Vertex corrections on the conductivity of high-Tc superconductors in the spin polaron formulation

This study investigates the vertex corrections of the optical conductivity in high-[Formula: see text] superconductors for hole-spin wave scattering in the superconducting state. The Feynman diagram technique is used to determine the mathematical expressions of the ladder diagrams in the calculation of the current–current correlation function. The sum of these vertex terms leads to a self-consistent form of the vertex function. By evaluating the frequency summation through contour integration, a general expression for the current–current correlation function is obtained, which allows us to determine the zeroth-order term and the first-order correction of the optical conductivity explicitly. Our findings for the dc conductivity in a clean superconductor indicate that the zeroth-order term is zero, a result attributed to the conservation of momentum and energy. Meanwhile, the first-vertex correction reveals the Drude behavior in the superconducting state at zero frequency.