Enhanced superconducting diode effects due to charging energy

Superconducting diode effect is the non-reciprocal phenomenon in inversion and time reversal-breaking systems. The non-reciprocal Josephson junctions give rise to a diode effect in the classical limit of zero charging energy. In particular, one can engineer a significant diode effect by including more and more harmonics in the current phase relationship. When a small but non-zero charging energy is introduced, it slightly smears the phase and reduces the harmonic amplitudes. In this context, we investigate Josephson junctions with multiple harmonics and including the charging energy. Our numerical calculations, considering up to the third harmonic, show that the inclusion of charging energy decreases the overall current amplitude. However, the rate of suppression is greater in the first half of the current cycle and less in the second half, thereby increasing the asymmetry. This increased asymmetry ultimately enhances the diode efficiency. This system, combining Josephson junctions and charging energy, has potential applications in designing circuits that integrate both classical and quantum computing on the same chip.