Protected 0-pi states in SIsFS junctions for Josephson memory and logic

We study the peculiarities in current-phase relations (CPR) of the SIsFS junction in the region of $0$ to $\pi $ transition. These CPR consist of two independent branches corresponding to $0-$ and $\pi-$ states of the contact. We have found that depending on the transparency of the SIs tunnel barrier the decrease of the s-layer thickness leads to transformation of the CPR shape going in the two possible ways: either one of the branches exists only in discrete intervals of the phase difference $\varphi$ or both branches are sinusoidal but differ in the magnitude of their critical currents. We demonstrate that the difference can be as large as $10\%$ under maintaining superconductivity in the s layer. An applicability of these phenomena for memory and logic application is discussed.