Measurement of magnetic penetration depth and superconducting energy gap in very thin epitaxial NbN films

Abstract

Abstract:We report the evolution of the magnetic penetration depth (λ) and superconducting energy gap (∆) in epitaxial NbN films with thickness (d) varying between 51-3nm. With decrease in film thickness T c and ∆(0) monotonically decreases, whereas λ(0) monotonically increases. Our results show that while the values of ∆(0) and λ(0) are well described by BardeenCooper-Schrieffer (BCS) theory, at elevated temperatures, films with d≤6.5nm show sudden drop in superfluid density associated with the Kosterlitz-Thouless-Berezinski (KTB) transition.We discuss the implication of these results on the time response of superconducting bolometers made out of ultrathin NbN films. * films with d>20nm, the thickness was measured using a stylus profilometer while for thinner films it was estimated from the time of deposition. λ was measured using a "two coil" mutual inductance technique operating at 60kHz. The main advantage of this technique is that it allows measurement of the absolute value of λ over the entire temperature range up to T c without any prior assumption about the temperature dependence of λ. In this technique, a 8mm diameter thin superconducting film is sandwitched between a quadrupole primary coil and a dipole secondary coil ( figure 1(a)). This technique operates on the principle that the thin superconducting film will partially shield the secondary coil from the magnetic field produced by the primary, the degree of shielding being dependent on λ. The mutual inductance between the primary and the secondary coil is measured as a function of temperature by passing a small a.c. excitation current (1mA) through the primary and measuring the in-phase and out-of-phase induced voltage in the secondary using a lock-in amplifier. λ is determined by evaluating the mutual inductance for different values of λ by numerically solving the Maxwell equations and comparing the measured value with the theoretically calculated value 10 . The quadrupole configuration of the primary coil ensures a fast radial decay of the magnetic field such that edge effects are minimized 11 . The excitation field was kept very low (~7mOe) and the cryostat was shielded from the earth's magnetic field using a mu-metal shield. ∆(Τ) was measured using a home built low temperature scanning tunneling microscope (STM) on freshly prepared NbN films using Pt-Ir tip. The show the tunneling spectra at various temperatures. ∆ is extracted by fitting these spectra to the tunneling equation,where,is the lifetime broadened BCS density of states. While the broadening parameter, ( ), formally incorporated 12 to take into account the lifetime (τ) of the quasiparticle, phenomenologically incorporates all sources of non-thermal broadening in the BCS DOS. We observe that the temperature dependence of ∆(Τ) (Fig. 2(c)-closely follows the BCS curve 13 within experimental accuracy.Figure 3(a) shows the temperature variation of λ −2 (Τ)∝n s (T) (where n s is the superfluid density). λ increases from 275nm to 529nm as the thickness decreases from 51nm to 3nm. The val...

Kinetic inductance magnetometer

“…Assuming the nominal geometry of the superconducting strip (l ¼ 80 mm, w ¼ 5 mm and h ¼ 165 nm), one can determine the penetration depth l ¼ 1,100 nm for the NbN thin film. The value is somewhat larger than the zero-temperature magnetic penetration depth in the impure limit l 0 ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ' r=ðm 0 pDÞ p ¼ 710 AE 40 nm, where : ¼ h/(2p) is the reduced Planck constant, r ¼ 750 ± 90 mO cm the film resisitivity at room temperature and D ¼ 2.5 meV the gap energy at zero temperature for NbN 24 .…”

“…Using this combined with the relation of the intrinsic quality factor Q i ¼ n s /(n qp o 0 t qp ), where t qp is the quasiparticle thermalization time with a superconductor lattice, and the current dependency of Q i gives n qp /n s E0. 1 24). Although this is likely somewhat suppressed at the operating point, it will give a worst-case estimate for the noise.…”

Magnetoresistance, Gating and Proximity Effects in Ultrathin NbN-Bi2Se3 Bilayers

“…The gap-like feature appearing at about 70 meV, is a result of several weak-links connected in series between the voltage contacts. Assuming an energy gap ∆ of 2 meV for the NbN islands [27] yields 35 such weak-links in series. The dips in the conductance spectra of the inset are due to heating effects as a result of reaching the critical current in the weak-links connecting the NbN islands [28].…”

Quantitative assessment of pinning forces and magnetic penetration depth in NbN thin films from complementary magnetic force microscopy and transport measurements

“…The results of the same fit also provide a local probe for the temperature-dependent penetration depth, 23,24,26,27 in our case given by λ(T ) ≈ [w(T ) − z − δ]/1.27. The first temperature-independent parameter z λ is fixed during measurement and known, so it can be easily subtracted (Fig.…”

“…this work [25,26] c T / T [26] [25] The solid line is a fit to an empirical model with a single s-wave gap. 22 The value of λ(0) for our film thickness was obtained by an interpolation of the d-dependent literature data, 23,24 as shown in the inset. The solid grey line is an empirical fit.…”