Ferroelectric Hysteresis in Superconducting Bilayers

Abstract

Recently, coexisting ferroelectricity and superconductivity were reported in bilayer T$_{\textrm{d}}$-MoTe$_2$ and twisted bilayer graphene. Importantly, it was observed that an applied displacement field switches the superconductivity with a ferroelectric hysteresis. Such direct coupling between the ferroelectricity and superconductivity offers promising pathways for developing low-power, non-volatile memory devices. However, the coupling mechanism between the ferroelectricity and superconductivity remains poorly understood. In this work, we demonstrate that in a superconducting bilayer, the hysteretic switching of superconductivity can arise from an interlayer pairing. By deriving the Landau Ginzburg free energy expansion for the interlayer pairing, we show that along the ferroelectric hysteresis loop, the hysteretic exceeding of the critical polarization $P_{\textrm{c}}$ that destroys the interlayer pairing leads to the hysteretic switching of superconductivity. The condition to have a ferroelectric hysteretic superconducting state is established to be $P_{\textrm{r}}<P_{\textrm{c}}<P_{\textrm{s}}$, where $P_{\textrm{r}}$ and $P_{\textrm{s}}$ denote the remanent and saturated polarization, respectively. Crucially, our scenario of interlayer pairing yields two predictions: (1) an enhancement of the upper critical displacement field with stronger interlayer coupling and (2) a pronounced, gate-tunable interlayer crossed Andreev reflection, both of which provide clear pathways for experimental verification.

Figures (3)

• Figure 1: Interplay between ferroelectric polarization and interlayer pairing. (a) At zero displacement field, the interlayer pairing coexists with the remanent electric polarization $P_{\textrm{r}}$ in bilayer T$_{\textrm{d}}$-MoTe$_2$. (b) Upon switching, the reversed ferroelectric polarization exceeds the critical polarization $P_{\textrm{c}}$ and abruptly destroys the interlayer pairing. (c) The electrostatic susceptibility $\chi_u$ in the superconducting regime with different interlayer couplings. Given $t\neq 0$, a finite $\chi_u$ at $T=0$ K enhances $u_{\textrm{c}}$ and stabilizes the interlayer pairing. (d) The $u$-$T$ phase diagram. The right $y$ axis shows the polarization $P$ corresponding to a given $u$ at $T=0.2T_{\textrm{c}0}$. The blue trajectory in the diagram manifests the ferroelectric switching of superconductivity: under an external displacement field at $T=0.2T_{\textrm{c}0}$, the polarization traces the ferroelectric hysteresis loop, and the hysteretic exceeding of $P_{\textrm{c}}$ leads to the hysteretic switching of superconductivity. Here, $T_{c0}$ denotes the critical temperature at $u=0$. The interlayer coupling is set to be $t=1.5\Delta_0$ with $\Delta_0$ being the pairing order parameter at $T=0$ and $u=0$.
• Figure 2: Hysteretic coupling between ferroelectricity and superconductivity. (a) Contour plot of the free energy density $f(P,\Delta)$ at zero displacement field ($E_z=0$). The global minimum of $f(P,\Delta)$ obtained at finite $P$ and $\Delta$ confirms the coexistence of ferroelectricity and superconductivity. (b) The ferroelectric hysteresis loop of the polarization $P$ under an external electric field $E_z$. The superconducting state, coexisting with the remanent polariation $P_r$ at $E_z=0$, is destroyed when $P$ abruptly exceeds $P_c$ at $|E_z|>E_{\textrm{c}}$. (c) The corresponding hysteresis of the superconducting order parameter $\Delta$. The switching of $\Delta$ between zero and a finite value directly manifests the resistance hysteresis that switches between finite and zero values. (d) Simulated temperature evolution of the coupled ferroelectricity and superconductivity. A dramatic increase in $T_c$ is observed as the ferroelectric polariation approaches reversal (indicated by arrows on top). Here $T_{\textrm{c},E_{\textrm{c}}}$ denotes the critical temperature just prior to the polarization reversal.
• Figure 3: Experimental implications of the interlayer pairing in a superconducting bilayer. (a) Schematics of the pressure-induced enhancement of the interlayer coupling, which further stabilizes the interlayer pairing. (b) The enhancement of the critical electrostatic potential energy $u_c$ with increasing the interlayer coupling $t$. (c) Schematic illustration of the interlayer crossed Andreev reflection at the normal metal-superconducting bilayer interface. Since an incoming electron in the top layer is reflected as a hole in the bottom layer, the voltage drop in the bottom electrode is along the same direction as that in the electron-injecting top electrode. (d) The interlayer differential conductance spectra obtained from the bilayer BTK model. The differential conductance is normalized by the local resistance $R_{\textrm{N}}$ of the normal junction. The conductance $dI_{\textrm{b}}/dV_{\textrm{t}}$ decreases with increasing $u$ due to the suppression of interlayer pairing, and vanishes entirely in the case of intralayer pairing. Here, $V_{\textrm{t}\left(\textrm{b}\right)}$ and $I_{\textrm{t}\left(\textrm{b}\right)}$ denote the voltage and current measured in the top (bottom) electrodes, respectively. In the simulation, we take $Z=0.2$ and $t=4.5\Delta$.