Induced superconductivity in noncuprate layers of the Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ high-temperature superconductor: Modeling of scanning tunneling spectra
Ilpo Suominen, Jouko Nieminen, R. S. Markiewicz, A. Bansil
备注：
9 pages, 2 figures. Accepted for publication in Phys. Rev. B
We analyze how the coherence peaks observed in Scanning Tunneling Spectroscopy (STS) of cuprate high temperature superconductors are transferred from the cuprate layer to the oxide layers adjacent to the STS microscope tip. For this purpose, we have carried out a realistic multiband calculation for the superconducting state of Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi2212) assuming a short range d-wave pairing interaction confined to the nearest-neighbor Cu $d_{x^2-y^2}$ orbitals. The resulting anomalous matrix elements of the Green's function allow us to monitor how pairing is then induced not only within the cuprate bilayer but also within and across other layers and sites. The symmetry properties of the various anomalous matrix elements and the related selection rules are delineated.
We present realistic multiband calculations of scanning tunneling spectra in Bi_{2}Sr_{2}CaCu_{2} O_{8+δ} over a wide doping range. Our modeling incorporates effects of a competing pseudogap and pairing gap as well as effects of strong electronic correlations, which are included by introducing self-energy corrections in the one-particle propagators. The calculations provide a good description of the two-gap features seen in experiments at low energies and the evolution of the Van Hove singularity (VHS) with doping, and suggest a possible quantum critical point near the point where the VHS cros…
Modeling scanning tunneling spectra of $Bi_2 Sr_2 CaCu_2 O_{8+δ}$
最近的角分辨光电子能谱和中子散射数据为解释Bi $_2$ Sr $_2$ CaCu $_2$ O $_{8+δ}$的扫描隧道谱提供了新的成分。我们分析了低温隧道谱，从氧过掺杂到欠掺杂样品，包括双层分裂和中子共振峰的细节。两个van Hove奇异性被确定：第一个是集成在相干峰，第二个是严重加宽在较高的结合能。隧道光谱的形状表明一个强耦合的准粒子的集体模式，和光电发射的比较表明，在隧道中的散射率是一个数量级小于ARPES。最后，用各向同性隧穿矩阵元计算的理论谱比用各向异性矩阵元计算的理论谱更符合实验数据。
We discuss how variations in the scanning tunneling microscope (STM) tip, whether unintentional or intentional, can lead to changes in topographic images and dI/dV spectra. We consider the possibility of utilizing functionalized tips in order to improve the sensitivity of STM experiments to local irregularities at the surface or hidden below the surface layers. The change in the tip symmetry can radically alter the contrast of the topographic image due to changes in tip-surface overlap. The dI/dV curves change their shape according to which sample bands the tip orbital tends to overlap. In add…
Pairing in the cuprate high-temperature superconductors and its origin remain among the most enduring mysteries in condensed matter physics. With cross-sectional scanning tunneling microscopy/ spectroscopy, we clearly reveal the spatial-dependence or inhomogeneity of the superconducting gap structure of Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi2212) and YBa$_2$Cu$_3$O$_{7-x}$ (YBCO) along their $c$-axes on a scale shorter than the interlayer spacing. By tunneling into the (100) plane of a Bi2212 single crystal and a YBCO film, we observe both U-shaped tunneling spectra with extended flat zero-conducta…
Using Scanning tunneling spectroscopy (STS), we report the correlation between spatial gap inhomogeneity and the zinc (Zn) impurity resonance in single crystals of Bi$_{\mathrm{2}}$Sr$_{\mathrm{2}}$Ca(Cu$_{\mathrm{1-}x}$Zn$_{x}$)$_{\mathrm{2}}$O$_{\mathrm{8+}δ}$ with different carrier (hole) concentrations ($p$) at a fixed Zn concentration ($x$ $\sim$ 0.5 % per Cu atom). In all the samples, the impurity resonance lies only in the region where the gap value is less than $\sim$ 60 meV. Also the number of Zn resonance sites drastically decreases with decreasing $p$, in spite of the fixed $x$. The…
We present a Green's function based framework for modeling the scanning tunneling spectrum from the normal as well as the superconducting state of complex materials where the nature of the tunneling process$-$ i.e. the effect of the tunneling 'matrix element', is properly taken into account. The formalism is applied to the case of optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi2212) high-Tc superconductor using a large tight-binding basis set of electron and hole orbitals. The results show clearly that the spectrum is modified strongly by the effects of the tunneling matrix element and that …
We observe proximity-induced superconductivity in the \textit{in situ} prepared heterostructures constructed by topological insulator Bi$_{2}$Te$_{3}$ thin films and high-temperature cuprate superconductors Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$. The superconducting gap maximum is about 7.6 meV on the surface of Bi$_{2}$Te$_{3}$ thin films with a thickness of two quintuple layers, and the gap value decreases with an increase in the film thickness. Moreover, the quasiparticle interference data show a clear evidence of a twofold symmetric superconducting gap with gap minima along one pair of the pr…
Unusual dependence of vortex core states on the superconducting gap in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$
利用扫描隧道谱研究了Bi $_2$ Sr $_2$ CaCu $_2$ O $_{8+δ}$中涡旋核的准粒子态.观察到的涡核态的能量与核外区域的超导能隙近似成线性比例。这清楚地将它们与传统的定域核心状态区分开来，并且是负责它们在高温超导体中离散外观的机制的签名。涡核态的能量标度也表明了Bi $_2$ Sr $_2$ CaCu $_2$ O $_{8+δ}$和YBa $_2$ Cu $_3$ O $_{7-δ}$中涡核的共同性质。最后，观察到的涡核状态不显示任何依赖于所施加的磁场的范围从1到6 T。
Anomalous dispersion in the autocorrelation of ARPES data of Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$
我们发现，在角分辨光电子能谱数据的自相关的峰值Bi $_2$ Sr $_2$ CaCu $_2$ O $_{8+δ}$在超导状态下的结合能小于最大超导能隙的色散行为。然而，对于更高的能量，观察到一个惊人的异常色散，这是电子与集体激发相互作用的结果。相比之下，在赝能隙阶段，我们只观察到自相关峰的无色散行为。我们的研究结果的影响方面的傅立叶变换扫描隧道光谱数据进行了讨论。
Scanning tunneling spectroscopy measurements on the high temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ have reported an enhanced spectral gap in the neighborhood of O dopant atoms. We calculate, within density functional theory (DFT), the change in electronic structure due to such a dopant. We then construct and discuss the validity of several tight binding (TB) fits to the DFT bands with and without an O dopant. With the doping-modulated TB parameters, we finally evaluate the spin susceptibility and pairing interaction within spin fluctuation theory. The d-wave pairing eigenvalues …
As a typical hole-doped cuprate superconductor, Bi 2 Sr 2 CaCu 2 O 8+δ (Bi2212) carrier doping is mostly determined by its oxygen content. Traditional doping methods can regulate its doping level within the range of hole doping. Here we report the first application of CaH 2 annealing method in regulating the doping level of Bi2212. By continuously controlling the anneal time, a series of differently doped samples can be obtained. The combined experimental results of x-ray diffraction, scanning transmission electron microscopy, resistance and Hall measurements demonstrate that the CaH 2 induced…
It is well established that the hole density in the prototypical superconductor La$_{2-x}$Sr$_x$CuO$_4$ is very inhomogeneous due to Sr-dopant induced disorder. On the other hand, until recently it is widely believed that the hole distribution in HgBa$_2$CuO$_{4+δ}$ and Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ doped by interstitial oxygen is much more uniform. Recent nuclear magnetic resonance measurements indicate, however, that the charge inhomogeneity in HgBa$_2$CuO$_{4+δ}$ is close to that in La$_{2-x}$Sr$_x$CuO$_4$. Calculations performed in the present paper confirm this observation. We also show t…
The pseudogap (PG) state and its related intra-unit-cell symmetry breaking remain the focus in the research of cuprate superconductors. Although the nematicity has been studied in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$, especially underdoped samples, its behavior in other cuprates and different doping regions is still unclear. Here we apply a scanning tunneling microscope to explore an overdoped (Bi, Pb)$_2$Sr$_2$CuO$_{6+δ}$ with a large Fermi surface (FS). The establishment of a nematic order and its real-space distribution is visualized as the energy scale approaches the PG.
A magnetic field applied to type-II superconductors introduces quantized vortices that locally quench superconductivity, providing a unique opportunity to investigate electronic orders that may compete with superconductivity. This is especially true in cuprate superconductors in which mutual relationships among superconductivity, pseudogap, and broken-spatial-symmetry states have attracted much attention. Here we observe energy and momentum dependent bipartite electronic superstructures in the vortex core of Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ using spectroscopic-imaging scanning tunneling microscop…
Angle Resolved Photoemission Spectroscopy (ARPES) probes the momentum-space electronic structure of materials, and provides invaluable information about the high-temperature superconducting cuprates. Likewise, the cuprate real-space, inhomogeneous electronic structure is elucidated by Scanning Tunneling Spectroscopy (STS). Recently, STS has exploited quasiparticle interference (QPI) - wave-like electrons scattering off impurities to produce periodic interference patterns - to infer properties of the QP in momentum-space. Surprisingly, some interference peaks in Bi_{2}Sr_{2}CaCu_{2}O_{8+δ} (Bi-…
Superconducting (SC) fluctuations in cuprate superconductors have been extensively studied to gain a deep insight into preformed Cooper pairs above the SC transition temperature $T_{\text{c}}$. While the various measurements, such as the terahertz (THz) optical conductivity, Nernst effect, angle-resolved photoemission spectroscopy (ARPES), and scanning tunneling microscopy (STM) measurements have provided the signature of the SC fluctuations, the onset temperature of the SC fluctuations depends on the measurement scheme. Here, we shed light on the Higgs mode to investigate the SC fluctuations,…
Thermodynamic transitions in inhomogeneous cuprate superconductors
扫描隧道光谱的研究表明，在间隙尺寸的大的空间变化的电子不均匀性的存在下，Bi $_2$ Sr $_2$ CaCu $_2$ O $_{8+δ}$。Andersen { \it et al}通过假设空间变化的配对相互作用来模拟这种变化。我们表明，他们的计算比热是不符合实验数据，表现出狭窄的转变。这就对现在普遍的间隙和配对不均匀性的假设提出了质疑。
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…
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…
We consider the problem of local tunneling into cuprate superconductors, combining model based calculations for the superconducting order parameter with wavefunction information obtained from first principles electronic structure. For some time it has been proposed that scanning tunneling microscopy (STM) spectra do not reflect the properties of the superconducting layer in the CuO$_2$ plane directly beneath the STM tip, but rather a weighted sum of spatially proximate states determined by the details of the tunneling process. These "filter" ideas have been countered with the argument that sim…
Strong variations in superconducting critical temperatures in different families of the cuprate perovskites, even with similar hole doping in their copper-oxygen planes, suggest the importance of lattice modulation effects. The one-dimensional incommensurate lattice modulation (ILM) of Bi_2Sr_2CaCu_2O_{8+y}, with the average atomic positions perturbed beyond the unit cell, offers an ideal test ground for studying the interplay between superconductivity and the long-range incommensurate lattice fluctuations. Here we report Scanning nano X-ray Diffraction (SnXRD) imaging of incommensurate lattic…
We describe the development and performance of an ultra-high vacuum scanning tunneling microscope working under combined extreme conditions of ultra-low temperatures and high magnetic fields. We combined a top-loading dilution refrigerator and a standard bucket dewar with a bottom-loading superconducting magnet to achieve 4.5 days operating time, which is long enough to perform various spectroscopic-imaging measurements. To bring the effective electron temperature closer to the mixing-chamber temperature, we paid particular attention to filtering out the radio-frequency noise, as well as enhan…
Pair Density Wave in the Pseudogap State of High Temperature Superconductors
最近的扫描隧道显微镜（STM）实验的Bi $_{2}$ Sr $_{2}$ CaCu $_{2}$ O $_{8+δ}$的电子态的实空间组织在低能量的赝能隙状态的证据。我们认为，基于对称性的考虑以及模型计算，实验观察到的调制是由于密度波的d波库珀对没有全局相位相干。我们表明，STM测量可以区分一对密度波从更典型的电子调制，如那些由于电荷密度波排序或散射从现场周期性电位。
Scanning tunneling microscopy (STM) measurements have observed modulations in the density of states (DOS) of a number of high-T$_c$ cuprates. These modulations have been interpreted in terms of electron-boson coupling analogous to the dispersion "kinks" observed by angle-resolved photoemission spectroscopy (ARPES). However, a direct a reconciliation of the energy scales and features observed by the two probes is presently lacking. In this paper we examine the general features of el-boson coupling in a $d-$wave superconductor using Eliashberg theory, focusing on the structure of the modulations…
Constraints on the Quasiparticle Density of States in High-$T_c$ Superconductors
在这封信中，我们提出了新的隧道YBa $_2$ Cu $_3$ O $_7$薄膜的低温扫描隧道光谱数据。在YBa $_2$ Cu $_3$ O $_7$中也发现了以前在Bi $_2$ Sr $_2$ CaCu $_2$ O $_{8+δ}$中报道的不寻常的峰-谷-驼峰特征。为了分析这些常见的签名，我们提出了一个新的启发式模型，其中，除了d-波对称性，间隙函数是能量依赖的。导出了一个简单的准粒子态密度的表达式，与实验符合得很好。讨论了准粒子态的动力学和超导转变的能量尺度。
Effects of a Collective Spin Resonance Mode on the STM Spectra of D-Wave Superconductors
在许多高温超导体中存在高能自旋共振模。受最近的扫描隧道显微镜（STM）实验的启发，我们在超导体Bi $_2$ Sr $_2$ CaCu $_2$ O $_{8+δ}$中研究了这种共振模式对局域态密度（LDOS）的影响. d波超导体中的电子与共振模之间的耦合在LDOS中产生高能峰，其显示围绕掺杂杂质的两个晶胞周期调制。这为我们提供了一种新的手段，不仅可以探测动态自旋集体模，而且可以研究它与电子激发的耦合。
We apply a recently developed method combining first principles based Wannier functions with solutions to the Bogoliubov-de Gennes equations to the problem of interpreting STM data in cuprate superconductors. We show that the observed images of Zn on the surface of Bi$_2$Sr$_2$CaCu$_2$O$_8$ can only be understood by accounting for the tails of the Cu Wannier functions, which include significant weight on apical O sites in neighboring unit cells. This calculation thus puts earlier crude "filter" theories on a microscopic foundation and solves a long standing puzzle. We then study quasiparticle …
Conductance-voltage characteristics (CVCs) for non-symmetric tunnel junctions between $d$-wave superconductors with charge-density waves (CDWs) and normal metals were calculated. It was shown that they have a V-like form at small voltages $V$ and are asymmetric at larger $V$ owing to the presence of CDW peak in one of the $V$-branches. The spatial scatter of the dielectric (CDW) order parameter smears the CDW peak into a hump and induces a peak-dip-hump structure (PDHS) typical of CVCs observed for such junctions. At temperatures larger than the superconducting critical temperature, the PDHS e…
Pairbreaking Without Magnetic Impurities in Disordered Superconductors
我们研究了短相干长度超导体中非均匀配对相互作用的影响，使用空间变化的Bogoliubov-deGennes模型。在玻恩近似下，它再现了所有标准的Abrikosov-Gor'kov对断裂和无隙效应，即使在没有实际磁性杂质的情况下。对于单个位点上的配对无序，T-矩阵引起BCS间隙内的束缚态。我们的研究结果进行了比较与最近的扫描隧道显微镜测量Bi $_2$ Sr $_2$ CaCu $_2$ O $_{8+δ}$与Zn或Ni杂质。
A recent discovery of the pair density wave (PDW) order creates a stir in understanding an underlying physics in the pseudogap states of the cuprate high temperature superconductors. We have performed a Spectroscopic Imaging Scanning Tunneling Microscopy (SI-STM) measurements on Bi$_2$Sr$_2$CaCu$_2$O$_8$+$δ$ and identified that spatially uniform d-wave superconductivity (DSC), d-symmetry charge density wave (CDW), and the PDW play important roles in an intertwined fashion. In this review, we show how these different electronic degrees of freedom emerges in electronic structures of the cuprate …
The highest temperature superconductors are electronically inhomogeneous at the nanoscale, suggesting the existence of a local variable which could be harnessed to enhance the superconducting pairing. Here we report the relationship between local doping and local strain in the cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$. We use scanning tunneling microscopy to discover that the crucial oxygen dopants are periodically distributed, in correlation with local strain. Our picoscale investigation of the intra-unit-cell positions of all oxygen dopants provides essential structural input for …
The importance of charge reservoir layers for supplying holes to the CuO$_2$ planes of cuprate superconductors has long been recognized. Less attention has been paid to the screening of the charge transfer by the intervening ionic layers. We address this issue in the case of YBa$_2$Cu$_3$O$_{6+x}$, where CuO chains supply the holes for the planes. We present a simple dielectric-screening model that gives a linear correlation between the relative displacements of ions along the $c$ axis, determined by neutron powder diffraction, and the hole density of the planes. Applying this model to the tem…
Determining the exact pairing symmetry of the superconducting order parameter in candidate unconventional superconductors remains an important challenge. Recently a new method, based on phase sensitive quasiparticle interference measurements, was developed to identify gap sign changes in isotropic multiband systems. Here we extend this approach to the single-band and multiband nodal $d$-wave superconducting cases relevant, respectively, for the cuprates and likely for the infinite-layer nickelate superconductors. Combining analytical and numerical calculations, we show that the antisymmetrized…
Effects of $τ_1$ Scattering on Fourier-Transformed Inelastic Tunneling Spectra in High-$T_c$ Cuprates with Bosonic Modes
研究了d波超导体中$τ_1$杂质诱导的$\mathbf{q}$空间能量导数局域态密度（LDOS）谱.我们的动机部分是最近的扫描隧道显微镜（STM）观察到的强间隙不均匀性与弱的电荷密度变化在Bi $_{2}$ Sr $_2$ CaCu $_2$ O $_{8+δ}$（BSCCO）。我们的假设是，间隙的不均匀性可能是由对电位的无序触发的。我们着重讨论了d波超导能隙移动时，电子耦合对各种玻色子模的影响。由于电子与$B_{1g}$声子模式的高度各向异性耦合的图案与BSCCO中的傅里叶变换非弹性电子隧道光谱（FT-IETS）STM实验的初步结果相似。我们讨论了我们的研究结果的背景下，在ARPES实验中看到的带重整化效应的影响，并提出了进一步探讨高$T_c$铜酸盐中的电子玻色子耦合的方法。
Tunneling spectra of $\mathrm{TaO}_x$ junctions for van der Waals superconductors
School of Physics and Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China（中国人民大学物理学院和量子态构建与操控教育部重点实验室）；School of Chemistry and Life Resources, Renmin University of China（中国人民大学化学与生命资源学院）
