Voltage-flux-characteristics of asymmetric dc SQUIDs

We present a detailed analysis of voltage-flux V(Φ)-characteristics for asymmetric dc SQUIDs with various kinds of asymmetries. For finite asymmetry α_I in the critical currents of the two Josephson junctions, the minima in the V(Φ)-characteristics for bias currents of opposite polarity are shifted along the flux axis by ΔΦ = α_Iβ_L relative to each other; β_L is the screening parameter. This simple relation allows the determination of α_I in our experiments on YBa₂Cu₃O_7-δ dc SQUIDs and comparison with theory. Extensive numerical simulations within a wide range of β_L and noise parameter Γ reveal a systematic dependence of the transfer function V_Φ on α_I and α_R (junction resistance asymmetry). As for the symmetric dc SQUID, V_Φ factorizes into g(Γβ_L)·f(α_I,β_L), where now f also depends on α_I. For β_L≲5 we find mostly a decrease of V_Φ with increasing α_I, which however can only partially account for the frequently observed discrepancy in V_Φ between theory and experiment for high-T_c dc SQUIDs.