We report vortex matching phenomenon in rectangular antidot array fabricated on epitaxial NbN thin film. The antidot array was fabricated using Focussed Ion Beam milling technique. The magneto-transport measurements points to a period doubling transition at higher magnetic field for rectangular lattices. The results are discussed within the light of several models including the multi-vortex model, the matched lattice model and the super-matched lattice model.
We examine a building block for logic devices in which the positions of superconducting vortices in coupled elongated antidots provide the elementary logic states of 0 and 1. We show analytically and through simulation the maximum operating frequency of a pair of antidots as a function of antidot spacing and elongation. At finite temperatures, a signal can propagate through a series of identically shaped antidots with correctly chosen spacing, with an exponential distribution of switching times for the signal to move over by one antidot.
We experimentally investigate the vortex induced energy losses in niobium coplanar waveguide resonators with and without quasihexagonal arrays of nanoholes (antidots), where large-area antidot patterns have been fabricated using self-assembling microsphere lithography. We perform transmission spectroscopy experiments around 6.25 and 12.5 GHz in magnetic field cooling and zero field cooling procedures with perpendicular magnetic fields up to B=27 mT at a temperature T=4.2 K. We find that the introduction of antidot arrays into resonators reduces vortex induced losses by more than one order of m…
Using the non-linear Ginzburg-Landau (GL) theory, we obtain the possible vortex configurations in superconducting thin films containing a square lattice of antidots. The equilibrium structural phase diagram is constructed which gives the different ground-state vortex configurations as function of the size and periodicity of the antidots for a given effective GL parameter $κ^{*}$. Giant-vortex states, combination of giant- and multi-vortex states, as well as symmetry imposed vortex-antivortex states are found to be the ground state for particular geometrical parameters of the sample. The antido…
The use of artificial defects is known to enhance the superconducting critical parameters of thin films. In the case of conventional superconductors, regular arrays of submicron holes (antidots) substantially increase the critical temperature Tc(H) and critical current Ic(H) for all fields. Using electrical transport measurements, we study the effect of placing an additional small antidot in the unit cell of the array. This composite antidot lattice consists of two interpenetrating antidot square arrays with a different antidot size and the same lattice period. The smaller antidots are located…
We have measured the in-plane anisotropy of the vortex mobility in a thin Pb film with a square array of antidots. The Lorentz force, acting on the vortices, was rotated by adding two perpendicular currents and keeping the amplitude of the net current constant. One set of voltage probes was used to detect the vortex motion. We show that the pinning landscape provided by the square antidot lattice influences the vortex motion in two different ways. First, the modulus of the vortex velocity becomes angular dependent with a lower mobility along the diagonals of the pinning array. Second, the vort…
We report robust vortex matching effects in antidot arrays fabricated on thin films of NbN. The near absence of hysteresis between field sweep directions indicates a negligible residual pinning in the host thin film. Owing to the very small coherence length of NbN thin films ($ξ< 5 nm$), the observations suggests the possibility of probing physics of vortices at true nanometer length scales in suitably fabricated structures.
We present a quantitative comparison between the measurements of the complex conductance at low (kHz) and high (GHz) frequency in a thin superconducting film of NbN and the theoretical predictions of the dynamical Beresinksii-Kosterlitz-Thouless theory. While the data in the GHz regime can be well reproduced by extending the standard approach to the realistic case of an inhomogeneous sample, the low-frequency measurements present an anomalously large dissipative response around Tc. This anomaly can only be accounted for by assuming a strong slowing down of the vortex diffusion in the kHz regim…
We explore the dynamic response of vortex lines in a Pb thin film with a periodic array of antidots by means of ac-susceptibility measurements. For low drive field amplitudes, within the Campbell regime, vortex motion is of intra-valley type and the penetration depth is related to the curvature of the pinning potential well, $α$. For dc-fields below the first matching field $H_1$, $α$ reaches its highest value associated with a Mott Insulator-like phase where vortex lines are strongly localized at the pinning sites. For $H_1<H_{dc}<H_2$, the response is mainly due to the interstitial vortices …
In superconducting thin films, engineered lattice of antidots (holes) act as an array of columnar pinning sites for the vortices and thus lead to vortex matching phenomena at commensurate fields guided by the lattice spacing. The strength and nature of vortex pinning is determined by the geometrical characteristics of the antidot lattice (such as the lattice spacing $a_0$, antidot diameter $d$, lattice symmetry, orientation, etc) along with the characteristic length scales of the superconducting thin films, viz., the coherence length ($ξ$) and the penetration depth ($λ$). There are at least tw…
We report measurements of voltage noise due to vortex motion in Niobium, a conventional low-Tc superconductor. A coherent oscillation leading to narrow band noise (NBN) is evidenced. Its characteristic frequency is a linear function of the overcritical transport current in the flux-flow regime, and hence scales as the main velocity of the vortex flow. The associated length scale is not the intervortex distance but the width of the sample, indicating temporal coherence at a large scale. NBN is also observed in the non linear part of the V(I) at the onset of depinning, in apparent disagreement w…
Non-reciprocity in the critical current has been observed in a variety of superconducting systems and has been called the superconducting diode effect. The origin underlying the effect depends on the symmetry breaking mechanisms at play. We investigate superconducting micro bridges of NbN and also NbN/magnetic insulator (MI) hybrids. We observe a large diode efficiency of $\approx$~30\% when an out-of-plane magnetic field as small as 25~mT is applied. In both NbN and NbN/MI hybrid, we find that the diode effect vanishes when the magnetic field is parallel to the sample plane. Our observations …
We investigate vortex pinning in thin superconducting films with a square array of rectangular submicron holes ("antidots"). Two types of antidots are considered: antidots fully perforating the superconducting film, and "blind antidots", holes that perforate the film only up to a certain depth. In both systems, we observe a distinct anisotropy in the pinning properties, reflected in the critical current Ic, depending on the direction of the applied electrical current: parallel to the long side of the antidots or perpendicular to it. Although the mechanism responsible for the effect is very dif…
The dynamics of the annihilation of a vortex-antivortex pair is investigated. The pair is activated magnetically during the run of a simulated hysteresis loop on a square mesoscopic superconducting cylinder with an antidot inserted at its center. We study the nucleation of vortices and antivortices by first increasing the magnetic field, applied parallel to the axis of the sample, from zero until the first vortex is created. A further increase of the field pulls the vortex in, until it reaches the antidot. As the polarity of the field is reversed, an antivortex enters the scene, travels toward…
Novel behavior of the critical current density $j_{c}$ of a regularly perforated superconducting film is found, as a function of applied magnetic field $H$. Previously pronounced peaks of $j_{c}$ at matching fields were always found to decrease with increasing $H$. Here we found a {\it reversal of this behavior} for particular geometrical parameters of the antidot lattice and/or temperature. This new phenomenon is due to a strong ``caging'' of interstitial vortices between the pinned ones. We show that this vortex-vortex interaction can be further tailored by an appropriate choice of the super…
We present a detailed study of the transport properties of a superconducting Pb/Cu microdot with a 2x2 antidot cluster. The superconducting-normal (S/N) phase boundary, critical currents and current-voltage characteristics of this structure have been measured. The S/N phase boundary as a function of field B (T_c(B)) reveals an oscillatory structure caused by the limited number of possible vortex configurations which can be realized in these small clusters of pinning centres (antidots). We have analyzed the stability of these configurations and discussed the possible dissipation mechanisms usin…
The vortex ratchet effect has been studied in Al films patterned with square arrays of submicron antidots. We have investigated the transport properties of two sets of samples: (i) asymmetrical antidots where vortices are driven by an unbiased ac current, and (ii) symmetrical antidots where in addition to the ac drive a dc bias was used. For each sample, the rectified (dc) voltage is measured as a function of drive amplitude and frequency, magnetic field, and temperature. As unambiguously shown by our data, the voltage rectification in the asymmetric antidots is induced by the intrinsic asymme…
We report the observation of a pronounced dip in the in-plane field (H//) dependence of the critical current density Jc(H) and a peak in resistance R(H) of a NbN-HoNi5 bilayer at temperatures below the magnetic ordering temperature (TCurie ~ 5.5 K) of HoNi5, which is lower than the onset temperature (~ 9 K) of superconductivity in the NbN layer. The extrema in Jc(H) and R(H) appear at fields much below the upper critical field of NbN. It is suggested that the origin of this feature is linked with the non-collinear magnetization of HoNi5 whose normal component assists in depairing of Pearl vort…
Thin film heterostructures provide a powerful means to study the antagonism between superconductivity (SC) and ferromagnetism (FM). One interesting issue in FM-SC hybrids which defies the notion of antagonistic orders is the observation of magnetic field induced superconductivity (FIS). Here we show that in systems where the FM domains/islands produce spatial inhomogeneities of the SC order parameter, the FIS can derive significant contribution from different mobilities of the magnetic flux identified by two distinct critical states in the inhomogeneous superconductor. Our experiments on nanoe…
We analyze the occurrence of the Beresinkii-Kosterlitz-Thouless transition in thin films of NbN at various film thickness, by probing the effect of vortex fluctuations on the temperature dependence of the superfluid density below $T_{BKT}$ and of the resistivity above $T_{BKT}$. By direct comparison between the experimental data and the theory we show the crucial role played by the vortex-core energy in determining the characteristic signatures of the BKT physics, and we estimate its dependence on the disorder level. Our work provides a paradigmatic example of BKT physics in a quasi-two-dimens…
Theoretical proposals for spin ice analogs based on nanostructured superconductors have suggested larger flexibility for probing the effects of fluctuations and disorder than in the magnetic systems. In this work, we unveil the particularities of a vortex ice system by direct observation of the vortex distribution in a kagome lattice of paired antidots using scanning Hall probe microscopy. The theoretically suggested vortex ice distribution, lacking long range order, is observed at half matching field (H_{1}/2). Moreover, the vortex ice state formed by the pinned vortices is still preserved at…
We studied the conduction noise spectrum in the vortex state of a high-temperature superconductor, Bi2Sr2CaCu2Oy, subject to a uniform driving force. Two characteristic features, a broadband noise (BBN) and a narrow-band noise (NBN), were observed in the vortex-solid phase. The origin of the large BBN was determined to be plastic motion of the vortices, whereas the NBN was found to originate from the washboard modulation of the translational velocity of the driven vortices. We believe this to be the first observation of
We investigate anisotropy in the vortex pinning in thin superconducting films with a square array of rectangular submicron holes ("antidots"). The size of the antidots is chosen in such a way that it corresponds to a saturation number n_s=1, i.e. each antidot can trap at most one flux quantum. Therefore, interstitial vortices, appearing when the magnetic field exceeds the first matching field, are "caged" at the interstitial positions by the repulsion from the saturated antidots. We observe an overall higher critical current Ic(H) when it is measured parallel to the long side of the antidots t…
We report on a study of vortex pinning in nanoscale antidot defect arrays in the context of the London Theory. Using a wire network model, we discretize the array with a fine mesh, thereby providing a detailed treatment of pinning phenomena. The use of a fine grid has enabled us to examine both circular and elongated defects, patterned in the form of a rhombus. The latter display pinning characteristics superior to circular defects constructed with the similar area. We calculate pinning potentials for defects containing zero and single quanta, and we obtain a pinning phase diagram for the seco…
Computer modeling is reported about the creation and pinning of a magnetic vortex-antivortex (V-AV) pair in a superconducting thin film, due to the magnetic field of a vertical magnetic dipole above the film, and two antidot pins inside the film. For film thickness $= 0.1ξ$, $κ= 2$, and no pins, we find the film carries two V-AV pairs at steady state in the imposed flux range $2.10Φ_0 < Φ^+ < 3.0Φ_0$, and no pairs below. With two antidot pins suitably introduced into the film, a single V-AV pair can be stable in the film for $Φ^+ \ge 1.3Φ_0$. At pin separation $\ge 17ξ$, we find the V-AV pair …
In this article, we present evidence for the existence of vortex-solid/glass (VG) to vortex-fluid (VF) transition in a type-II superconductor (SC), NbN. We probed the VG to VF transition in both 2D and 3D films of NbN through studies of magnetoresistance and current-voltage characteristics. The dynamical exponents corresponding to this phase transition were extracted independently from the two sets of measurements. The $H$-$T$ phase diagram for the 2D and 3D SC are found to be significantly different near the critical point. In the case of 3D SC, the exponent values obtained from the two indep…
Moving vortex matter, driven by transport currents independent of time, in which vortices and anti-vortices coexist is investigated theoretically in thin superconducting films with nanostructured defects. A simple London model is proposed for the vortex dynamics in films with periodic arrays of nanomagnets or cylindrical holes (antidots). Common to these films is that vortex anti-vortex pairs may be created in the vicinity of the defects by relatively small transport currents, because it adds to the current generated by the defects - the nanomagnets screening current, or the antidots backflow …
We studied a thin superconducting NbN film in magnetic fields up to 8 T above the zero- temperature limit by means of time-domain terahertz and scanning tunneling spectroscopies in order to understand the vortex response. Scanning tunneling spectroscopy was used to determine the optical gap and the upper critical field of the sample. The obtained values were subsequently used to fit the terahertz complex conductivity spectra in the magnetic field in the Faraday geometry above the zero temperature limit. These spectra are best described in terms of the Coffey-Clem self-consistent solution of a …
The transport properties of Nb/CuMn multilayers with a regular array of electron beam lithography obtained antidots have been measured at different temperatures in the presence of external perpendicular magnetic fields. Hysteretical I-V characteristics have been observed which disappear when approaching the upper critical magnetic field curve H_{c2}(T). Comparing these data with other results (Arrhenius plots of resistive transition curves, logV-logI characteristics) we have been able to relate the onset of the hysteresis to the presence of an irreversibility line. We discuss several possible …
The operation of superconducting coplanar waveguide cavities, as used for circuit quantum electrodynamics and kinetic inductance detectors, in perpendicular magnetic fields normally leads to a reduction of the device performance due to energy dissipating Abrikosov vortices. We experimentally investigate the vortex induced energy losses in such Nb resonators with different spatial distributions of micropatterned pinning sites (antidots) by transmission spectroscopy measurements at 4.2 K. In comparison to resonators without antidots we find a significant reduction of vortex induced losses and th…
The influence of the spatial asymmetry of the pinning potential on the spectral composition of the voltage, induced in perforated superconducting Al bridges by the injection of a sinusoidal bias current, was investigated. The loss of the mirror symmetry of the pinning potential leads to the appearance of even Fourier components in the induced voltage in the vicinity of the superconducting phase transition line on the H-T diagram (H is the external magnetic field, T is temperature). Artificially-introduced asymmetry for vortex motion makes it possible to create low-resistive materials, in which…
The experimental investigation of the $I_c(B)$--$T_c(B)$ phase boundary of superconducting niobium films with large area quasihexagonal hole arrays is reported. The hole arrays were patterned with microsphere photolithography. We investigate the perforated niobium films by means of electrical directed current transport measurements close to the transition temperature $T_c$ in perpendicularly applied magnetic fields. We find pronounced modulations of the critcal current with applied magnetic field, which we interpret as a consequence of commensurable states between the Abrikosov vortex lattice …
Giant second-harmonic generation (SHG) in the terahertz (THz) frequency range is observed in a thin film of an s-wave superconductor NbN, where the time-reversal ($\mathcal{T}$-) and space-inversion ($\mathcal{P}$-) symmetries are simultaneously broken by supercurrent injection. We demonstrate that the phase of the second-harmonic (SH) signal flips when the direction of supercurrent is inverted, i.e., the signal is ascribed to the nonreciprocal response that occurs under broken $\mathcal{P}$- and $\mathcal{T}$-symmetries. The temperature dependence of the SH signal exhibits a sharp resonance, …
The work reported in my doctoral thesis is an experimental study of vortex dynamics and phase transitions in thin films of type II superconductors using scanning tunneling spectroscopy, low frequency ac susceptibility measurements and complimentary transport measurements. Chapter I and II cover basics of superconductivity and methodologies used in the thesis. Chapter III discusses the effect of periodic pinning centers on the geometry and dynamics of vortex lattice in NbN thin films. Consequent study of dynamic transition of vortex Mott-like to vortex metal-like state is described. In Chapter …
We have studied the dynamic response of Pb thin films with a square array of antidots by means of ac susceptibility chi(T,H) measurements. At low enough ac drive amplitudes h, vortices moving inside the pinning potential give rise to a frequency- and h-independent response together with a scarce dissipation. For higher amplitudes, the average distance travelled by vortices surpasses the pinning range and a critical state develops. We found that the boundary h*(H,T) between these regimes smoothly decreases as T increases whereas a step-like behavior is observed as a function of field. We demons…
We explore the flux-jump regime in type-II Pb thin films with a periodic array of antidots by means of magneto-optical measurements. A direct visualization of the magnetic flux distribution allows to identify a rich morphology of flux penetration patterns. We determine the phase boundary $H^*(T)$ between dendritic penetration at low temperatures and a smooth flux invasion at high temperatures and fields. For the whole range of fields and temperatures studied, guided vortex motion along the principal axes of the square pinning array is clearly observed. In particular, the branching process of t…
We present results from an extensive study of fluctuation phenomena in superconducting nanowires made from sputtered NbN. Nanoscale wires were fabricated in form of a meander and operated at a constant temperature T~0.4Tc(0). The superconducting state is driven close to the electronic phase transition by a high bias current near the critical one. Fluctuations of sufficient strength temporarily drive a section of the meander structure into the normal conducting state, which can be registered as a voltage pulse of nanosecond duration. We considered three different models (vortex-antivortex pairs…
dc and ac magnetic properties of two thin-walled superconducting Nb cylinders with a rectangular cross-section are reported. Magnetization curves and the ac response were studied on as-prepared and patterned samples in magnetic fields parallel to the cylinder axis. A row of micron-sized antidots (holes) was made in the film along the cylinder axis. Avalanche-like jumps of the magnetization are observed for both samples at low temperatures for magnetic fields not only above $H_{c1}$, but in fields lower than $H_{c1}$ in the vortex-free region. The positions of the jumps are not reproducible and…
We study experimentally the critical depinning current Ic versus applied magnetic field B in Nb thin films which contain 2D arrays of circular antidots placed on the nodes of quasiperiodic (QP) fivefold Penrose lattices. Close to the transition temperature Tc we observe matching of the vortex lattice with the QP pinning array, confirming essential features in the Ic(B) patterns as predicted by Misko et al. [Phys. Rev. Lett, vol.95, 177007 (2005)]. We find a significant enhancement in Ic(B) for QP pinning arrays in comparison to Ic in samples with randomly distributed antidots or no antidots.
We investigate the origin of matching effect observed in disordered superconducting NbN thin films with periodic array of holes. In addition to the periodic variation in the electrical resistance just above the superconducting transition temperature, Tc0, we find pronounced periodic variations with magnetic field in all dynamical quantities which can be influenced by flux-line motion under an external drive such as the magnetic shielding response and the critical current which survive in some samples down to temperatures as low as 0.09Tc0. In contrast, the superconducting energy gap, D which i…
Shapiro voltage steps at voltages V_n=nV_0 (n integer) have been observed in the voltage-current characteristics of a superconducting film with a square lattice of perforating microholes (antidots)in the presence of radiofrequent radiation. These equidistant steps appear at the second matching field H_2 when the flow of the interstitial vortex lattice in the periodic potential created by the antidots and the vortices trapped by them, is in phase with the applied rf frequency. Therefore, the observation of Shapiro steps clearly reveals the presence of mobile intersitial vortices in superconduct…
Occurrence of the Berezinskii-Kosterlitz-Thouless (BKT) transition is investigated by superfluid density measurements for two-dimensional (2D) disordered NbN films with disorder level very close to a superconductor-insulator transition (SIT). Our data show a robust BKT transition even near this 2D disorder-tuned quantum critical point (QCP). This observation is in direct contrast with previous data on deeply underdoped quasi-2D cuprates near the SIT. As our NbN films approach the QCP, the vortex-core energy, an important energy scale in the BKT transition, scales with the superconducting gap, …
The vortex-state electrodynamics of s-wave superconductors has been studied by infrared spectroscopy. Far-infrared transmission and reflection spectra of superconducting NbTiN and NbN thin films were measured in a magnetic field perpendicular to the film surface, and the optical conductivity was extracted. The data show clear reduction of superconducting signature. We consider the vortex state as a two-component effective medium of normal cores embedded in a BCS superconductor. The spectral features are well explained by the Maxwell-Garnett theory. Our analysis supports the presence of magneti…
We performed ac-susceptibility measurements to explore the vortex dynamics and the flux pinning properties of superconducting Pb films with an array of micro-holes (antidots) and non-fully perforated holes (blind holes). A lower ac-shielding together with a smaller extension of the linear regime for the lattice of blind holes indicates that these centers provide a weaker pinning potential than antidots. Moreover, we found that the maximum number of flux quanta trapped by a pinning site, i.e. the saturation number ns, is lower for the blind hole array.
The multilayer thin film structure of the superconductor has been proposed by A. Gurevich to enhance the maximum gradient of SRF cavities. The lower critical field Hc1 at which the vortex starts penetrating the superconducting material will be improved by coating Nb with thin film superconductor such as NbN. It is expected that the enhancement of Hc1 depends on the thickness of each layer. In order to determine the optimum thickness of each layer and to compare the measurement results with the theoretical prediction proposed by T. Kubo, we developed the Hc1 measurement system using the third h…
We investigate the nucleation of superconductivity in a uniform perpendicular magnetic field H in aluminum microsquares containing a few (2 and 4) submicron holes (antidots). The normal/superconducting phase boundary T_c(H) of these structures shows a quite different behavior in low and high fields. In the low magnetic field regime fluxoid quantization around each antidot leads to oscillations in T_c(H), expected from the specific sample geometry, and reminiscent of the network behavior. In high magnetic fields, the T_c(H) boundaries of the perforated and a reference non-perforated microsquare…
In a sandwich consisting of two superconducting films, one weakly pinning and one strongly pinning, the vortex positions in both films are determined by the strongly pinning material and the vortex lattice is disordered in both films. We used (strongly pinning) NbN and (weakly pinning) MoGe and studied, by directly imaging the vortex core positions with a scanning tunnelling microscope, how this disorder is restored with increasing thickness of MoGe layer or when the interface is made insulating. For clean interfaces we find that the first reordering of the vortex lattice is found at a layer t…
We study the transport of vortices excited by an ac current in an Al film with an array of nanoengineered asymmetric antidots. The vortex response to the ac current is investigated by detailed measurements of the voltage output as a function of ac current amplitude, magnetic field and temperature. The measurements revealed pronounced voltage rectification effects which are mainly characterized by the two critical depinning forces of the asymmetric potential. The shape of the net dc voltage as a function of the excitation amplitude indicates that our vortex ratchet behaves in a way very differe…
As a part of my doctoral thesis, I studied the effect of phase fluctuations in two dimensional (2D) and three dimensional (3D) superconducting films of conventional s-wave superconductor, NbN, by measuring the electrodynamics response through magnetic penetration depth at low frequency and the complex conductivity at microwave frequencies. We show that the phase transition in 2D or quasi-2D superconductors can be reconciled with the standard Berezinskii-Kosterlitz-Thouless (BKT) transition when the small vortex core energy is taken into consideration. In 3D NbN films, we show that in presence …
The dynamical response of the Abrikosov vortex lattice in the presence of an oscillating driving field is calculated by constructing an analytical solution of the time-dependent Ginzburg-Landau equation. The solution is steady-state, and work done by the input signal is dissipated through vortex cores, mainly by scattering with phonons. The response is nonlinear in the input signal, and is verified for consistency within the theory. The existence of well-defined parameters to control nonlinear effects is important for any practical application in electronics, and a normalised distance from the…
Using scanning tunneling spectroscopy (STS), we address the problem of the superconductor-insulator phase transition (SIT) in homogeneously disordered ultrathin (2-15 nm) films of NbN. Samples thicker than 8 nm, for which the Ioffe-Regel parameter $k_F l \geq 5.6$, manifest a conventional superconductivity : A spatially homogeneous BCS-like gap, vanishing at the critical temperature, and a vortex lattice in magnetic field. Upon thickness reduction, however, while $k_F l$ lowers, the STS revealed striking deviations from the BCS scenario, among which a progressive decrease of the coherence peak…
We show that under an a.c. magnetic field excitation the vortex lattice in a superconductor with periodic array of holes can undergo a transition from a Mott-like state where each vortex is localized in a hole, to a metal-like state where the vortices get delocalized. The vortex dynamics is studied through the magnetic shielding response which is measured using a low frequency two-coil mutual inductance technique on a disordered superconducting NbN film having periodic array of holes. We observe that the shielding response of the vortex state is strongly dependent on the amplitude of the a.c. …
The fabrication of high-quality thin superconducting films is essential for single-photon detectors. Their device performance is crucially affected by their material parameters, thus requiring reliable and nondestructive characterization methods after the fabrication and patterning processes. Important material parameters to know are the resistivity, superconducting transition temperature, relaxation time of quasiparticles, and uniformity of patterned wires. In this work, we characterize micro-patterned thin NbN films by using transport measurements in magnetic fields. We show that from the in…
