Analytical results of the Fokker–Planck equation derived for one superconducting nanowire quantum interference device and for DC SQUIDs-asymmetric devices

The internal Shapiro effect in some portions of the parameter space of asymmetric two-junction SQUIDs and its influences

“…In general, the SSLSs in VCCs depend on various parameters and have various behaviors. In the large-loopinductance limit that we studied here, in contrast to the case for the small-loop-inductance limit [20,21], the effects of the applied magnetic flux mainly appear as a phase shift.…”

“…Here, we assume T = 77 K (any exception is specified), and for the applied flux values equivalent to ϕ x = 0 or ϕ x = π/2 (considering that V is π periodic) and for the other parameters, we assume values around practical values [19]. In contrast to the case for the small-inductance limit [20][21][22], in the large-inductance limit, α and R appear in simple forms as in equation (1). So, V e α/2 /R is independent of α and R. In [18], we inspected the voltage modulation and its interesting behavior due to the asymmetry of junctions and the presence of second harmonics.…”

The influences of the second harmonics together with the asymmetries of junctions on the voltage–current characteristics of high TC DC SQUIDs

“…According to our previous formulations [9,10], for DC SQUIDs with small inductances the presence of a second harmonic may give raise to the half-flux quantum periodicity of VFC and the reduction of modulation depth. In the present formulation as is seen from (46)-(48) the influence of inductance on the voltage modulation is factored out, so that below we consider the reduced voltage modulation exp(a/2)DV/R which depends on the q; I C1 ; c 1 , I C2 and c 2 .…”

“…Subsequently Greenberg extended his formulation for the asymmetric DC SQUIDs [7] (see also [8]). In a recent work, by defining the loop inductance for NQUID (nanowire superconducting quantum interference device) and by considering Sin Fourier series for the CPRs of its nanowires, we obtained analytical expressions for the characteristics of the symmetric [9] and asymmetric [10] two-junction devices. In spite of intensive theoretical studies [4][5][6][7][8] and computer simulations [11,12] that have been performed to investigate the dependences of high T C DC SQUID behaviors on various parameters, still a marked disagreement of the theoretical predictions and numerical simulations with experiment is observed.…”

“…For optimization the applicable SQUID characteristics or for developing the research methods based on SQUID characteristics, the exact analytic formulations for VCC and VFC which incorporate the mentioned facts are necessary. To arrive these needs extensive works have been done [4][5][6][7][8][9][10]. Usually one assumes the non-equilibrium phenomena are localized and takes a set of simple expressions for the superconducting current, the quasiparticle current and the fluctuating current and makes two coupled Langevin type equations for the DC SQUID.…”