Nernst effect and its thickness dependence in superconducting NbN films

TL;DR

This work analyzes the Nernst effect in granular NbN thin films (4–30 nm) across the superconducting transition to test Gaussian fluctuation theory. The authors combine resistivity and Nernst measurements, showing a linear $α_{xy}$ vs. reduced temperature but a thickness-dependent amplitude, which points to a 2+1D fluctuation regime where the c-axis length is capped by film thickness. They extract a thickness-dependent effective coherence length along the c-axis, $ξ_0^N≈2–3$ nm, and demonstrate that a finite thickness reconciles 2D temperature scaling with 3D amplitude. The Nernst signal evolves continuously across $T_c$, linking vortex transport below $T_c$ and short-lived Cooper-pair fluctuations above it, thus challenging strict separations between vortex and Gaussian fluctuation pictures and highlighting a nuanced dimensional crossover in thin-film superconductors.

Abstract

Superconducting thin films and layered crystals display a Nernst signal generated by short-lived Cooper pairs above their critical temperature. Several experimental studies have broadly verified the standard theory invoking Gaussian fluctuations of a two-dimensional superconducting order parameter. Here, we present a study of the Nernst effect in granular NbN thin films with a thickness varying from 4 to 30 nm, exceeding the short superconducting coherence length and putting the system in the three-dimensional limit. We find that the Nernst conductivity decreases linearly with reduced temperature ($α_{xy}\propto \frac{T-T_c}{T_c}$), but the amplitude of $α_{xy}$ scales with thickness. While the temperature dependence corresponds to what is expected in a 2D picture, scaling with thickness corresponds to a 3D picture. We argue that this behavior indicates a 2+1D situation, in which the relevant coherence length along the thickness of the film has no temperature dependence. We find no visible discontinuity in the temperature dependence of the Nernst conductivity across T$_c$. Explaining how the response of the superconducting vortices evolves to the one above the critical temperature of short-lived Cooper pairs emerges as a challenge to the theory.

Figures (7)

• Figure 1: Temperature dependence of the electrical resistivity of the five samples used in this study, in a semi-log plot. With decreasing thickness, the amplitude of normal state resistivity increases and the temperature dependence, a mild decrease with cooling due to weak localization becomes more pronounced. The inset shows the data in a linear plot near the superconducting transition. One can see that resistivity in thinner samples starts to decrease above the transition, as consequence of enhanced fluctuations.
• Figure 2: Temperature dependence of the electrical resistivity of the five samples in the presence of the magnetic field (a-e). Critical temperature decreases with increasing magnetic field. However, superconductivity is not fully suppressed by 12 T, our largest magnetic field. f) The variation of T$_c$ with magnetic field. The slope at low fields ($\le$4T) was used to determine the upper critical field at zero temperature, $H_{c2} (0)$, and the superconducting coherence length $\xi_0$.
• Figure 3: Experimental configurations for measuring the electric resistivity (a) and the Nernst signal (b). The temperature dependence of $N$ and $\rho$ in the 12.5 nm sample (c,e) and in the 20 nm sample (d, f). In both samples, at low temperature, when there is no resistivity, the Nernst signal is zero. It peaks during the transition and attains an amplitude of the order of the $\rm \mu V/K$ and then decreases but remains finite above the critical temperature. Note the non-monotonic variation of the amplitude of the Nernst peak with magnetic field in the 20 nm sample.
• Figure 4: The Nernst signal as a function of the magnetic field below (a-c) and above (d-f) the critical temperature in three samples with different thicknesses. The amplitude of $N$ decreases with increasing thickness. Note the warming-induced shift of the peaks in opposite directions below and above T$_c$.
• Figure 5: The Nernst coefficient, $\nu=N/B$ above the critical temperature plotted versus magnetic field for a) 4 nm b) 8 nm and c) 30 nm samples. At the low field limit, $\nu$ is constant and is solely set by the temperature. At 10 T, curves start to collapse on one another. A regime where $\nu$ is temperature independent and only set by the magnetic field starts to emerge.