In the field of modern condensed matter physics, a significant and unresolved question over the past two decades has been the comprehension of dissipation in two-dimensional (2D) superconductors when subjected to external perturbations. Previous research efforts have primarily focused on investigating energy dissipation under the influence of a perpendicular magnetic field, using small current excitations. Unfortunately, the behavior of 2D superconductors under large current excitations remains largely unexplored.

The phenomenon of pair-breaking imposes an upper theoretical limit on the maximum current that a superconductor can sustain without experiencing dissipation [1]. However, in actual experimental conditions, finite dissipation always sets in at much lower current densities, well before reaching the pair-breaking limit. Understanding this discrepancy is not only crucial for addressing fundamental questions regarding the nature and origin of superconductivity but also holds great importance in realizing future applications such as superconducting digital memory, particle accelerator cavities, terahertz radiation sources, etc.

In one dimension, phase slip centers are the primary cause of dissipation [2]. In 2D, an additional complication arises due to a topological phase transition belonging to the Berezinskii Kosterlitz Thouless (BKT) universality class [3]. Below the BKT phase transition temperature (T_BKT), bound vortex-antivortex pairs are the bare topological excitations that become unbound above the T_BKT. Nonetheless, some bound pairs still exist even in the temperature range T_BKT ≤ T ≤T_C (T_C is superconducting transition temperature)  under zero electrical current. Application of current leads to a further increase in free vortex density due to unbinding of bound vortex-antivortex pairs. Subsequently, these free vortices begin to move due to the Magnus force induced by the applied current, becoming a significant source of dissipation. As the current continues to increase, these vortices can reach extremely high velocities. Although the existence of ultra-fast moving vortices has been demonstrated previously, what happens to these topological defects just before the system undergoes breakdown remains an enigma. 

In the context of bulk type II superconductors in the mixed state, Larkin and Ovchinnikov (LO) [4] had proposed that when a vortex core passes through a specific location (Fig. 1), the spectrum of quasiparticles undergoes a rapid transition from the superconducting (S) branch to the normal (N) branch. However, due to the finite inelastic scattering time, this switching process does not occur instantaneously. Consequently, at large vortex velocities, the normal vortex core exhibits more superconducting characteristics (S-like), compared to the equilibrium case where the vortex velocity is zero. This enhanced S-like quality of the vortex core can be visualized as an effective contraction of the vortex diameter leading to flux flow instability (FFI). When FFI occurs, the voltage drop across the sample increases abruptly, which can be measured through current-voltage (I-V ) characteristics measurements. Further, the voltage instability under the backward current sweep happens at a lower current than in the forward sweep leading to an anticlockwise hysteresis.

In this work, through extensive transport measurements and analysis, we successfully demonstrate that the newly discovered KTaO₃ (111) based interfacial superconductors could serve as an ideal platform for understanding dissipation mechanisms under large current drives. Fig. 2a shows one representative set of I-V curves taken in forward and backward sweeps at several fixed temperatures from 1.26 K to 10 K under zero magnetic field for a 7 nm AlO_x/KTaO₃ (111) sample which exhibits 2D interfacial superconductivity with T_C ∼ 1.55 K. While the features at low temperatures and low currents are well understood in context of BKT systems, the dissipation at large currents (especially before going to normal state) happens via discrete jumps followed by an anticlockwise hysteresis. Our comprehensive analysis of temperature and magnetic field data strongly suggests the presence of LO-type FFI in association with some Joule heating effects which becomes more dominant below the T_BKT. Most surprisingly. the nature of hysteresis changes completely from anticlockwise to clockwise above a certain temperature (highlighted by arrows in Fig. 2a). Such clockwise hysteresis is extremely rare [5] and has been never observed in any interfacial superconductors to the best of our knowledge. 

To visualize this drastic change in I-V hysteresis, we further plot the maximum width of hysteresis (δI_c) as a function of temperature for two samples (Fig. 2b and Fig. 2c). As clearly evident, hysteresis always changes its sign around the T_BKT and vanishes around T_C. Long back in 1995, Samoilov et. al. [5] had proposed that, once the superconductor is driven into the normal resistive state in the forward current sweep, the electron-electron (inelastic) scattering rate becomes higher. Within the framework of LO theory, it can be shown that such a phenomenon would move the I-V curve towards the higher current under the backward sweep, resulting in a clockwise hysteresis. Further, with increasing temperature, the evolution of hysteresis from anticlockwise to clockwise should be smooth as observed here. We also note that the vanishing of clockwise hysteresis near T_C is consistent with the fact that vortices do not exist above T_C.

Several recent studies, including those focused on magic-angle twisted bilayer graphene, MoS₂, and NbSe₂, have observed anomalies in high current I-V characteristics, which have been explained qualitatively in terms of vortex instability/phase-slip events. Our findings of FFI across the BKT phase transition could serve as a framework for comprehending dissipation in such a diverse class of 2D superconductors subjected to large currents. Further exploration of this highly non-equilibrium phenomenon in other systems that exhibit BKT transition, such as trapped atomic gases and neutral superfluids, would be of significant interest.

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