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

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 $d_{x^2-y^2}$ gap, the most stable realization of a mixed order parameter has a time-reversal breaking $d_{x^2-y^2}+ \imath d_{xy}$ 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 $La_{2-x}Sr_xCuO_2$ and $YBa_2Cu_3O_{7-\delta}$.