Quantum crossover in moderately damped epitaxial NbN/MgO/NbN junctions with low critical current density
Luigi Longobardi, D. Massarotti, G. Rotoli, D. Stornaiuolo, Gian Paolo Papari, Akira Kawakami, Giovanni Piero Pepe, Antonio Alci Barone, Francesco Tafuri
High quality epitaxial NbN/MgO/NbN Josephson junctions have been realized with MgO barriers up to a thickness of d = 1 nm. The junction properties coherently scale with the size of barrier, and low critical current densities down to 3 A/cm2 have been achieved for larger barriers. In this limit, junctions exhibit macroscopic quantum phenomena for temperatures lower than 90 mK. Measurements and junction parameters support the notion of a possible use of these devices for multiphoton quantum experiments, taking advantage of the fast non equilibrium electron-phonon relaxation times of NbN.
High quality epitaxial NbN/MgO/NbN Josephson junctions have been realized with MgO barriers up to a thickness of d = 1 nm. The junction properties coherently scale with the size of barrier, and low critical current densities down to 3 A/cm2 have been achieved for larger barriers. In this limit, junctions exhibit macroscopic quantum phenomena for temperatures lower than 90 mK. Measurements and junction parameters support the notion of a possible use of these devices for multiphoton quantum experiments, taking advantage of the fast non equilibrium electron-phonon relaxation times of NbN.
Superconducting qubit circuits require high quality low critical current density Josephson tunnel junctions. We have developed high quality epitaxial NbN/AlN/NbN tunnel junctions with critical current density, Jc, ranging from as low as a few A/cm2to a few tens of kA/cm2. In this work, we measured current-voltage characteristics for junctions with a Jc~ 32 A/cm2in the temperature range from 17 mK to above 6.7 K. All the junctions are in good quality and have a high gap voltage (>; 5.5 mV). We found that the junctions' sub-gap resistances were temperature dependent above 2.5 K and saturated at temperatures below 2.5 K. A junction sub-gap leakage current Irof about 23 pA was measured. The voltage noise power spectral density for 3 junctions with different sizes has been measured at the base temperature of 17 mK with the junctions biased above the gap voltage. The spectral densities clearly show 1/fbehavior at low frequency and are proportional to the junction's linear dimension.
Abstract In this work, we report the electrical properties of NbN internally shunted Josephson junctions with NbN x barriers. Cross-sectional scanning transmission electron microscopy analysis shows that all layers have the same cubic structure; NbN/NbN x /NbN trilayers were epitaxially grown on MgO substrates. The resistivity of the NbN x films could be varied in the range of 1–104 mΩ cm by controlling both the N2 partial pressure and the deposition time during reactive sputtering. The temperature dependence of the critical current density (J c) and characteristic voltage (I c R n) of the junctions with different barrier resistivities were measured for various barrier thicknesses. For the 10 nm-thick NbN x layer with resistivities of 73.44, 385.72, and 711 mΩ cm, the coherence length of the barrier was determined to be 5.55 ± 0.07, 4.88 ± 0.06, and 1.40 ± 0.13 nm, respectively, corresponding to carrier diffusion rates of 2.741 ± 0.004, 1.211 ± 0.002, and 0.008 ± 0.001 cm2 s−1, respectively. Thus, the reduction in barrier resistivity leads to a larger coherence length and a faster diffusion rate, which will further increase the J c and I c R n of the junction. By adjusting the barrier resistivity and thickness, the J c of the junction can be easily tuned over more than four orders of magnitude, and an I c R n value of 0.97 ± 0.07 mV was obtained at 10 K. The results indicate that the all-NbN self-shunt junction is a promising candidate in high-speed and high-temperature applications.
We report on measurements of the switching current probability both in the thermal and quantum regime on moderately damped NbN/MgO/NbN Josephson junctions with very low critical current density (’ 2A/cm2). We observed three distinct regimes: below 90 mK the width of the switching distributions is constant within the experimental error, while from 90 mK to 1.6 K the width increases with temperature, this change of behavior signaling the standard transition from macroscopic quantum tunneling (MQT) to thermal activation (TA) regime respectively. Above 1.6 K we find effects of anti-correlation between the bath temperature and thermal fluctuations since the width of the histograms starts to collapse, and indications of a transition to a third regime called Phase Diffusion (PD) are evident, such as the change of the switching distributions symmetry. Experimental data have been analyzed through numerical fitting of the switching probability and Monte Carlo simulations, and we found a good agreement with theoretical expectations based on multiple re-trapping processes, which strongly depend on the junction damping. The parameters which completely characterize the dynamics of such moderately damped Josephson junctions have been also extracted.
We have developed resistively shunted NbN junctions to realize superconducting single flux quantum circuits operating at 10 K and/or high speed. The junctions consist of epitaxial NbN/AlN/NbN tunnel junctions and molybdenum (Mo) resistors fabricated on single-crystal MgO substrates. The junction qualities are systematically investigated in a wide range of critical current density (Jc). The gap voltage and the ratio of Rsg/RN were about 5.6 mV and 11 for the junctions with the Jc of 10 kA/cm2, respectively. The overdamped Josephson junctions with parallel Mo resistors having a nominal sheet resistance showed non-hysteretic current-voltage characteristics for the junctions with Jc of 10 kA/cm2.
The topic of the PhD project is a comparative study of phase dynamics and macroscopic quantum phenomena in moderately damped NbN, YBaCuO grain boundary (GB) Josephson junctions (JJs) and hybrid devices. This type of research activity responds to the needs of better identifying phase dynamics in JJs in the moderately damped regime, which is going to be more and more common in hybrid nanostructures. Issues on a more detailed understanding of coherence, dissipation and noise in the various devices have a relevant role in the progress of quantum circuits.
In the last few years, studies of phase dynamics and macroscopic quantum phenomena have been extended to junctions composed of materials other than the traditional low critical temperature superconductors (LTS) and to novel types of structures with unconventional barriers composed for instance of graphene sheets or of grain boundaries. Progress in engineering new materials into junctions and in understanding and controlling the physics of interfaces may offer novel solutions for junctions of superior quality and complementary functionalities, and therefore may lead in the long run to improve also specific qubit performances.
For LTS JJs, once the barrier thickness and the critical current density (Jc) have been fixed, a reduction in its size unavoidably leads to a lowering of the critical current and determines a quite different phase dynamics re-normalized to the new scaling energy. Lower critical currents Ic result in lower Josephson energies EJ, and higher levels of dissipation are expected. The range of the energy dynamical parameters is significantly enlarged, and it is technologically easier to reproducibly realize nontrivial configurations. These devices are characterized by intermediate levels of dissipation (moderately damped regime) and by phase diffusion phenomena. The low Jc limit seems to be characteristic also of all futuristic nanohybrids devices incorporating nanowires, and the moderately damped regime (MDR) is intrinsically more common than it could be expected.
Measurements of switching current distribution (SCD) in these last years have turned to be standard tools to investigate phase dynamics in unconventional and hybrid systems and nanostructures. High critical temperature superconductors (HTS) are an example of unconventional systems, because of the d-wave order parameter symmetry and of the presence of low-energy quasiparticles, which are expected to induce high level of dissipation and as a consequence to spoil macroscopic quantum coherence. A comparative study in systems so different and complementary is of great interest.
During the PhD program, we have performed measurements of SCD, both in the thermal and quantum regime down to 20 mK, on moderately damped NbN/MgO/NbN JJs and on YBCO biepitaxial GB JJs. The NbN JJs exhibit a crossover from thermal activation (TA) to macroscopic quantum tunneling (MQT) regime at about 90 mK. After the MQT saturation, the width of the SCD follows the expected dependence in the TA regime. Deviations are evident in proximity and above the crossover temperature T* (about 1.6K) where we find effects of anti-correlation between the bath temperature and thermal fluctuations since the width of the histograms starts to collapse, and indications of a transition to a third regime called phase diffusion (PD) are evident, such as the change of the switching distributions symmetry.
Experimental data have been analyzed through numerical fitting of the switching probability and Monte Carlo simulations, and we found a good agreement with theoretical expectations based on multiple re-trapping processes, which strongly depend on the junction damping. The combined analysis of these three regimes allowed us to extract the fundamental parameters, which completely characterize the dynamics of such moderately damped NbN JJs. In addition, clear signatures of the PD regime have been detected and numerical methods have been developed to estimate the dissipation level in the MDR.
As a term of comparison, the studies on moderately damped systems have been also carried out on HTS junctions, which have different levels of intrinsic dissipation induced by low energy quasi-particles, and are for this reason of great impact as a reference.
In such JJs we have clearly observed a direct transition from the MQT to the PD regime. The width of the SCDs is constant below 100mK, which is a clearly indication of a quantum activation regime. Above 100mK the negative temperature derivative of the width is consistent with a diffusive motion due to multiple escape and re-trapping in the potential wells. Thermal behavior of the width has been fitted through numerical simulations, thus providing the estimate of the damping factor. These conclusions of a PD regime also in YBaCuO JJs are supported by data in presence of an externally applied magnetic field, and are consistent with the numerical outcomes.
Numerical simulations of the thermal behavior of the SCD width for different values of the quality factor ranging from 1 to 10 have been carried out. Such numerical simulations allow us to reconstruct a (Q, kBT/EJ) phase diagram summarizing the various activation regimes. The transition curve between the PD regime and the running state following thermal or quantum activation has been determined numerically by varying the damping factor Q as function of the ratio between the thermal energy and the Josephson energy. The result of the calculation is a universal curve. A phase diagram valid in a large range of dissipation conditions emerges as a functional guide to classify the switching behavior and to settle the fundamental junction parameters and energies in the MDR. It is therefore a reference for phase dynamics of novel types of junction and system for which the nature of the current induced transition from the superconducting to the normal state has not been completely clarified.
Abstract In this work, we present a detailed study of the electrical properties of stacked NbN/(TaN/NbN) N Josephson junctions. Cross-sectional scanning transmission electron microscopy analysis of the 5-stacked junction shows that the multilayer interface is very flat, each barrier has the same thickness, and the sidewalls of the junctions are nearly perpendicular to the substrate. Stacked junctions of different sizes and stacking numbers all have only one transition in their current–voltage curves. This indicates that the critical currents of the junctions in the stacked junctions are almost the same, showing the stability and repeatability of the multilayer fabrication and etching process. At 4.2 K, the 4-stacked junction shows excellent Josephson properties with characteristic voltage V c of 3.54 mV, which is about four times the 0.88 mV of the single junction. The temperature dependence of critical current density J c and V c of the stacked junction with N = 1, 2, 4 were measured, all of which can be fitted with dirty-limit theory. Stacked junctions with larger V c or more stacked layers can be achieved by optimizing electrode and barrier thickness, barrier resistivity, and thermal relaxation rate, etc.