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 are enhanced above the pure system without O dopant, supporting the picture of enhanced local pairing around such a defect.
We have performed an angular-resolved photoemission study of underdoped, optimally doped and overdoped Bi$_{2}$Sr$_2$CaCu$_2$O$_{8+x}$ samples using a wide photon energy range (15 - 100 eV). We report a small and broad non-dispersive A$_{1g}$ peak in the energy distribution curves whose intensity scales with doping. We attribute it to a local impurity state similar to the one observed recently by scanning tunneling spectroscopy and identified as the oxygen dopants. Detailed analysis of the resonance profile and comparison with the single-layered Bi$_{2}$Sr$_2$CuO$_{6+x}$ suggest a mixing of th…
A new theoretical model is presented to study the nanoscale electronic inhomogeneity in high-$T_c$ cuprates. In this model, we argue that the randomly distributed out-of-plane interstitial oxygen dopants induces locally the off-diagonal (i.e., hopping integral) disorder. This disorder modulates the superexchange interaction resulting from a large-$U$ Hubbard model, which in turns changes the local pairing interaction. The microscopic self-consistent calculations shows that the large gap regions are registered to the locations of dopants. Large gap regions exhibit small and broader coherence pe…
The coexistence of a homogeneous d-wave gap and short-ranged pairing density waves (PDW) accounts for the apparent "ring" charge order in all directions of the copper oxide plane, observed by recent RIXS measurements in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$
We study the inhomogeneity of the electronic pairing gap observed by STM near the surface of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ to be correlated with interstitial O defects. We treat the problem in a slave boson mean field theory of a disordered $t-t^{\prime}-J$ model, and identify three aspects of the O defects related to the inhomogeneity: (1)the superexchange interaction is locally enhanced in their vicinity, which enhances the local pairing gap and reduces the coherence peak; (2)they donate holes into CuO$_2$ plane, which reduces the spinon density of states of and hence the average gap a…
Since the discovery of high temperature superconductivity in cuprates, Josephson junction based phase-sensitive experiments are believed and used to provide the most convincing evidence for determining the pairing symmetry. Regardless of different junction materials and geometries used, quantum tunneling involved in these experiments is essentially a nanoscale process, and thus, actual experimental results are extremely sensitive to atomic details of the junction structures. The situation has led to controversial results as to the nature of the pairing symmetry of cuprates: while in-plane junc…
Using a new variant of photoelectron spectroscopy, we measure the homogeneous near-nodal pairing ($Δ$) and pair-breaking self-energy ($Γ_S$) processes for a wide range of doping levels of Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$. For all samples we find that the pairing extends above the superconducting transition T$_c$ to a scale T$_{Pair}$ that is distinct from the antinodal pseudogap scale T$^*$ and near but slightly above T$_c$. We find that $Δ$ and T$_{Pair}$ are related with a strong coupling ratio 2$Δ$ /k$_B$T$_{Pair}\approx6$ across the entire doping phase diagram, i.e. independent of the effects…
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 w…
Recent experiments on Bi-based cuprate superconductors have revealed an unexpected enhancement of the pairing correlations near the interstitial oxygen dopant ions. Here we propose a possible mechanism -- based on local screening effects -- by which the oxygen dopants do modify the electronic parameters within the CuO_2 planes and strongly increase the superexchange coupling J. This enhances the spin pairing effects locally and may explain the observed spatial variations of the density of states and the pairing gap.
Since the nature of pairing interactions is manifested in the superconducting gap symmetry, the exact gap structure, particularly any deviation from the simple d_{x^2-y^2} symmetry, would help elucidating the pairing mechanism in high-T_c cuprates. Anisotropic heat transport measurement in Bi_{2}Sr_{2}CaCu_{2}O_{8+δ} (Bi-2212) reveals that the quasiparticle populations are different for the two nodal directions and thus the gap structure must be uniquely anisotropic, suggesting that pairing is governed by interactions with a rather complicated anisotropy. Intriguingly, it is found that the "pl…
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…
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…
Break-junction tunneling spectroscopy at temperatures 30-50 mK in high magnetic field is used to directly probe the quasiparticle density of states within the energy gap in a single crystal Bi2212 high-$T_c$ superconductor. The measured tunneling conductances $dI/dV(V)$ in the subgap region have a zero flat region with no evidence for a linear increase of the density of states with voltage. A number of tunnel break-junctions exhibited $dI/dV(V)$ curves with a second energy gap structure at the average magnitude 2$Δ_{p-p}/e=13$ mV. Our data cannot be explained by either a pure $s$ pairing or a …
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…
Scanning tunneling spectroscopy has recently discovered a positive correlation between the magnitude of the superconducting gap and positions of dopant oxygen atoms in Bi-based cuprates. We propose a microscopic mechanism that could be responsible for this effect. In particular, we demonstrate that the dopant-induced spatial variation of the atomic levels always enhances the superexchange interaction.
Recent scanning tunneling spectroscopy experiments have provided evidence that dopant impurities in high- Tc superconductors can strongly modify the electronic structure of the CuO2 planes nearby, and possibly influence the pairing. To investigate this connection, we calculate the local magnetic superexchange J between Cu ions in the presence of dopants within the framework of the three-band Hubbard model, up to fifth-order in perturbation theory. We demonstrate that the sign of the change in J depends on the relative dopant-induced spatial variation of the atomic levels in the CuO2 plane, con…
Scanning tunneling spectroscopy studies on Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ suggest the presence of electronic inhomogeneity with a large spatial variation in gap size. Andersen {\it et al} have modelled this variation by assuming a spatially-varying pairing interaction. We show that their calculated specific heat is incompatible with the experimental data which exhibit narrow transitions. This calls into question the now-common assumption of gap and pairing inhomogeneity.
Using ultrafast optical techniques, we probe the hole-doping dependence of the electron-boson coupling constant $λ$ in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$. In the overdoped region, we observe a correlation between ($λ$) and the superconducting transition temperature $T_{c}$. Upon performing the McMillan analysis, however, we find that $λ$ is too small to explain the high $T_{c}$'s, and that the Coulomb pseudopotential $μ^{\ast}$ is negative. Our analysis therefore reveals two components in the mechanism of high-$T_{c}$ superconductivity -- a dominant pre-existing pairing interaction, together …
Recent scanning tunneling microscopy studies have shown that local nanoscale pairing inhomogenities are correlated with interstitial oxygen dopants in Bi-2212. Combining electrostatic and cluster calculations, in this paper the impact of a dopant on the local Madelung and charge transfer energies, magnetic exchange J, Zhang-Rice mobility, and interactions with the lattice is investigated. It is found that electrostatic modifications locally increases the charge transfer energy and slightly suppresses J. It is further shown that coupling to c-axis phonons is strongly modified near the dopant. T…
Fluctuating superconductivity - vestigial Cooper pairing in the resistive state of a material - is usually associated with low dimensionality, strong disorder or low carrier density. Here, we report single particle spectroscopic, thermodynamic and magnetic evidence for persistent superconducting fluctuations in heavily hole-doped cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ ($T_c$ = 66~K) despite the high carrier density. With a sign-problem free quantum Monte Carlo calculation, we show how a partially flat band at ($π$,0) can help enhance superconducting phase fluctuations. Finally, w…
We perform time resolved photoelectron spectroscopy measurements of optimally doped $\tn{Bi}_2\tn{Sr}_2\tn{CaCu}_2\tn{O}_{8+δ}$ (Bi-2212) and $\tn{Bi}_2\tn{Sr}_{2-x}\tn{La}_{x}\tn{Cu}\tn{O}_{6+δ}$ (Bi-2201). The electrons dynamics show that inelastic scattering by nodal quasiparticles decreases when the temperature is lowered below the critical value of the superconducting phase transition. This drop of electronic dissipation is astonishingly robust and survives to photoexcitation densities much larger than the value sustained by long-range superconductivity. The unconventional behaviour of qu…
On the theory of supermodulation of the superconducting order parameter created by structural supermodulation of apex distance in optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$
Georgi Nadjakov Institute of Solid State Physics, Bulgarian Academy of Sciences（保加利亚科学院格奥尔吉·纳贾科夫固体物理研究所）
The ferroelectric degenerate semiconductor Sn$_{1-δ}$Te exhibits superconductivity with critical temperatures, $T_c$, of up to 0.3 K for hole densities of order 10$^{21}$ cm$^{-3}$. When doped on the tin site with greater than $x_c$ $= 1.7(3)%$ indium atoms, however, superconductivity is observed up to 2 K, though the carrier density does not change significantly. We present specific heat data showing that a stronger pairing interaction is present for $x > x_c$ than for $x < x_c$. By examining the effect of In dopant atoms on both $T_c$ and the temperature of the ferroelectric structural phase…
The local density of states power spectrum of optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (BSCCO) has been interpreted in terms of quasiparticle interference peaks corresponding to an "octet'' of scattering wave vectors connecting k-points where the density of states is maximal. Until now, theoretical treatments have not been able to reproduce the experimentally observed weights and widths of these "octet'' peaks; in particular, the predominance of the dispersing "q$_1$'' peak parallel to the Cu-O bond directions has remained a mystery. In addition, such theories predict "background'' featur…
We study analytically the effects of inhomogeneous pairing interactions in short coherence length superconductors, using a spatially varying Bogoliubov-deGennes model. Within the Born approximation, it reproduces all of the standard Abrikosov-Gor'kov pairbreaking and gaplessness effects, even in the absence of actual magnetic impurities. For pairing disorder on a single site, the T-matrix gives rise to bound states within the BCS gap. Our results are compared with recent scanning tunneling microscopy measurements on Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ with Zn or Ni impurities.
We use the tomographic density of states (TDoS), which is a measure of the density of states for a single slice through the band structure of a solid, to study the temperature evolution of the superconducting gap in the cuprates. The TDoS provides unprecedented accuracy in determining both the superconducting pair-forming strength, $Δ$, and the pair-breaking rate, $Γ$. In both optimally- and under-doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$, we find the near-nodal $Δ$ smoothly evolves through the superconducting transition temperature - clear evidence for the existence of pre-formed pairs. Additionall…
We propose a model for high-Tc superconductors that includes both the spin fluctuations of the Cu++ magnetic ions and of the spins of O-- doped holes (spinons). The charge of the dopants (holons) is associated to quantum skyrmion excitations of the Cu++ spin background. The quantum skyrmion effective interaction potential is evaluated as a function of doping and temperature, indicating that Cooper pair formation is determined by the competition between these two types of spin fluctuations. The superconducting transition occurs when the effective potential allows for skyrmion bound states. Our …
We calculate the specific heat of a weakly interacting dilute system of bosons on a lattice and show that it is consistent with the measured electronic specific heat in the superconducting state of underdoped cuprates with boson concentration $ρ\sim x/2$, where $x$ is the hole (dopant) concentration. As usual, the $T^3$ term is due to Goldstone phonons. The zero-point energy, through its dependence on the condensate density $ρ_0(T)$, accounts for the anomalous $T$-linear term. These results support the split-pairing mechanism, in which spinons (pure spin) are paired at $T^*$ and holons (pure c…
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…
We consider 2D surface superconductivity in high magnetic fields parallel to the surface. We demonstrate that the spin-orbit interaction at the surface changes the properties of the inhomogeneous superconducting Larkin-Ovchinnikov-Fulde-Ferrell state that develops above fields given by the paramagnetic criterion. Strong spin-orbit interaction significantly broadens the range of existence of the LOFF phase, which takes the form of periodic superconducting stripes running along the field direction on the surface, leading to the anisotropy of its properties. In connection with experiments by J.H.…
Quantum confinement in a thin-film geometry offers viable routes for tuning the critical properties of superconductors through modification of both density of states and pairing interaction. Low-density systems like doped strontium titanate are especially susceptible to these confinement-induced effects. In this paper, we show that the superconducting critical temperature $T_c$ is enhanced through quantum confinement in SrTiO$_3$/SrTi$_{1-x}$Nb$_x$O$_3$/SrTiO$_3$ heterostructures at $x=1\%$ concentration, by measuring resistivity transitions and the Hall carrier density for different thickness…
Phase-sensitive evidence for pair density waves in a kagome superconductor
Southern University of Science and Technology（南方科技大学）；High Magnetic Field Laboratory of Chinese Academy of Sciences（中国科学院合肥物质科学研究院强磁场科学中心）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；Johns Hopkins University（约翰斯·霍普金斯大学）；The University of Tokyo（东京大学）；Peking University（北京大学）；Paul Scherrer Institute（保罗谢尔研究所）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Nanjing University（南京大学）；University of Wurzburg（维尔茨堡大学）；ETH Zürich（苏黎世联邦理工学院）
Emergency of superconductivity at the instabilities of antiferromagnetism (AFM), spin/charge density waves has been widely recognized in unconventional superconductors. In copper-oxide superconductors, spin fluctuations play a predominant role in electron pairing with electron dopants yet composite orders veil the nature of superconductivity for hole-doped family. However, in electron-doped ones the ending point of AFM is still in controversy for different probes or its sensitivity to oxygen content. Here, by carefully tuning the oxygen content, a systematic study of Hall signal and magnetores…
Explaining the mechanism of superconductivity in the high-$T_c$ cuprates requires an understanding of what causes electrons to form Cooper pairs. Pairing can be mediated by phonons, the screened Coulomb force, spin or charge fluctuations, excitons, or by a combination of these. An excitonic pairing mechanism has been postulated, but experimental evidence for coupling between conduction electrons and excitons in the cuprates is sporadic. Here we use resonant inelastic x-ray scattering (RIXS) to monitor the temperature dependence of the $\underline{d}d$ exciton spectrum of Bi$_2$Sr$_2$CaCu$_2$O$…
Within a gauge approach to the t-J model, we propose a new, non-BCS mechanism of superconductivity for underdoped cuprates. We implement the no-double occupancy constraint with a (semionic) slave-particle formalism. The dopant generates a vortex-like quantum distortion of the AF background centered on the empty sites, with opposite chirality for cores on the two Néel sublattices. Empty sites are described in terms of spinless fermionic holons and the long-range attraction between spin vortices on two opposite Néel sublattices is the holon pairing force, leading eventually to SC. The spin fluct…
The recent observation of an electronic cluster glass state composed of random domains with unidirectional modulation of charge density and/or spin density on Bi_{2}Sr_{2}CaCu_{2}O_{8+δ} reinvigorates the debate of existence of competing interactions and their importance in high temperature superconductivity. By using a variational approach, here we show that the presence of the cluster glass state is actually an inherent nature of the model based on the antiferromagnetic interaction (J) only, i.e. the well known t-J model. There is no need yet to introduce a competing interaction to understan…
