Charge pairing, superconducting transition and supersymmetry in high-temperature cuprate superconductors

Abstract

We propose a model for high-T${}_c$ superconductors, valid for $0\le \delta \le {\delta }_{SC}$, that includes both the spin fluctuations of the Cu${}^{++}$ magnetic ions and of the O${}^{--}$ doped holes. Spin-charge separation is taken into account with the charge of the doped holes being associated to quantum skyrmion excitations (holons) of the Cu${}^{++}$ spin background. The holon effective interaction potential is evaluated as a function of doping, indicating that Cooper pair formation is determined by the competition between the spin fluctuations of the Cu${}^{++}$ background and of spins of the O${}^{--}$ doped holes (spinons). The superconducting transition occurs when the spinon fluctuations dominate, thereby reversing the sign of the interaction. At this point ($\delta ={\delta }_{SC}$), the theory is supersymmetric at short distances and, as a consequence, the leading order results are not modified by radiative corrections. The critical doping parameter for the onset of superconductivity at T=0 is obtained and found to be a universal constant determined by the shape of the Fermi surface. Our theoretical values for ${\delta }_{SC}$ are in good agreement with the experiment for both LSCO and YBCO.

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References in corpus (1)

• Phase Structure and Universality in Two-Dimensional Disordered Quantum Antiferromagnets

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• Antiferromagnetic phase diagram of the cuprate superconductors
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