Dissipation processes in superconducting NbN nanostructures

In this paper, we present a comprehensive study of electrical transport measurements on a superconducting film of NbN (thickness, d ∼ 50 nm) and its nanostructures fabricated using Focused Ion Beam (FIB) in the form of one bridge (width, w ∼ 50 µm) and three meanders (w ∼ 500 nm, 250 nm, and 100 nm). The resistance (R) and current–voltage [V(I)] characteristics are measured as a function of temperature (2 K–16 K) and magnetic field (0 T–7 T). The photoresponse is measured under quasi-monochromatic light irradiation (wavelength of ∼800 nm). All our samples with w ≫ ξ and d > ξ are dimensionally on the borderline of the three-dimensional limit. However, the film and bridge samples show quasi-2D signatures of Brzezinski–Kosterlitz–Thouless transition in the R(T) and V(I) characteristics. On the other hand, our meander samples show two slope transitions in R(T) that seem to fit well with the thermally activated phase slip (TAPS) near the superconducting onset and quantum phase slip (QPS) at lower temperatures, expected in quasi-1D superconductors. The presence of TAPS and QPS in all the meander samples is further supported by several other observations at B = 0: (i) linear V(I) at lower excitation currents in the entire transition region; (ii) nonlinear and non-hysteretic V(I) at higher currents in the TAPS region; (iii) in the QPS region, at higher currents, the V(I) curves show a quadratic V ∝ I2 dependence before hysteretic and stepped jumps; and (iv) the switching current (IC*) reduces significantly to 5 μA–25 μA (T = 2 K) when compared to nearly ∼875 μA (T = 10.5 K) in the bridge sample. With the application and increase in the magnetic field, at fixed temperatures in the QPS region of the meander samples, the V(I) characteristics show a crossover to TAPS. This seems to be correlated with a drastic reduction in the activation barrier (Ub) extracted from the R(T,B) data. Typically, for B = 0 T–7 T, Ub varies from ∼3000 K–1200 K (film sample) to ∼1100 K–220 K (bridge sample) and ∼250 K–50 K, ∼150 K–20 K, and ∼50 K–6 K for the 500 nm, 250 nm, and 100 nm meander samples, respectively. Using the Langer, Ambegaokar, McCumber, and Halperin theory [J. S. Langer and V. Ambegaokar, Phys. Rev. 164(2), 498 (1967); D. E. McCumberand B. I. Halperin, Phys. Rev. B 1, 1054 (1970)] and considering the normal state transport properties reported earlier [Joshi et al., AIP Adv. 8, 055305 (2018)], these results are shown to be consistent with disorder induced nano-paths of ∼50 nm, ∼12 nm, ∼10 nm, and ∼7 nm width developed in the FIB fabricated bridge and 500 nm, 250 nm, and 100 nm meander samples, respectively.