Unconventional superconductivity in ultrathin superconducting NbN films studied by scanning tunneling spectroscopy

Using scanning tunneling spectroscopy, we address the problem of the superconductor-insulator phase transition in homogeneously disordered ultrathin (2–15 nm) films of NbN. Samples thicker than 8 nm, for which the Ioffe-Regel parameter $k_{F}l\ge 5.6$, manifest a conventional superconductivity: a spatially homogeneous BCS-like gap, vanishing at the critical temperature, and a disordered vortex lattice in magnetic field. Upon thickness reduction, however, while $k_{F}l$ lowers, the STS reveals striking deviations from the BCS scenario, among which a progressive decrease of the coherence peak height and small spatial inhomogeneities. In addition, the gap below $T_C$ develops on a spectral background, which becomes more and more “V-shaped” approaching the localization. The thinnest film (2.16 nm), while not being exactly at the superconductor-insulator transition (SIT) ($T_C\approx 0.4T_C^{\mathrm{bulk}}$), showed unconventional signatures such as the vanishing of the coherence peaks and the absence of vortices. This behavior suggests a weakening of long-range phase coherence, when approaching the SIT in this quasi-2D limit.

Figure 1

(a) Square resistivity vs temperature dependence of the studied samples; the dashed line indicates $h/4e^2$ as the quantum resistance for pairs; $T_C$ decreases with film thickness [$T_C^{15\mathrm{nm}}=15.0$ K (not shown), $T_C^{8\mathrm{nm}}=14.5$ K, $T_C^{4\mathrm{nm}}=13.3$ K, $T_C^{2.33\mathrm{nm}}=9.4$ K, $T_C^{2.16\mathrm{nm}}=6.7$ K]. We defined $T_C$ by the temperature reached when the resistivity equals $10\%$ of its 40 K value. (b) Typical topographic STM image of the surface (15-nm-thick film, $T=4.2$ K, image size; $1\mu \text{m}\times 1\mu \text{m}$). (c) Evolution of the tunneling conductance spectra (thin black lines) with temperature; bottom thick blue line: BCS fit at 2.3 K. (d) $dI/dV$ conductance map at $V=0$ in magnetic field ($B=1$ T), revealing a disordered vortex lattice.

Figure 2

From left to right column: tunneling characteristics of 8-, 4-, and 2.33-nm-thick films. From top to bottom: the first row shows normalized STS conductance maps representing the color-coded spatial variations of the $dI/dV$ signal measured at $2.3$ K at the gap onset (for $V=1.7$, $1.7$, and $1.1$ mV); second row: normalized individual tunneling conductance spectra representative of the spatial variations observed among the local conductance spectra (red and blue curves) at $2.3$ K; the black curves show typical spectra measured at $4.0$ K in magnetic field ($B=1$, 1, and 2 T) at the vortex centers and outside the vortex (gray curves); third row: $dI/dV$ conductance maps at $V=0$ showing images of the vortex lattices at $4.0$ K (for $B=1$, $B=1$, and 2 T); fourth row: temperature evolution of the normalized $dI/dV\left(V\right)$ tunneling spectra (vertically shifted for clarity); the temperature is indicated below the corresponding spectra. Red (black) curves correspond to the SC (normal) state. The bottom thick blue lines are BCS $dI/dV$ calculations at the indicated temperature; an additional broadening parameter was needed to fit the data (see text).

Figure 3

Tunneling characteristics of the 2.16-nm-thick film at 2.3 K. Zero-bias STS conductance maps at (a) $B=0$ and (b) 3 T. Typical variations among the corresponding local spectra for (c) $B=0$ and (d) 3 T. (e) Evolution of the $dI/dV\left(V\right)$ spectra with temperature. The bottom thick blue line is a BCS calculation at 2.3 K with an additional broadening parameter (see text). (f) Zoom on $R\left(T\right)$ of the 2.16–8-nm films compared to their (g) temperature dependence of the zero-bias tunneling conductance $dI(V=0)/dV$.

Figure 4

Schematic view of the NbN thin films grown on sapphire substrate measured by STM. The figure emphasizes the fact that from one sapphire atomic terrace to another, the local thickness of the NbN film might slightly vary, leading to sensitive changes of the electronic properties observed in STS conductance maps [see Fig. 3a].

Figure 5

(a) Square resistance vs temperature dependence of a thick 17.5-nm film with $T_C^{17.5\mathrm{nm}}=15$ K, for different magnetic fields in the range 0–9 T. (b) Square resistivity vs temperature dependence of a thin 2.16-nm film with $T_C^{2.16\mathrm{nm}}=6.5$ K for different magnetic fields in the range 0–9 T.

Figure 6

Superconducting layer coupled to a normal layer in the framework of the McMillan model[29] for different values of the coupling parameter ${\Gamma }_N=1$, 10, and 50 meV, and assuming a ratio of 20 (a)–(c) and 0.82 (d)–(f) between the integrated density of states $\frac{N_S{d}_S}{N_N{d}_N}\approx 20$, where $N_S$ and $N_N$ are the density of states by unit volume in the superconducting and normal layers, respectively. Black: partial DOS in the superconducting layer. Blue: partial DOS in the proximity layer. Red: simulated tunneling conductance at $T=2.3$ K.

Figure 7

Dependence of $T_C/T_{C\text{-bulk}}$, the superconducting critical temperature normalized by the bulk one, as a function of their square resistance $R_{\mathrm{sq}}$ in the normal state at 40 K, for ultrathin NbN films. Squares: experimental data extracted from resistivity measurements; continuous line: fit by the Finkel'stein model (see text).