Nodeless Bulk Superconductivity in the Time-Reversal Symmetry Breaking Bi/Ni Bilayer System

Epitaxial bilayer films of Bi(110) and Ni host a time-reversal symmetry breaking superconducting order with an unexpectedly high transition temperature $T_c=4.1\mathrm{K}$. Using time-domain THz spectroscopy, we measure the low energy electrodynamic response of a Bi/Ni bilayer thin film from 0.2 to 2 THz as a function of temperature and magnetic field. We analyze the data in the context of a Bardeen-Cooper-Schrieffer-like superconductor with a finite normal-state scattering rate. In a zero magnetic field, all states in the film become fully gapped, providing important constraints into possible pairing symmetries. Our data appear to rule out the odd-frequency pairing that is natural for many ferromagnetic-superconductor interfaces. By analyzing the magnetic field-dependent response in terms of a pair-breaking parameter, we determine that superconductivity develops over the entire bilayer sample which may point to the $p$-wave like nature of unconventional superconductivity.

Figure 1

(a) Real and (b) imaginary parts of the zero-field complex conductance of sample $A$ as a function of frequency from ($5\mathrm{K}>T_c$) to ($1.6\mathrm{K}\ll T_c$) with fits (dashed lines) to the data using Mattis-Bardeen theory for a BCS superconductor with a finite normal-state scattering rate. Inset: extracted temperature dependent energy gap with fit (solid line) to a BCS superconductor in the weak coupling limit. (c) Temperature dependent superfluid spectral weight, $S_{\delta }$. Red squares show the difference between the spectral weights of $G_1(\omega )$ at 5 K and various temperatures below $T_c$. Blue squares show $\underset{\omega \to 0}{\lim }\omega G_2$. The dashed line is the predicted superfluid spectral weight for a weakly coupled BCS superconductor. The error bars represent 2 standard deviations.

Figure 2

(a),(b) In-plane field dependent real $G_1(\omega )$ and imaginary part $G_2(\omega )$ (solid lines) of the complex conductance for Bi/Ni bilayer sample $B$ at 1.6 K with fits (dashed lines) modeled using Mattis-Bardeen theory for an effective spectroscopic gap, ${\mathrm{\Omega }}_G$. (c) Field dependence of pair-breaking parameter $\mathrm{\Gamma }$, determined from optical conductance along with fit $\mathrm{\Gamma }=b{H}^2$ (dashed line). Inset: the field dependence of ${\mathrm{\Omega }}_G$ (green dots) and pair-correlation gap ${\mathrm{\Delta }}_p$ (orange squares) for the Bi/Ni bilayer. The error bars represent the 95% confidence interval.

Figure 3

(a) Out-of-plane field dependent real part, $G_1(\omega )$, (solid lines) of the complex conductance for Bi/Ni bilayer sample $C$ at 1.6 K. The dashed lines are fits obtained by modeling the response within Maxwell-Garnett theory, with the Drude model for the normal component and Mattis-Bardeen theory with effective spectroscopic gap ${\mathrm{\Omega }}_G$ for the superconducting component. (b) Field dependent ${\mathrm{\Omega }}_G$ (blue dots) and the normal-volume fraction $f$ (green squares) with fit $f=H/H_{c2}$ (solid line). The dashed blue line is a guide to the eye. Horizontal and vertical dashed lines represent $f=1$ and $H_{c2}$, respectively. (c) Field dependent pair-breaking parameter $\mathrm{\Gamma }$ fit to $\mathrm{\Gamma }=bH$ (dashed line). The error bars represent the 95% confidence interval.