On the Evaluation of Higher Harmonic Current Responses in Disordered Superconductors

We discuss a formalism which allows for the calculation of a higher harmonic current response to an applied electric field for disordered superconducting systems described on the basis of tight-binding models. The theory is based on an expansion of the density matrix in powers of the field amplitudes where we solve the equation of motion for the individual components. This allows the evaluation of higher order response functions on significantly larger lattices than one can achieve with a previously used approach, which is based on a direct temporal integration of the equation of motion for the complete density matrix. In case of small lattices, where both methods can be applied by including also the contribution of collective modes, we demonstrate the agreement of the corresponding results.