Moiré pattern multiplicity driven by electronic effects in two-dimensional CrCl3/Au heterostructures

TL;DR

This work addresses the discrepancy between diffraction and STM observations of moiré patterns by examining CrCl3 on Au(111) for which several moiré orders coexist at fixed twist. The authors combine real-space STM topography, Fourier-space analysis, and energy-resolved dI/dV maps to reveal multiple moiré components whose spectral weight depends on electron energy, demonstrating an electronic rather than structural origin. They map the moiré patterns to specific Bragg-vector pairings and show that near-degenerate Bragg vectors can produce long-wavelength moiré modulations that are not evident in topography but emerge in reciprocal-space data. The findings imply that realistic moiré models should permit multiple concurrent periodicities, with important implications for electronic, magnetic, and possibly superconducting phenomena in van der Waals heterostructures.

Abstract

Moiré patterns are a central motif in van der Waals heterostructures arising from the superposition of two-dimensional (2D) incommensurate lattices. These patterns reveal a wealth of correlated effects, influencing electronic, magnetic, and structural phenomena. While diffraction techniques typically resolve multiple moiré wave-vectors corresponding to the incommensurate nature of the underlying lattices, Scanning Tunneling Microscopy (STM) often reveals only a dominant superperiod. In this work, we address this apparent discrepancy through an STM study of a twisted monolayer of CrCl3 on Au(111). We observe the coexistence of several moiré patterns at a fixed twist angle, whose relative intensity depends on the tunneling bias. Fourier analysis of STM data uncovers hidden higher-order moiré components not visible in STM topographic images, while spectroscopy maps reveal that the spectral weight of each pattern varies with electron energy. Our results establish that STM selectively probes on the same area distinct moiré modulations depending on electronic confinement, providing a unified framework that reconciles real space and reciprocal space observations of complex moiré superstructures.

Figures (4)

• Figure 1: STM topography of CrCl3 islands deposited on Au(111). (a) Large scale STM topography displaying the two types of CrCl3 islands: $\ch{CrCl3}^{\alpha}$ and $\ch{CrCl3}^{\beta}$. Their atomic lattices are twisted by 30 with respect to each other and their surfaces show two distinct moiré patterns. (b) STM topography of a $\ch{CrCl3}^{\beta}$ island, the moiré pattern has a periodicity of 1.6. Tunneling parameters: (a) $V = \qty{1.2}{\volt}$, $I = \qty{100}{\pico\ampere}$; (b) $V = \qty{1.4}{\volt}$, $I = \qty{100}{\pico\ampere}$.
• Figure 2: Analysis of multiple moiré patterns observed in CrCl3$^{\beta}$ islands. (a),(b) STM topographies of $\beta$ islands with atomic lattices rotated by 30 and 35 relative to the <1$\overline{1}$0>$_\text{Au}$ direction. Tunneling parameters: $V = \qty{1.5}{\volt}$, $I = \qty{100}{\pico\ampere}$. (c),(d) Corresponding Fourier transform images. (e),(f) Same FT images as in (c),(d), with highlighted Bragg spots: the CrCl3 spots are marked by red and black circles, while the moiré spots are located at the vertices of colored hexagons. (g),(h) Graphical constructions of the CrCl3 (violet) and Au (blue) reciprocal lattices for twist angles of 30 and 35. Colored arrows indicate the Bragg spot pairs responsible for the distinct moiré patterns.
• Figure 3: (a) STM topography of a $\ch{CrCl3}^{\beta}$ island twisted of approximately 32 relative to the <1$\overline{1}$0>$_\text{Au}$ direction, showing a weak, long-wavelength moiré modulation ($\sim$20) superimposed on the dominant $\sim$1.6 moiré pattern. Tunneling parameters: $V = \qty{1.2}{\volt}$, $I = \qty{100}{\pico\ampere}$. (b) Graphical construction of CrCl3 and Au reciprocal lattices. The Bragg spot pair generating the longer period moiré is circled in pink.
• Figure 4: (a) STM topography of 31 twisted $\ch{CrCl3}^{\beta}$ domain. Tunneling parameters: $V=\qty{1.8}{\volt}$, $I=\qty{200}{\pico\ampere}$. (b) Reciprocal lattice construction of CrCl3 and Au. (c),(e) FT of $\mathrm{d}I/ \mathrm{d}V$ map at .33, having distinct moiré components (green, red, pink). (d) Energy dependence of FT intensities extracted from the $\mathrm{d}I/ \mathrm{d}V$ maps for different moiré components.