Zero-field superconducting diode effect induced by magnetic flux in a van der Waals superconductor trigonal PtBi$_2$

Abstract

The superconducting diode effect is one of the nonreciprocal transport phenomena, where the critical current depends on the current direction. This effect is typically realized in superconductors with broken spatial-inversion and time-reversal symmetry. To break the time-reversal symmetry, external magnetic fields are commonly used. Here, we demonstrate a sign-controllable superconducting diode effect under zero external magnetic field in a van der Waals superconductor trigonal PtBi$_2$. The sign of the zero-field superconducting diode effect is controlled by the poling magnetic field, that is a large magnetic field applied prior to measurements. This result indicates that trapped magnetic flux are responsible for breaking the time-reversal symmetry. Our findings highlight the crucial role of trapped magnetic flux in generating the superconducting diode effect and provide a general pathway for realizing a zero-field superconducting diode effect.

Figures (14)

• Figure 1: (a) Crystal structure of trigonal PtBi$_2$. (b) Crystal structure of trigonal PtBi$_2$ viewed along the $c$-axis. The black lines represent the mirror planes. (c) Temperature dependence of resistance measured with a typical device (device A; thickness $95~\mathrm{nm}$). The inset shows an optical microscope image of device A. (d) Polarization analysis of the SHG signal for device A. The red circles represent the experimental data, while the black solid line denotes the fitting result. The observed six-lobe pattern corresponds to the mirror plane orientations. The angle $0^{\circ}$ is defined along the current flow direction (see Appendix A for details).
• Figure 2: (a) Schematic illustration of the measurement configuration under an in-plane magnetic field. (b), (c) $I_{\text{dc}}$ dependence of $\text{d}V/\text{d}I$ at 0 mT and 50 mK for (b) $\mu_0 H_{\rm p} = 1$ T and (c) $\mu_0 H_{\rm p} = -1$ T. Red and blue curves are measured with positive and negative $I_{\text{dc}}$. (d), (e) $I_{\text{ac}}$ dependence of (d) $V^{1\omega}$ and (e) $V^{2\omega}$ at 0 mT and 50 mK. Red and blue curves represent data for $\mu_0 H_{\rm p} = 1$ T and $\mu_0 H_{\rm p} = -1$ T, respectively.
• Figure 3: (a), (b) In-plane magnetic field dependence of $I_{\text{c}}$ at 50 mK for (a) $\mu_0 H_{\rm p} = 1$ T and (b) $\mu_0 H_{\rm p} = -1$ T. Red and blue curves correspond to opposite $I_{\text{dc}}$ directions. (c), (d) In-plane magnetic field dependence of (c) $\Delta I_{\rm c}$ and (d) $R^{\rm 2\omega, peak}$ at 50 mK for $\mu_0 H_{\rm p} = 1$ T (red) and $\mu_0 H_{\rm p} = -1$ T (blue). (e), (f) $\text{d}V/\text{d}I$ as a function of $I_{\text{dc}}$ and $\mu_0 H$ at 50 mK, measured after applying (e) $\mu_0 H_{\rm p} = 1$ T and (f) $\mu_0 H_{\rm p} = -1$ T.
• Figure 4: (a) Schematic illustration of the measurement configuration under an in-plane magnetic field parallel to the current. (b), (c) $\Delta I_{\rm c}$ (b) and $R^{\rm 2\omega, peak}$ (c) at 50 mK for $\mu_0 H_{\rm p} = 1$ T (red) and $\mu_0 H_{\rm p} = -1$ T (blue) as a function of in-plane magnetic field parallel to the current. (d), (e) $\text{d}V/\text{d}I$ as a function of $I_{\text{dc}}$ and $\mu_0 H$ along the current direction, measured at 50 mK after applying (d) $\mu_0 H_{\rm p} = 1$ T and (e) $\mu_0 H_{\rm p} = -1$ T.
• Figure 5: (a) Schematic illustration of the measurement configuration under an out-of-plane magnetic field. (b)-(d) $\text{d}V/\text{d}I$ as a function of $I_{\text{dc}}$ under (b) $\mu_0 H = 1$, (c) 0, and (d) $-1$ mT at 50 mK. Red and blue curves correspond to opposite $I_{\text{dc}}$ directions, showing both increasing and decreasing processes of $I_{\text{dc}}$. (e) Out-of-plane magnetic field dependence of $I_{\rm c}$ at 50 mK. Red and blue curves are measured with positive and negative $I_{\text{dc}}$, respectively. (f) $\text{d}V/\text{d}I$ as a function of $I_{\text{dc}}$ and $\mu_0 H$ at 50 mK, with $H \parallel c$. (g), (h) $I_{\text{ac}}$ dependence of (f) $V^{1\omega}$ and (g) $V^{2\omega}$ at 50 mK. Red, green and blue curves represent data under 1 mT, 0 mT and $-1$ mT, respectively. (i) Out-of-plane magnetic field dependence of $R^{\rm 2\omega, peak}$ and $\Delta I_{\rm c}$ at 50 mK.