductivity in Electron-doped Layers in Four-layered Ba2Ca3Cu4O8F2 : A New Phenomenon in an Electron Underdoped RegimePhenomenon in an Electron Underdoped Regime
We present a theoretical model to show that the transition from an antiferromagnetic (AFM) phase to the $d_{x^2-y^2}$-wave superconductivity occurs through a robust companion of a finite momentum pairing between $({\bf k},\uparrow)$ and $(-{\bf k}-{\bf Q},\downarrow)$ electrons, namely pair-density wave (PDW) state, where ${\bf Q}=(π,π)$ is the AFM wavevector. Interestingly, the spatial structure of the PDW is constrained to be a $p+ip$-wave symmetry, which follows $p_{\bf k}=p_{-{\bf k}-{\bf Q}}$ under fermions exchange in cuprates, dictating a spin-singlet pairing. Furthermore, the PDW state…
The antiferromagnetism (AFM) and chiral-d wave superconductivity (SC) in a honeycomb lattice close to an antiferromagnetic (AF) Mott state at half band filling are studied with a t-J model and slave boson mean field theory. The order parameters and single particle dispersion relations at different band filling fractions are investigated. It is found that the AFM enhances the SC, and leads to nodal single particle dispersion relations at two band filling fractions. These unexpected nodal dispersion relations out of nodeless chiral-d wave superconducting order are discussed. A comparison between…
A nodeless superconducting (SC) gap was reported in a recent scanning tunneling spectroscopy experiment of a copper-oxide monolayer grown on the Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi2212) substrate [Y. Zhong {\it et al.}, Sci. Bull. {\bf 61}, 1239 (2016)], which is in stark contrast to the nodal d-wave pairing gap in the bulk cuprates. Motivated by this experiment, we first show with first-principles calculations that the tetragonal CuO (T-CuO) monolayer on the Bi2212 substrate is more stable than the commonly postulated CuO$_{2}$ structure. The T-CuO monolayer is composed of two CuO$_2$ layers sh…
Uniform mixing of antiferromagnetism and high-T_c superconductivity in multilayered copper oxides Ba_2Ca_{n-1}Cu_nO_{2n}F_2 with apical fluorines (n=2,3,4): Cu-NMR/NQR and F-NMR
Polarized inelastic neutron scattering experiments were performed to study magnetic excitations in the normal and superconducting phases of Co-underdoped BaFe$_2$As$_2$, which exhibits coexistence of antiferromagnetic order and superconductivity. In the normal state the antiferromagnetic order results in broadened spin gaps opening in all three spin directions that are reminiscent of the magnetic response in pure antiferromagnetic BaFe$_2$As$_2$. In particular longitudinal excitations exhibit a large gap. In the superconducting state we find two distinct resonance excitations, which both are a…
The pairing mechanism of high-temperature superconductivity in cuprates remains the biggest unresolved mystery in condensed matter physics. To solve the problem, one of the most effective approaches is to investigate directly the superconducting CuO2 layers. Here, by growing CuO2 monolayer films on Bi2Sr2CaCu2O8+δ substrates, we identify two distinct and spatially separated energy gaps centered at the Fermi energy, a smaller U-like gap and a larger V-like gap on the films, and study their interactions with alien atoms by low-temperature scanning tunneling microscopy. The newly discovered U-lik…
Competing unconventional superconductivity and antiferromagnetism widely exist in several strongly correlated quantum materials whose direct simulation generally suffers from fermion sign problem. Here we report unbiased Quantum Monte Carlo (QMC) simulations on a sign-problem-free repulsive toy model with same onsite symmetries as the standard Hubbard model on a 2D square lattice. Using QMC, supplemented with mean-field and continuum field-theory arguments, we find that it hosts three distinct phases: a nodal d-wave phase, an antiferromagnet, and an intervening phase which hosts coexisting ant…
Competition between superconductivity and magnetic/nematic order as a source of anisotropic superconducting gap in underdoped Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$
使用隧道二极管谐振器技术在Ba $_{1-x}$ K $_{x}$ Fe $_{2}$ As $_{2}$的单晶中测量了面内伦敦穿透深度$Δλ(T)$，掺杂水平$x$的范围从严重欠掺杂$x$ =0.16（$T_{c}$ =7~K）到接近最佳掺杂$x$ = 0.34（$T_{c}=$ 39 K）。指数饱和的$Δλ(T)$中的$T\to0$极限被发现在最佳掺杂的样品中，与超流密度$ρ_{s}(T)\equiv(λ(0)/λ(T))^{2}$定量描述的自洽的$γ$ -模型与两个无节点的各向同性的超导间隙。随着掺杂水平在$x$ =0.16处朝向超导圆顶的极端降低，$Δλ(T)$的低温行为变得非指数并且最好由幂律$Δλ(T)\propto T^{2}$描述，这是强各向异性间隙的特征。这两个制度之间的变化发生在共存的磁/磁有序和超导性，$x<0.25$的范围内，并伴随着一个快速上升的绝对值$Δλ(T)$与欠掺杂。这种效应是超导性和其他有序态之间竞争的特征，与电子掺杂的Ba（Fe $_{1-x}$ Co $_{x}$）$_{2}$ As $_{2}$化合物中观察到的效应非常相似，但幅度明显较小。我们的研究表明，空穴掺杂的化合物中的超导性和磁/磁有序之间的竞争比电子掺杂的化合物中的弱，并且欠掺杂的铁磷属元素化物中的超导态的各向异性是由磁和磁长程有序促进的配对相互作用和能隙函数的各向异性变化的结果。
We measured the optical conductivity of superconducting single crystals of Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ with $x$ ranging from 0.40 (optimal doping, $T_c = 39$ K) down to 0.20 (underdoped, $T_c = 16$ K), where a magnetic order coexists with superconductivity. In the normal state, the low-frequency optical conductivity can be described by an incoherent broad Drude component and a coherent narrow Drude component: the broad one is doping-independent, while the narrow one shows strong scattering in the heavily underdoped compound. In the superconducting state, the formation of the condensate l…
Disorder Effects on Competition between Antiferromagnetism and Superconductivity in Cuprate Superconductors through the Enhancement in Charge Susceptibility
Multilayered cuprates possess not only the highest superconducting temperature transition but also offer a unique platform to study disorder-free CuO$_2$ planes and the interplay between competing orders with superconductivity. Here, we study the underdoped trilayer cuprate HgBa$_2$Ca$_2$Cu$_3$O$_{8+ δ}$ and we report the first quantum oscillation and Hall effect measurements in magnetic field up to 88 T. A careful analysis of the complex spectra of quantum oscillations strongly supports the coexistence of an antiferromagnetic order in the inner plane and a charge order in the outer planes. Th…
The thermal conductivity kappa of the iron-arsenide superconductor Ba1-xKxFe2As2 was measured for heat currents parallel and perpendicular to the tetragonal c axis at temperatures down to 50 mK and in magnetic fields up to 15 T. Measurements were performed on samples with compositions ranging from optimal doping (x = 0.34; Tc = 39 K) down to dopings deep into the region where antiferromagnetic order coexists with superconductivity (x = 0.16; Tc = 7 K). In zero field, there is no residual linear term in kappa(T) as T goes to 0 at any doping, whether for in-plane or inter-plane transport. This s…
Superconductivity often emerges in proximity of other symmetry-breaking ground states, such as antiferromagnetism or charge-density-wave (CDW) order. However, the subtle inter-relation of these phases remains poorly understood, and in some cases even the existence of short-range correlations for superconducting compositions is uncertain. In such circumstances, ultrafast experiments can provide new insights, by tracking the relaxation kinetics following excitation at frequencies related to the broken symmetry state. Here, we investigate the transient terahertz conductivity of BaPb1-xBixO3 - a m…
Superfluid stiffness $ρ_s$ is a defining characteristic of the superconducting state, allowing phase coherence and supercurrent. It is accessible experimentally through the penetration depth. Coexistence of $d$-wave superconductivity with other phases in underdoped cuprates, such as antiferromagnetism (AF) or charge-density waves (CDW), may drastically alter $ρ_s$. To shed light on this physics, the zero-temperature value of $ρ_s=ρ_{zz}$ along the $c$-axis was computed for different values of Hubbard interaction $U$ and different sets of tight-binding parameters describing the high-temperature…
The t-J model is a paradigmatic model for the study of strongly correlated electron systems. In particular, it has been argued that it is an appropriate model to describe the cuprate high-Tc superconductors. It turns out that a comprehensive understanding of the gamut of physics encoded by the t-J model is still an open problem. In recent years some remarkable experiments on the cuprates, for example, discovery of nodeless superconductivity in underdoped samples (PNAS 109, 18332 (2012)), discovery of s-wave like gap in the pseudogap phase (Phys. Rev. Lett. 111, 107001 (2013)), and observation …
Controlled point-like disorder introduced by 2.5 MeV electron irradiation was used to probe the superconducting state of single crystals of \CaKx\ superconductor at $x = 0$ and 0.05 doping levels. Both compositions show an increase of the residual resistivity and a decrease of the superconducting transition temperature, $T_c$ at the rate of $dT_c/dρ(T_c) \approx$ 0.19 K(\textmu$Ω$cm)$^{-1}$ for $x=0$ and 0.38 K(\textmu$Ω$cm)$^{-1}$ for $x=\:$0.05, respectively. In Ni - doped, $x = 0.05$, compound the coexisting spin-vortex crystal (SVC) magnetic phase is suppressed at the rate of $dT_N/dρ(T_N)…
Novel Superconducting Phases in Copper Oxides and Iron-oxypnictides: NMR Studies
我们重新研究了新的反铁磁性（AFM）相图和高Tc的$ superconductivity (HTSC) for a disorder-free CuO$ _2 $ plane based on an evaluation of local hole density ($ p PDMATHABMO_2 $ plane in an underdoped regime of HTSC. The $ T $=0 phase diagram of AFM constructed here is in quantitative agreement with the theories in a strong correlation regime which is unchanged even with mobile holes. This {\it Mott physics} plays a vital role for mediating the Cooper pairs to make $ T_c $ of HTSC very high. By contrast, we address from extensive NMR studies on electron-doped iron-oxypnictides La1111 compounds that the increase in $ T…
Doping dependence of the superconducting state structure and spin-fluctuation pairing mechanism in the $Ba(Fe_{1-x}Co_{x})_{2}As_{2}$ family is studied. BCS-like analysis of experimental data shows that in the overdoped regime, away from the AFM transition, the spin-fluctuation interaction between the electron and hole gaps is weak, and $Ba(Fe_{1-x}Co_{x})_{2}As_{2}$ is characterized by three essentially different gaps. In the three-gap state an anisotropic (nodeless) electron gap $Δ_e (x, ϕ)$ has an intermediate value between the dominant inner $Δ_{2h}(x)$ and outer $Δ_{1h}(x)$ hole gaps. Clo…
