Josephson coupling in the dissipative state of a thermally hysteretic μ -SQUID

Abstract

Micron-sized superconducting interference devices (µ-SQUIDs) based on constrictions optimized for minimizing thermal runaway are shown to exhibit voltage oscillations with applied magnetic flux despite their hysteretic behavior. We explain this remarkable feature by a significant supercurrent contribution surviving deep into the resistive state, due to efficient heat evacuation. A resistively shunted junction model, complemented by a thermal balance determining the amplitude of the critical current, describes well all experimental observations, including the flux modulation of the (dynamic) retrapping current and voltage by introducing a single dimensionless parameter. Thus hysteretic µ-SQUIDs can be operated in the voltage read-out mode with a faster response. The quantitative modeling of this regime incorporating both heating and phase dynamics paves the way for further optimization of µ-SQUIDs for nano-magnetism.

A Josephson junction based on a highly disordered superconductor/low-resistivity normal metal bilayer

“…To calculate the CPR we numerically solve Equation 1-Equation 3 and Equation 5 by using an iteration procedure with fixed δϕ. When self-consistency is achieved (we stop the calculations when the maximal relative change of Δ between consequent iterations is less than 10 −4 ) the Green's functions are used to calculate j s and the supercurrent per unit of width, I s : (9) We also compare the calculated CPR with the CPR of a 1D S'-S-S' system with a large ratio between the diffusion coefficients D S′ /D S ≫ 1 (the length of the superconductor S is equal to a). For these calculations we use a 1D Usadel equation.…”

“…The absence of hysteresis in the current-voltage characteristics is important for devices based on Josephson junctions. The hysteresis in Dayem bridge, variable-thickness, S'-S-S' or S-N-S junctions is mainly caused by the temperature rise in the weak-link region in the resistive state due to Joule heating and the formation of hot spots [7][8][9]. A relatively large gap Δ in superconducting banks plays an important role here because it prohibits heat dissipation from the S or the N link at low temperatures k B T < Δ and it leads to hysteresis even for S-N-S junctions of variable thickness [22].…”

“…S-c-S Josephson junctions (where "c" is a geometric constriction) have a small capacitance of the weak link and a high critical current (about the magnitude of the depairing current of a superconductor), which allows one to obtain high noise immunity. But due to large critical current and bad heat dissipation their IVCs are hysteretic due to Joule heating ( ) and the subsequent formation of a stable region with suppressed superconductivity (a so-called "hot spot") at I > I c [6][7][8][9]. At temperatures near the critical temperature T c the hysteresis is absent because of the low I c and, therefore, small dissipation, but this leads to a small voltage V c .…”

Accurate Determination of the Josephson Critical Current by Lock-In Measurements

“…The latter are particularly large in quantum devices, such as qubits, and require statistical determination of with a large number of measurements [ 2 , 5 , 6 , 7 ]. Fluctuations are significant, even for classical devices containing small JJs, such as sensors [ 8 ], nano-SQUIDs [ 9 , 10 , 11 , 12 , 13 ] and low-dissipation digital electronics [ 1 , 14 ], and for JJs used in fundamental studies of unconventional superconductors [ 15 , 16 , 17 ]. Second, dc measurements are strongly affected by the flicker noise.…”

Josephson junction based on highly disordered superconductor/low-resistive normal metal bilayer

“…Tunnel superconductor-insulator-superconductor (S-I-S) junctions is characterized by small critical current densities and hysteretic IVC (the latter is related with large capacitance of the insulator layer) which restricts their applicability. S-N-S and S-S'-S junctions (where N is a normal metal and S' is the geometric constriction or superconductor with smaller critical current) have small capacitance of the weak link but IV curves are hysteretic due to Joule dissipation [3,[5][6][7].…”