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 dx2-y2 gap, the most stable realization of a mixed order parameter has a time-reversal breaking dx2-y2+?dxy 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 La2-xSrxCuO2 and YBa2Cu3O7-y.