Strong Spin–Charge Coupling and Its Manifestation in the Quasiparticle Structure, Cooper Instability, and Electromagnetic Properties of Cuprates

Abstract

The Fermi excitation spectrum, the problem of Cooper instability, and the Londons magnetic field penetration depth in cuprate superconductors are considered using the unified conception based on accounting for the strong coupling between the spin of copper ions and holes at oxygen ions. This coupling leads to strong renormalization of the primary spectrum of oxygen holes with the formation of spin-polaron quasiparticles. Analysis of Cooper instability performed using the spin-polaron concept for different channels has shown that only the superconducting d-wave pairing occurs in the ensemble of spin-polaron quasiparticles, and there are no solutions corresponding to the s-wave pairing. It has been demonstrated that the superconducting d-wave pairing is not suppressed by the Coulomb repulsion of holes located at neighboring oxygen ions. This effect is due to peculiarities in the crystallographic structure of the CuO₂ plane and the aforementioned strong spin–fermion coupling. As a result, such interaction of holes is omitted in the kernel of the integral equation for the superconducting order parameter with the d-wave symmetry. It has been shown the Hubbard repulsion of holes and their interaction for the second coordination sphere of the oxygen sublattice for actual intensities of the interaction do not suppress the d-wave type of superconductivity. For the spin-polaron ensemble, we have analyzed the dependence of the Londons magnetic field penetration depth on the temperature and hole concentration. It has been established that the peculiarities of this dependence are closely related to specific features of the spin-polaron spectrum.

APPENDIX

Functions $S_{{ij}}^{{(l)}}$(k, ω) appearing in the expressions for anomalous Green functions F_ij(k, ω) have the form

$$\begin{gathered} S_{{11}}^{{(1)}}(k,\omega ) = {{Q}_{{3y}}}(k, - \omega ){{Q}_{{3y}}}(k,\omega ), \\ S_{{11}}^{{(2)}}(k,\omega ) = S_{{21}}^{{(1)}}(k,\omega ) = {{Q}_{3}}(k, - \omega ){{Q}_{{3y}}}(k,\omega ), \\ S_{{11}}^{{(3)}}(k,\omega ) = S_{{12}}^{{(1)}}(k,\omega ) = S_{{11}}^{{(2)}}(k, - \omega ), \\ S_{{11}}^{{(4)}}(k,\omega ) = S_{{12}}^{{(2)}}(k,\omega ) \\ = S_{{21}}^{{(3)}}(k,\omega ) = S_{{22}}^{{(1)}}(k,\omega ) = {{Q}_{3}}(k, - \omega ){{Q}_{3}}(k,\omega ), \\ S_{{11}}^{{(5)}}(k,\omega ) = - {{Q}_{y}}(k, - \omega ){{Q}_{y}}(k,\omega ), \\ \end{gathered} $$

$$\begin{gathered} S_{{12}}^{{(3)}}(k,\omega ) = {{Q}_{{3y}}}(k, - \omega ){{Q}_{{3x}}}(k,\omega ), \\ S_{{21}}^{{(2)}}(k,\omega ) = S_{{12}}^{{(3)}}(k, - \omega ), \\ S_{{12}}^{{(4)}}(k,\omega ) = S_{{22}}^{{(3)}}(k,\omega ) = {{Q}_{3}}(k, - \omega ){{Q}_{{3x}}}(k,\omega ), \\ S_{{21}}^{{(4)}}(k,\omega ) = S_{{22}}^{{(2)}}(k,\omega ) = S_{{12}}^{{(4)}}(k, - \omega ), \\ \end{gathered} $$

$$\begin{gathered} S_{{12}}^{{(5)}}(k,\omega ) = - {{Q}_{y}}(k, - \omega ){{Q}_{x}}(k,\omega ), \\ S_{{21}}^{{(5)}}(k,\omega ) = S_{{12}}^{{(5)}}(k, - \omega ), \\ S_{{22}}^{{(4)}}(k,\omega ) = {{Q}_{{3x}}}(k, - \omega ){{Q}_{{3x}}}(k,\omega ), \\ S_{{22}}^{{(5)}}(k,\omega ) = - {{Q}_{x}}(k, - \omega ){{Q}_{x}}(k,\omega ), \\ \end{gathered} $$

((30))

$$\begin{gathered} S_{{31}}^{{(1)}}(k,\omega ) = - {{K}_{k}}{{Q}_{y}}(k, - \omega ){{Q}_{{3y}}}(k,\omega ), \\ S_{{31}}^{{(2)}}(k,\omega ) = - {{K}_{k}}{{Q}_{x}}(k, - \omega ){{Q}_{{3y}}}(k,\omega ), \\ S_{{31}}^{{(3)}}(k,\omega ) = S_{{32}}^{{(1)}}(k,\omega ) = - {{K}_{k}}{{Q}_{y}}(k, - \omega ){{Q}_{3}}(k,\omega ), \\ S_{{31}}^{{(4)}}(k,\omega ) = S_{{32}}^{{(2)}}(k,\omega ) = - {{K}_{k}}{{Q}_{x}}(k, - \omega ){{Q}_{3}}(k,\omega ), \\ \end{gathered} $$

$$\begin{gathered} S_{{31}}^{{(5)}}(k,\omega ) = {{Q}_{{xy}}}(k, - \omega ){{Q}_{y}}(k,\omega ), \\ S_{{32}}^{{(3)}}(k,\omega ) = - {{K}_{k}}{{Q}_{y}}(k, - \omega ){{Q}_{{3x}}}(k,\omega ), \\ S_{{32}}^{{(4)}}(k,\omega ) = - {{K}_{k}}{{Q}_{x}}(k, - \omega ){{Q}_{{3x}}}(k,\omega ), \\ S_{{32}}^{{(5)}}(k,\omega ) = {{Q}_{{xy}}}(k, - \omega ){{Q}_{{3x}}}(k,\omega ), \\ \end{gathered} $$

$$\begin{gathered} S_{{33}}^{{(1)}}(k,\omega ) = - K_{k}^{2}S_{{11}}^{{(5)}}(k,\omega ), \\ S_{{33}}^{{(2)}}(k,\omega ) = K_{k}^{2}S_{{12}}^{{(5)}}(k, - \omega ), \\ S_{{33}}^{{(3)}}(k,\omega ) = S_{{33}}^{{(2)}}(k, - \omega ), \\ S_{{33}}^{{(4)}}(k,\omega ) = K_{k}^{2}S_{{22}}^{{(5)}}(k,\omega ), \\ S_{{33}}^{{(5)}}(k,\omega ) = {{Q}_{{xy}}}(k, - \omega ){{Q}_{{xy}}}(k,\omega ). \\ \end{gathered} $$

These expression include functions

$${{Q}_{{x(y)}}}(k,\omega ) = (\omega - {{\xi }_{{x(y)}}}){{J}_{{y(x)}}} + {{t}_{k}}{{J}_{{x(y)}}},$$

$$\begin{gathered} {{Q}_{3}}(k,\omega ) = (\omega - {{\xi }_{L}}){{t}_{k}} + {{J}_{x}}{{J}_{y}}{{K}_{k}}, \\ {{Q}_{{3x(3y)}}}(k,\omega ) = (\omega - {{\xi }_{L}})(\omega - {{\xi }_{{x(y)}}}) - J_{{x(y)}}^{2}{{K}_{k}}, \\ \end{gathered} $$

((31))

$${{Q}_{{xy}}}(k,\omega ) = (\omega - {{\xi }_{x}})(\omega - {{\xi }_{y}}) - t_{k}^{2}.$$