Optical and transport properties of NbN thin films revisited

TL;DR

This work shows that quantum corrections to conductivity are essential to correctly describe the optical response of highly disordered NbN thin films. By extending the Drude-Lorentz model with a quantum-corrected conduction term and a Lorentzian inter-band component, the authors obtain a consistent set of electronic parameters that agree with transport measurements and ab initio calculations, including $\hbar\Gamma \approx 1.8~\mathrm{eV}$, $v_F \approx 0.7\times10^6~\mathrm{m\,s^{-1}}$, and $N(E_F)=2$ states/(eV·f.u.). The model explains the observed anti-Drude peak and the double ENZ behavior, and reconciles discrepancies between optical and transport studies, highlighting the significance of quantum corrections in disordered NbN. The findings reinforce the link between optical properties, diffusion, and electronic structure in NbN and provide a framework for consistent interpretation across experimental probes and theory.

Abstract

Highly disordered NbN thin films exhibit promising superconducting and optical properties. Despite extensive study, discrepancies in its basic electronic properties persist. Analysis of the optical conductivity of disordered ultra-thin NbN films, obtained from spectroscopic ellipsometry by standard Drude-Lorentz model, provides inconsistent parameters. We argue that this discrepancy arise from neglecting the presence of quantum corrections to conductivity in the IR range. To resolve this matter, we propose a modification to the Drude-Lorentz model, incorporating quantum corrections. The parameters obtained from the modified model are consistent not only with transport and superconducting measurements but also with ab initio calculations. The revisited values describing conduction electrons, which differ significantly from commonly adopted ones, are the electron relaxation rate $Γ\approx1.8~\textrm{eV}/\hbar$, the Fermi velocity $v_F \approx 0.7 \times 10^{6}~\textrm{ms}^{-1}$ and the electron density of states $N(E_F)=2~$states of both spins/eV/$V_{\textrm{f.u.}}$.

Figures (6)

• Figure 1: Open circles: Real and imaginary parts of the optical conductivity for NbN films of various thicknesses, determined by spectroscopic ellipsometry. Thin lines: Fits to Eq. (\ref{['eq:TheModel']}). Solid circles: Room-temperature DC conductivities measured using the van der Pauw method. a) Optical conductivity from visible-range SE measured shortly after deposition. b) Visible and mid-IR range SE data measured one year after deposition. The visible-range data alone are used in the fit.
• Figure 2: The real part of the dielectric function $\epsilon(\omega)$ corresponding to the conductivities in Fig. \ref{['fig:se']} a). The inset shows the lower plasma frequencies (frequencies at which $\epsilon(\omega)=0$) dependent on quantumness $\mathcal{Q}$. The solid line is a plot according to Eq. (\ref{['eq:wp2']})
• Figure 3: Magnetic field variation of the temperature-dependent sheet resistance $R_\square(T)$ for the 10 nm sample. Black lines are given by the maximal slope of $R_\square(T)$ curves and the temperature of the superconducting transition is determined by the intersect of the maximal slope line (black solid lines) and the zero resistance line (black dotted line).
• Figure 4: Temperature dependence of the upper critical field $B_{c2}$. The solid lines are linear fits to the $B_{c2}(T)$ data. The color-coding is same as in Fig. \ref{['fig:se']}. The inset shows a comparison of the diffusivity obtained from the slope of $B_{c2}(T)$ (green) and that estimated from the proposed optical model (blue).
• Figure 5: a) Prediction of Maxwell-Garnet theory for a metallic inclusion in a niobium oxide matrix for various volume fractions of the inclusion. b) Thin lines are the Drude-Smith model curves obtained as best fit to data from ellipsometry depicted by thick lines. Points at zero frequency are the measured DC conductivities.