We demonstrate control of the thermal hysteresis in superconducting constrictions by adding a resistive shunt. In order to prevent thermal relaxation oscillations, the shunt resistor is placed in close vicinity of the constriction, making the inductive current-switching time smaller than the thermal equilibration time. We investigate the current-voltage characteristics of the same constriction with and without the shunt-resistor. The widening of the hysteresis-free temperature range is explained on the basis of a simple model.
INTRODUCTIONA superconducting weak-link (WL), such as a constriction, between two bulk superconductors is of interest for its Josephson junction-like properties and subsequent application to micron size superconducting quantum interference devices (µ-SQUIDs) [1,2]. The latter can be used in probing magnetism at small scales [3][4][5][6]. Hysteresis present in current-voltage characteristics (IVCs) is a limiting factor in WL-based SQUIDs. In a hysteretic IVC when the current is ramped up from zero, the device typically switches to a non-zero voltage state at the critical current I c . The subsequent current ramp-down gives a switching to zero-voltage state at a smaller current, called re-trapping current I r . Hysteresis in IVCs is seen at low temperatures and disappears above a crossover temperature T h as I c and I r meet [7][8][9]. In a conventional tunnel-barrier type Josephson-junction, hysteresis arises from large junction capacitance and can be eliminated by adding a shunt-resistor in parallel to the junction [1,10]. The effect of the shunt resistor on nano-wire based WL devices was modeled recently using resistively and capacitively shunted junction (RCSJ) model with an effective capacitive time [11]. The hysteresis in similar devices is well understood using the thermal model [12]. The hysteresis in WLs is due to local Joule-heating [13,14], which gives rise to a self-sustained resistive hot-spot in the WL region, even below I c .Eliminating thermal hysteresis in WLs has been the subject of intense research in the past years. A normal metal shunt directly on top of the constriction [15][16][17] has been tried, but it affects both the superconductivity and thermal properties in a way that depends on the interface transparency. Using a bilayer with a superconductor (that can locally etched with a Focussed Ion Beam) covering a normal metal film allows one to obtain a WL that is also a good thermal bath [18]. A parallel shunt resistor far away from the WL [19] is more flexible approach, but it gives rise to relaxation oscillations due to large inductive time for switching of the current between the WL and the shunt. The performance of such SQUIDs with a distant shunt-resistor is eventually similar to that of the hysteretic ones [3,19]. A systematic study of the ability of a parallel shunt in preventing both the thermal runaway and hysteresis is thus highly desirable.The role of a shunt-resistor can be understood using a simple quasi-static thermal model discussed by Tinkham et al. [12...