The influence of the atomic-scale inhomogeneities of the pairing interaction strength on the superconducting order parameter and the conductance spectra measurable by STM is studied in the framework of weak-coupling BCS-like theory for two-dimensional lattice model. First of all, it is found that the inhomogeneity having the form of atomic-scale regions of enhanced pair interaction increases the ratio of the local low-temperature gap in differential conductance spectra to the local temperature of vanishing the gap $2Δ_g/T_p$. Even in the framework of mean-field treatment this ratio is shown to be larger than the one corresponding to the homogeneous case. It is shown that the effect of thermal phase fluctuations of the superconducting order parameter can further increase this ratio. Taking them into account in the framework of a toy model we obtained the ratio $2Δ_g/T_p$ to be $\sim 7-8$. It is found that the additional atomic-scale hopping element disorder and weak potential scatterers, which can also take place in cuprate materials, have no considerable effect on the statistical properties of the system, including the distribution of the gaps, $T_p$ and the ratio $2Δ_g/T_p$. The second consequence of the atomic-scale order parameter inhomogeneity is the anticorrelation between the low-temperature gap and the high-temperature zero-bias conductance. The obtained results could bear a relation to recent STM measurements.
The atomically clean surface of the iron-based superconductor FeTe0.55Se0.45 is investigated by low-temperature STM with different tip apex states. By manipulating a single Fe atom onto the tip apex, signatures of the orbital nature of the subsurface Fe layer of FeTe0.55Se0.45 can be identified. By preparing a charged tip state, the intrinsic spatial inhomogeneity of the chemical potential of FeTe0.55Se0.45 can be revealed. As a result, three different types of vortex bound states originating from locally varying topological properties of the FeTe0.55Se0.45 surface are observed by scanning tun…
An attempt is made at reconciling the results of the prime experiments on the high temperature superconducting cuprates from Loram et al. and Davis et al. relating to electronic specific heat and to energy-resolved scanning tunnelling microscopy (STM), respectively, over the question of electronic inhomogeneity. I see the latter, at the appropriate level, as being essential to the evolution of HTSC in these materials, and try to bring into alignment the above key works, not only with each other, but with a wealth of related work. This is undertaken around a negative-U scenario long advocated b…
Recent scanning tunnelling microscopy (STM) studies on Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi-2212) revealed the presence of severe inhomogeneity with length scale $L_0 \approx ξ_0$, the coherence length. Other studies have been interpreted in terms of mesoscale or nanoscale phase segregation. Here we analyze heat capacity and NMR data on Bi-2212 and (Y,Ca)Ba$_2$Cu$_3$O$_{7-δ}$ and find no evidence for phase segregation or gross inhomogeneity. For Bi-2212 the coherence scale $L_0$ increases with doping from 5 to 17$ξ_0$ and the hole density inhomogeneity decreases from 0.028 to 0.005 holes/Cu. We c…
This paper seeks to synthesize much recent work on the HTSC materials around the latest STM results from Davis and coworkers. The conductance diffuse scattering results in particular are used as point of entry to discuss bosonic modes, both of condensed and uncondensed form. The bosonic mode picture is essential to understanding an ever growing range of observations within the HTSC field. The work is expounded within the context of the negative-U, boson-fermion modelling long advocated by the author. This general approach is presently seeing much theoretical development, into which I have look…
We discuss a wealth of data from various types of experiments which together suggest that the superconducting state of optimally to overdoped BSCCO-2212 can be well-described by the BCS theory with a d-wave gap together with small-angle scattering from out-of-plane defects. These include scanning tunnelling Fourier transform spectroscopy observation of nanoscale inhomogeneity in the local gap edge position, the narrowing of the antinodal ARPES spectrum when BSCCO becomes superconducting, as well as the behavior of the microwave and thermal conductivities. We suggest that the large amount of sm…
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 nanometer-scale gap inhomogeneity revealed by recent STM images of BSCCO surface suggests that the ``gap coherence length'' is of that order. Thus a robust pairing gap can develop despite the poorly screened Coulomb interaction. This can be taken as an evidence that the pairing in high $T_c$ materials occurs primarily in the neutral (spin) sector. We provide theoretical support for this point of view.
We present a detailed quantitative comparison between theoretical calculations of the local density of states and recent experimental measurements of scanning tunneling spectra around Ni impurities in BSCCO(2212). A double-peak structure on the hole side of the spectrum at the Ni site is identified as the spin-split van Hove singularity in the band structure. The Ni atom induces local changes in hopping matrix elements comparable in size to the induced on-site spin-dependent potential. We find evidence from the measurements of order parameter suppression in the vicinity of the Ni impurity. The…
We study the $τ_1$-impurity induced $\mathbf{q}$-space pattern of the energy derivative local density of states (LDOS) in a d-wave superconductor. We are motivated in part by the recent scanning tunneling microscopy (STM) observation of strong gap inhomogeneity with weak charge density variation in Bi$_{2}$Sr$_2$CaCu$_2$O$_{8+δ}$ (BSCCO). The hypothesis is that the gap inhomogeneity might be triggered by the disorder in pair potential. We focus on the effects of electron coupling to various bosonic modes, at the mode energy shifted by the d-wave superconducting gap. The pattern due to a highly…
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…
We report that four properties of cuprates and their evolution with doping are consequences of simply counting four-site plaquettes arising from doping: (1) the universal Tc phase diagram (superconductivity between \approx0.05 and \approx0.27 doping per CuO2 plane, and optimal Tc at \approx0.16), (2) the universal doping dependence of the room-temperature thermopower, (3) the superconducting neutron spin resonance peak (the "41 meV peak"), and (4) the dispersionless scanning tunneling conductance incommensurability. Properties (1), (3), and (4) are explained with no adjustable parameters, and …
Tunneling spectroscopy of epitaxial (110) Y1-xCaxBa2Cu3O7-d films reveals a doping dependent transition from pure d(x2-y2) to d(x2-y2)+is or d(x2-y2)+idxy order parameter. The subdominant (is or idxy) component manifests itself in a splitting of the zero bias conductance peak and the appearance of subgap structures. The splitting is seen in the overdoped samples, increases systematically with doping, and is found to be an inherent property of the overdoped films. It was observed in both local tunnel junctions, using scanning tunneling microscopy (STM), and in macroscopic planar junctions, for …
Comparison of recent experimental STM data with single-impurity and many-impurity Bogoliubov-de Gennes calculations strongly suggests that random out-of-plane dopant atoms in cuprates modulate the pair interaction locally. This type of disorder is crucial to understanding the nanoscale electronic structure inhomogeneity observed in BSCCO-2212, and can reproduce observed correlations between the positions of impurity atoms and various aspects of the local density of states such as the gap magnitude and the height of the coherence peaks. Our results imply that each dopant atom modulates the pair…
We derive the shape of the high-energy features due to a weakly coupled boson in cuprate superconductors, as seen experimentally in Bi_2 Sr_2 Ca_1 Cu_2 O_8+x (BSCCO) by Lee et al. [Nature (London) 442, 546 (2006)]. A simplified model is used of d-wave Bogoliubov quasiparticles coupled to Einstein oscillators with a momentum-independent electron-boson coupling and an analytic fitting form is derived, which allows us (a) to extract the boson mode's frequency and (b) to estimate the electron-boson coupling strength. We further calculate the maximum possible superconducting gap due to an Einstein …
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 Low-Temperature Phenomenology of Gap Inhomogeneity in the Cuprate Superconductors: High-Energy Granularity, Low-Energy Homogeneity, and Spectral Kinks
Bulk FeSe is a special iron-based material in which superconductivity emerges inside a well-developed nematic phase. We present a microscopic model for this nematic superconducting state, which takes into account the mixing between $s-$wave and $d-$wave pairing channels and the changes in the orbital spectral weight promoted by the sign-changing nematic order parameter. We show that nematicity gives rise to a $\cos2θ$ variation of the pairing gap on the hole pocket that agrees with ARPES and STM data for experimentally-extracted Fermi surface parameters. We further argue that, in BCS theory, $…
Magnetic Quantum Criticality inside the Superconducting State Revealed by Penetration Depth Scaling with Local $T_{\mathrm c}$
Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory（斯坦福材料能源科学研究所，SLAC国家加速器实验室）；Geballe Laboratory for Advanced Materials, Stanford University（斯坦福大学先进材料格巴莱实验室）；College of Science, Ibaraki University（茨城大学理学院）；Research and Education Center for Atomic Sciences, Ibaraki University（茨城大学原子科学研究与教育中心）
