Possible secondary component of the order parameter observed in London penetration depth measurements

Abstract

We discuss the effect of a secondary component of the superconducting order parameter on the superfluid density in the cuprates. If we assume a main ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ gap, the most stable realization of a mixed order parameter has a time-reversal breaking ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}+\ifmmode \imath \else \i \fi{}{d}_{xy}$ symmetry. In this state the nodes are removed and the temperature dependence of the superfluid density changes from the linear behavior of a pure $d$ wave to a more rounded shape at low temperature. The latter is compatible with the behavior experimentally observed in the in-plane magnetic field penetration depth of optimally doped ${\text{La}}_{2\ensuremath{-}x}{\text{Sr}}_{x}{\text{CuO}}_{2}$ and ${\text{YBa}}_{2}{\text{Cu}}_{3}{\text{O}}_{7\ensuremath{-}y}$.