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Register a new userJosephson Scanning Tunneling Spectroscopy in $d_{x^2-y^2}$-wave superconductors: a probe for the nature of the pseudo-gap in the cuprate superconductors
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Recent advances in the development of Josephson scanning tunneling spectroscopy (JSTS) have opened a new path for the exploration of unconventional superconductors. We demonstrate that the critical current, $I_c$, measured via JSTS, images the spatial form of the superconducting order parameter in $d_{x^2-y^2}$-wave superconductors around defects and in the Fulde-Ferrell-Larkin-Ovchinnikov state. Moreover, we show that $I_c$ probes the existence of phase-incoherent superconducting correlations in the pseudo-gap region of the cuprate superconductors, thus providing unprecedented insight into its elusive nature. These results provide the missing theoretical link between the experimentally measured $I_c$, and the spatial structure of the superconducting order parameter.
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Many cuprate superconductors possess an unusual charge-ordered phase that is characterized by an approximate $d_{x^2-y^2}$ intra-unit cell form factor and a finite modulation wavevector $bq^ast$. We study the effects impurities on this charge ordered phase via a single-band model in which bond order is the analogue of charge order in the cuprates. Impurities are assumed to be pointlike and are treated within the self-consistent t-matrix approximation (SCTMA). We show that suppression of bond order by impurities occurs through the local disruption of the $d_{x^2-y^2}$ form factor near individual impurities. Unlike $d$-wave superconductors, where the sensitivity of $T_c$ to impurities can be traced to a vanishing average of the $d_{x^2-y^2}$ order parameter over the Fermi surface, the response of bond order to impurities is dictated by a few Fermi surface hotspots. The bond order transition temperature $T_mathrm{bo}$ thus follows a different universal dependence on impurity concentration $n_i$ than does the superconducting $T_c$. In particular, $T_mathrm{bo}$ decreases more rapidly than $T_c$ with increasing $n_i$ when there is a nonzero Fermi surface curvature at the hotspots. Based on experimental evidence that the pseudogap is insensitive to Zn doping, we conclude that a direct connection between charge order and the pseudogap is unlikely. Furthermore, the enhancement of stripe correlations in the La-based cuprates by Zn doping is evidence that this charge order is also distinct from stripes.
The mysterious pseudo-gap (PG) phase of cuprate superconductors has been the subject of intense investigation over the last thirty years, but without a clear agreement about its origin. Owing to a recent observation in Raman spectroscopy, of a precursor in the charge channel, on top of the well known fact of a precursor in the superconducting channel, we present here a novel idea: the PG is formed through a Higgs mechanism, where two kinds of preformed pairs, in the particle-particle and particle-hole channels, become entangled through a freezing of their global phase. Remarkably, this entanglement is equivalent to fractionalizing a Cooper pair density wave (PDW) into its elementary parts; the particle-hole pair, giving rise to both density modulations and current modulations, and the particle-particle counterpart, leading to the formation of Cooper pairs. From this perspective, the fractionalized PDW becomes the central object around the formation of the pseudo-gap. The locking of phases between the charge and superconducting modes gives a unique explanation for the unusual global phase coherence of short-range charge modulations, observed below $T_{c}$ on phase sensitive scanning tunneling microscopy (STM). A simple microscopic model enables us to estimate the mean-field values of the precursor gaps in each channel and the PG energy scale, and to compare them to the values observed in Raman scattering spectroscopy. We also discuss the possibility of a multiplicity of orders in the PG phase and give an overview of the phase diagram.
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 similar conductance patterns have been seen around impurities and charge ordered states in systems with atomically quite different barrier layers. Here we use a recently developed Wannier function based method to calculate topographies, spectra, conductance maps and normalized conductance maps close to impurities. We find that it is the local planar Cu $d_{x^2-y^2}$ Wannier function, qualitatively similar for many systems, that controls the form of the tunneling spectrum and the spatial patterns near perturbations. We explain how, despite the fact that STM observables depend on the materials-specific details of the tunneling process and setup parameters, there is an overall universality in the qualitative features of conductance spectra. In particular, we discuss why STM results on Bi$_2$Sr$_2$CaCu$_2$O$_8$ and Ca$_{2-x}$Na$_x$CuO$_2$Cl$_2$ are essentially identical.
Quasiparticle tunneling spectra of both hole-doped (p-type) and electron-doped (n-type) cuprates are studied using a low-temperature scanning tunneling microscope. The results reveal that neither the pairing symmetry nor the pseudogap phenomenon is universal among all cuprates, and that the response of n-type cuprates to quantum impurities is drastically different from that of the p-type cuprates. The only ubiquitous features among all cuprates appear to be the strong electronic correlation and the nearest-neighbor antiferromagnetic Cu^{2+}-Cu^{2+} coupling in the CuO_2 planes.
The pairing state symmetry of the electron-doped cuprate superconductors is thought to be s-wave in nature, in contrast with their hole-doped counterparts which exhibit a d-wave symmetry. We re-examine this issue based on recent improvements in our electron-doped materials and our measurement techniques. We report microwave cavity perturbation measurements of the temperature dependence of the penetration depth of Pr_(2-x)Ce_(x)CuO_(4-y) and Nd_(2-x)Ce_(x)CuO_(4-y) crystals. Our data strongly suggest that the pairing symmetry in these materials is not s-wave.
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