Programmable, Spontaneous Superlattice Memory in a Monolayer Topological Insulator

Abstract

Memory is a foundational concept across disciplines, from neurobiology and electronics to artificial intelligence and quantum gravity. In materials, memory effects typically arise from ferroic orders, such as ferroelectricity and ferromagnetism, where information is stored in charge or spin degrees of freedom. Here, we report a surprising discovery of a nonvolatile superlattice memory effect in monolayer TaIrTe4, a dual quantum spin Hall insulator, where information is encoded through sharply contrasting lattice periodicities. In particular, in a pristine monolayer, we observe the spontaneous emergence of a long-period superlattice that can be programmed ON and OFF in a nonvolatile manner by electrostatic tuning of low-energy electronic states. This switching toggles the system between two structural configurations with unit cell areas differing by nearly two orders of magnitude. Mechanistically, our results reveal two independent and distinct instabilities, one in the lattice and the other in the QSH electrons, which are coupled, leading to electrostatic control of lattice configurations with nonvolatile memory. This finding is enabled by combining linear and nonlinear transport measurements, Raman spectroscopy, and scanning tunneling microscopy, which probe complementary aspects of the underlying orders. Remarkably, this nonvolatile memory effect stabilizes a spontaneous superlattice with a periodicity on the few-nanometer scale that remains robust across a wide doping range, persists over days, and survives above 70 K. Combined with the QSH topology, this stability offers a promising route to nonvolatile memory control of topological flat bands and their filling enabled quantum states. Our preliminary data indeed show the emergence of new insulating states at fractional superlattice fillings, which can be clearly switched ON and OFF together with the superlattice.

Figures (16)

• Figure 1: Nonlinear Hall characterization of the dual QSH state in monolayer TaIrTe$_4$.a-c, Illustration of the (a) charge, (b) spin and (c) superlattice memories. d, Top view of the atomic lattice structure with a mirror plane $\mathcal{M}_{a}$, which permits a Berry curvature dipole $\mathbf{\Lambda}$ along $\hat{a}$. e, Calculated spectral weight projected along $k_\mathrm{a}$, showing QSH edge states within the bulk band gap and VHSs in the bulk conduction band. f, Calculated density of state (DOS) versus energy, where a large DOS is observed at the VHSs. g, The linear resistance $R_{xx}$ as a function of carrier density $n$ at $T=4$ K, where two resistance peaks are observed corresponding to the single-particle band gap ($n = 0$, CNP) and the correlated band gap ($n = n_e$), respectively. Inset shows the optical image of Device 1, scale bar, 5 $\mu$m. h, The second order ($2\omega$) nonlinear Hall voltage $V^{2\omega}_{baa}$ versus $n$, measured with an AC current $I^{\omega} = 1 \, \mu\mathrm{A}$ at $\omega = 17.777 \, \mathrm{Hz}$ and $T = 4 \, \mathrm{K}$. Large $V^{2\omega}_{baa}$ responses are observed near the CNP and $n_e$.
• Figure 1: Key characteristics of Berry curvature nonlinear Hall responses.a, Optical image of Device 1, scale bar, 5 $\mu$m. b-d, Characteristics of the nonlinear Hall response close to the CNP: (1) The longitudinal $V_{aaa}^{2\omega}$ is significantly smaller than $V_{baa}^{2\omega}$. Note that the two $V_{baa}^{2\omega}$ curves are measured from two parallel sets of Hall probes and exhibit highly consistent results. (2) Angular dependence of the nonlinear Hall response $V^{2\omega}$, consistent with the mirror symmetry $\mathcal{M}_\mathrm{a}$. Here, $\theta$ represents the angle between the crystal axis ($\hat{a}$ direction) and the injection current direction $I^\mathrm{\omega}$, as illustrated in panel a. (3) The scaling relationship between the nonlinear Hall conductivity $\sigma_{baa}^{2\omega}$ and the Drude conductivity $\sigma_{aa}$ is investigated. $\sigma_{baa}^{2\omega}$ can be obtained from: $\sigma_{baa}^{2\omega} \sim \frac{V_{baa}^{2\omega} \, l}{I_a^2 \, R_{aa}^3},$ where $I_a$ is the injected current along $\hat{a}$, $R_{aa}$ is the longitudinal resistance, and $l$ is the sample length, respectively. The observed linear relationship between $\sigma_{baa}^{2\omega}$ and $\sigma_{aa}$ indicates that $\sigma_{baa}^{2\omega}$ depends linearly on $\tau$, consistent with the Berry curvature-induced nonlinear Hall effect. e-g, Similar characteristics are observed close to $n = n_\mathrm{e}$. Notably, the angular dependence is interestingly sharper.
• Figure 2: Observation of a hidden state beyond the dual QSH state.a–b, Linear resistance $R_\mathrm{xx}$ as a function of carrier density $n$ and temperature $T$ during warm-up from 40 K. Resistance peaks are observed at the CNP and at $n_e$, corresponding to the single-particle and correlated QSH gaps, respectively. As the temperature increases from 4 K to 40 K, the correlated-gap peak shifts to lower carrier density; consequently, $n_e$ appears on the slightly right side of the resistance peak in this panel (Extended Data Fig. \ref{['gap_size']}a). c, Temperature dependence of $R_{xx}$ measured at fixed density $n = n_h$ ($R_{xx}|{n_h}$) during warm-up. d–e, Nonlinear Hall voltage $V_{baa}^{2\omega}$ measured simultaneously with the data in panel (b). f, Temperature dependence of $V_{baa}^{2\omega}$ measured simultaneously with the data in panel (c) at $n_h$ ($V_{baa}^{2\omega}|{n_h}$). The detection sensitivity of $V_{baa}^{2\omega}$—defined as the normalized jump across the transition—is 45%, compared to just 0.13% in $R_{xx}$, highlighting the enhanced sensitivity of nonlinear Hall measurements in revealing the hidden state. Additional data and analysis are presented in Extended Data Figs. \ref{['Temperature_hysteresis']}--\ref{['gap_size']}.
• Figure 2: Temperature dependence of nonlinear Hall and linear resistance responses at $n_h$ and $n_e$.a, Temperature dependence of $V^{2\omega}_{baa}$ at $n_h$. The cooldown measurement is not straightforward because, to trigger the $n_h$ response during cooling, the carrier density must first be tuned to $n_e$ or above. The corresponding measurement protocol and raw data are shown in Extended Data Fig. \ref{['Cooling+scan_phase']}d (left). The warm-up measurement is more straightforward, as the system is prepared in the ON state and held at fixed $n_h$. b, Temperature dependence of $R_{xx}$, as the system is prepared in the ON state and held at fixed $n_h$. Inset shows a zoomed-in view of the resistance jump near $T \sim 76$ K. c-d, Temperature dependence of $V_{baa}^{2\omega}$ and $R_{xx}$ at $n_e$.
• Figure 3: Memory effect of the hidden state revealed by cooling-dependent protocols.a-c, Cooling process 1: The sample is cooled from 100 K to 50 K at a fixed doping level of $n_\mathrm{cool} = -10 \times 10^{12}$ cm$^{-2}$, followed by $V_{baa}^{2\omega}$ measurements at 50 K during both forward (yellow) and backward (green) doping scans. The signal $V_{baa}^{2\omega}|{n_h}$ remains negligible (OFF state) and shows no dependence on the perpendicular electric field $E$. d-f, Cooling process 2: Same as in (a) but with $n_\mathrm{cool} = +10 \times 10^{12}$ cm$^{-2}$. At 50 K, $V_{baa}^{2\omega}|{n_h}$ exhibits a strong response (ON state), again independent of $E$. g, Summary of $V_{baa}^{2\omega}|{n_h}$ responses at 50 K across multiple cooling cycles with varying $n_\mathrm{cool}$. A critical doping threshold, $n_\mathrm{cool} = n_e$, corresponding to the carrier density of the correlated QSH gap, is identified—above which the hidden state is activated. h, Both ON and OFF states of $V_{baa}^{2\omega}|{n_h}$ persist for several days, limited only by the duration of our measurement.