Limitations of the current-phase relation measurements by an asymmetric dc-SQUID

Exotic quantum transport phenomena established in Josephson junctions (JJs) are reflected by a non-sinusoidal current-phase relation (CPR). The solidified approach to measure the CPR is via an asymmetric dc-SQUID with a reference JJ that has a high critical current. We probed this method by measuring CPRs of hybrid JJs based on a 3D topological insulator (TI) Bi$_2$Te$_2$Se with a nanobridge acting as a reference JJ. We captured both highly skewed and sinusoidal critical current oscillations within single devices which contradicts the uniqueness of the CPR. This implies that the widely used method provides inaccurate CPR measurement and leads to misinterpretation. It was shown that the accuracy of the CPR measurement is mediated by the asymmetry in derivatives of the CPRs but not in critical currents as was previously thought. We provided considerations for an accurate CPR measurement that encourage future experiments with reference CPRs different from those that were used before.