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Register a new userDoping and momentum dependence of coupling strength in cuprate superconductors
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Superconductivity is caused by the interaction between electrons by the exchange of collective bosonic excitations, however, this bosonic glue forming electron pairs is manifested itself by the coupling strength of the electrons to collective bosonic excitations. Here the doping and momentum dependence of the coupling strength of the electrons to spin excitations in cuprate superconductors is studied within the framework of the kinetic-energy-driven superconducting mechanism. The normal self-energy in the particle-hole channel and pairing self-energy in the particle-pariticle channel generated by the interaction between electrons by the exchange of spin excitation are employed to extract the coupling strengths of the electrons to spin excitations in the particle-hole and particle-particle channels, respectively. It is shown that below the superconducting transition temperature, both the coupling strengths in the particle-hole and particle-particle channels around the antinodes consist of two peaks, with a sharp low-energy peak located at around 5 meV in the optimally doped regime, and a broad band with a weak peak centered at around 40 meV. In particular, this two-peak structure in the coupling strength in the particle-hole channel can persist into the normal-state, while as a consequence of the d-wave type symmetry of the superconducting gap, the coupling strength in the particle-particle channel vanishes at the nodes. However, the positions of the peaks in the coupling strengths in the underdoped regime shift towards to higher energies with the increase of doping. More specifically, although the positions of the peaks in the coupling strengths move to lower energies from the antinode to the hot spot on the electron Fermi surface, the weights of the peaks decrease smoothly with the move of the momentum from the antinode to the hot spot, and fade away at the hot spots.
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The study of the electromagnetic response in cuprate superconductors plays a crucial role in the understanding of the essential physics of these materials. Here the doping dependence of the electromagnetic response in cuprate superconductors is studied within the kinetic-energy driven superconducting mechanism. The kernel of the response function is evaluated based on the linear response approximation for a purely transverse vector potential, and can be broken up into its diamagnetic and paramagnetic parts. In particular, this paramagnetic part exactly cancels the corresponding diamagnetic part in the normal-state, and then the Meissner effect is obtained within the entire superconducting phase. Following this kernel of the response function, the electromagnetic response calculation in terms of the specular reflection model qualitatively reproduces many of the striking features observed in the experiments. In particular, the local magnetic-field profile follows an exponential law, while the superfluid density exhibits the nonlinear temperature behavior at the lowest temperatures, followed by the linear temperature dependence extending over the most of the superconducting temperature range. Moreover, the maximal value of the superfluid density occurs at around the critical doping $delta_{rm critical}sim 0.16$, and then decreases in both lower doped and higher doped regimes. The theory also shows that the nonlinear temperature dependence of the superfluid density at the lowest temperatures can be attributed to the nonlocal effects induced by the d-wave gap nodes on the electron Fermi surface.
Scanning tunneling spectroscopy (STS) studies reveal long-range (~100 nm) spatial homogeneity in optimally and underdoped superconducting YBa_2Cu_3O_{7-delta} (YBCO) single crystals and thin films, and macroscopic spatial modulations in overdoped (Y_{0.7}Ca_{0.3})Ba_2Cu_3O_{7-delta} (Ca-YBCO) epitaxial films. In contrast, STS on an optimally doped YBa_2(Cu_{0.9934}Zn_{0.0026}Mg_{0.004})_3O_{6.9} single crystal exhibits strong spatial modulations and suppression of superconductivity over a microscopic scale near the Zn or Mg impurity sites, and the global pairing potential is also reduced relative to that of optimally doped YBCO, suggesting strong pair-breaking effects of the non-magnetic impurities. The spectral characteristics are consistent with d_{x^2-y^2} pairing symmetry for the optimally and underdoped YBCO, and with (d_{x^2-y^2}+s) for the overdoped Ca-YBCO. The doping-dependent pairing symmetry suggests interesting changes in the superconducting ground state, and is consistent with the presence of nodal quasiparticles for all doping levels. The maximum energy gap Delta_d is non-monotonic with the doping level, while the (2Delta_d/k_BT_c) ratio increases with decreasing doping. The similarities and contrasts between the spectra of YBCO and of Bi_2Sr_2CaCu_2O_{8+x} (Bi-2212) are discussed.
The low-energy quasiparticle excitations in hole- and electron-type cuprate superconductors are investigated via both experimental and theoretical means. It is found that the doping and momentum dependence of the empirical low-energy quasiparticle excitations is consistent with a scenario of coexisting competing orders and superconductivity in the ground state of the cuprates. This finding, based on zero-field quasiparticle spectra, is further corrobarated by the patially resolved vortex-state scanning tunneling spectroscopy, which reveals pseudogap-like features consistent with a remaining competing order inside the vortex core upon the suppression of superconductivity. The competing orders compatible with empirical observations include the charge-density wave and spin-density wave. In contrast, spectral characteristics derived from incorporating the $d$-density wave as a competing order appear unfavorable in comparison with experiments.
Starting from a spin-fermion model for the cuprate superconductors, we obtain an effective interaction for the charge carriers by integrating out the spin degrees of freedom. Our model predicts a quantum critical point for the superconducting interaction coupling, which sets up a threshold for the onset of superconductivity in the system. We show that the physical value of this coupling is below this threshold, thus explaining why there is no superconducting phase for the undoped system. Then, by including doping, we find a dome-shaped dependence of the critical temperature as charge carriers are added to the system, in agreement with the experimental phase diagram. The superconducting critical temperature is calculated without adjusting any free parameter and yields, at optimal doping $ T_c sim $ 45 K, which is comparable to the experimental data.
A model of charged hole-pair bosons, with long range Coulomb interactions and very weak interlayer coupling, is used to calculate the order parameter -Phi- of underdoped cuprates. Model parameters are extracted from experimental superfluid densities and plasma frequencies. The temperature dependence -Phi(T)- is characterized by a trapezoidal shape. At low temperatures, it declines slowly due to harmonic phase fluctuations which are suppressed by anisotropic plasma gaps. Above the single layer Berezinski-Kosterlitz-Thouless (BKT) temperature, Phi(T) falls rapidly toward the three dimensional transition temperature. The theoretical curves are compared to c-axis superfluid density data by H. Kitano et al., (J. Low Temp. Phys. 117, 1241 (1999)) and to the -transverse nodal velocity- measured by angular resolved photoemmission spectra on BSCCO samples by W.S. Lee et al., (Nature 450, 81 (2007)), and by A. Kanigel, et al., (Phys. Rev. Lett. 99, 157001 (2007)).
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