Eliashberg theory prediction of critical currents in superconducting thin films under DC electric fields

TL;DR

This work addresses the microscopic mechanism by which DC electric fields suppress superconductivity in thin-film NbN and links it to the supercurrent–induced depairing through Eliashberg theory in the dirty limit. By solving coupled Eliashberg equations with a finite pair momentum and computing the resulting $J_s(T)$, the authors extract a critical kinetic energy $s_c$ at which depairing occurs and use it to predict the corresponding external field $E_{cr}$ via a simple phenomenological relation, $E_{cr}(T)=rac{2 s_c(T)}{e \, \xi_0(T)}$ (or $oldsymbol{\xi}$ for disorder), with an effective internal field profile $ar{E}$ accounting for screening. The model operates without adjustable parameters, once the electron-phonon spectral function $oldsymbol{ extalpha^{2}F(oldsymbol{oldOmega})}$ and the Coulomb pseudopotential $oldsymbol{ extmu^{*}(oldsymbol{ ildeoldsymbol{oldsymbolrequency_c})}}$ are specified and disorder is embedded via $oldsymbol{ extGamma^N}$; it reproduces the normal-state resistivity and matches experimental $E_{cr}$ trends. Key findings show that stronger disorder raises $E_{cr}$ and flattens the $J_c(T)$ dependence, while reducing disorder lowers the critical field and increases $J_c$, suggesting practical routes to minimize gating fields in superconducting electronics. The approach offers a framework to quantify gating effects and can be extended to multiband or unconventional order parameters in future work.

Abstract

Superconducting thin metallic films, functioning as supercurrent gate-tunable transistors, have considerable potential for future quantum electronic devices. Despite extensive research, a comprehensive microscopic quantitative mechanism that elucidates the control or suppression of supercurrents in thin films remains elusive. Focusing on NbN, a prototypical material, and starting from a phenomenological ansatz that links the critical electric field with the kinetic energy parameter needed to break Cooper pairs, we provide a quantitative analysis of the critical current using Eliashberg theory in the dirty limit without adjustable parameters. The critical kinetic energy value is identified, corresponding to the maximum supercurrent that can flow in the thin film. The peak in supercurrent density as a function of the Cooper pairs' kinetic energy arises from the interplay between the increase in supercurrent due to increased kinetic energy and the depairing effect when the kinetic energy becomes sufficiently large. The critical value of the pair's kinetic energy is subsequently employed to estimate the critical value of an external electric field required to suppress superconductivity in the sample. This estimation is in parameter-free agreement with the experimental observations. Although the disorder reduces the temperature dependence of the gating effect on the critical current, at the same time, it increases the unscreened critical electric field needed to suppress superconductivity. This enables the proposal of methods to control and reduce the critical field value necessary to suppress superconductivity in superconducting electronics.

Figures (6)

• Figure 1: (Color online) Schematic of the two equivalent physical systems, or protocols, studied in this paper. (a) The supercurrent travels inside the thin film. (b) An external electric field applied transverse to the thin film produces the same Cooper depairing effect as the supercurrent in panel (a).
• Figure 2: (Color online) The calculated density of supercurrent $J_s$ as a function of the parameter $s$ is shown for different temperatures. The maximum of $J_s$ corresponds to $J_c$ and identifies the critical value $s_c$carbiIc1. The "real case" (significant disorder) is shown in the upper panel, the "ideal case" (low disorder) is shown in the lower panel.
• Figure 3: (Color online) The calculated critical density of supercurrent $J_c$ as a function of temperature in the real case (red full circles) and ideal case (dark blue squares) case. The inset shows the electron-phonon Eliashberg spectral function $\alpha^{2}F(\Omega)$ of NbN.
• Figure 4: (Color online) The calculated critical field $E_{cr}(T)$ as a function of temperature in the real case, with significant disorder (red full circles) and the ideal case, with low disorder (dark blue circles).
• Figure 5: (Color online) Upper panel: The calculated density of supercurrent $J_s$ is linked to the electric field at $T=4.0$$K$ (filled black squares), $T=10.0$$K$ (filled red circles), and $T=12.5$$K$ (filled dark blue triangles). Lower panel: The calculated density of supercurrent $J_s$ is linked to the electric field at $T=4.0$$K$ (filled black squares), $T=10.0$$K$ (filled red circles), and $T=11.0$$K$ (filled dark blue triangles) in the ideal case.