Real-Space Imaging of Moiré-Confined Excitons in Twisted Bilayer MoS$_2$

Abstract

Twisted two-dimensional semiconductors generate a moiré landscape that confines excitons (bound electron-hole pairs) into programmable lattices, offering routes to efficient light sources, sensing, and room-temperature information processing. However, direct real-space imaging of confined excitonic species within a moiré unit cell remains challenging; existing claims are inferred from spatially averaged far-field signals that are intrinsically insufficient to resolve nanometre-scale variations. Here, we imaged excitons across the moiré of a 2$^{\circ}$ twisted bilayer MoS$_2$ with nanometre resolution using room-temperature photocurrent atomic force microscopy. We directly resolved site-selective confinement: direct and indirect excitons localize at different stacking registries of the moiré, with contrast governed by alignment between site-selective generation and confinement minima. A Wannier-based moiré-exciton model reproduces the measured energies and the moiré-induced localization of the exciton wavefunction. These species-specific, unit-cell-resolved measurements constrain microscopic models of moiré excitons, provide benchmarks for excitonic order, and establish a device-compatible route to engineering excitonic lattices in van der Waals heterostructures.

Figures (8)

• Figure 1: Moiré lattice and photocurrent spectroscopy in twisted bilayer MoS$_2$.a, The rigid structural model of twisted bilayer MoS$_2$ labeling the three high-symmetry registries ($R_{M}^{M}$ and $R_{M}^{X}$ and $R_{X}^{M}$, marked with the corresponding colors). b, Optical microscopy image of our $\theta=2^{\circ}$ MoS$_2$ bilayer on hBN on mica sample. The different regions on the sample are marked: (1) mica, (2) hBN, (3) bottom MoS$_2$, (4) top MoS$_2$, (5) graphene contact. c, Large-area c-AFM image resolving a uniform hexagonal moiré lattice. d, Cross-sections acquired along the two lines in (c) showing the moiré periodicity $\lambda_{\mathrm{m}}\approx 9~\mathrm{nm}$ and the size of the different domains, with the bridges extended similarly to the nodes. e, Atomic-resolution c-AFM zoom showing the moiré lattice and the $1\times1$ MoS$_2$ lattice (see also inset for a zoom-in). The three high-symmetry sites ($R_{M}^{M}$ and two 3R sites) and the intersections (bridges) are marked in the image. f, FFT of the moiré marking all the relevant spots, consistent with $\alpha\approx 0.32~\mathrm{nm}$, $\lambda\approx 9~\mathrm{nm}$ and $\theta\approx2.0^{\circ}$. g, PPS of monolayer MoS$_2$ (orange) showing room-temperature A$_{1s}$ and B$_{1s}$ excitons at $1.87$ and $2.03~\mathrm{eV}$ (splitting $\sim160~\mathrm{meV}$). PPS (green) and SPI (blue) of the $2^{\circ}$ twisted bilayer exhibit A$_{1s}$/B$_{1s}$ peaks at $1.87$ and $2.02~\mathrm{eV}$ and additional structure near $2.2~\mathrm{eV}$ consistent with higher-order Rydberg states. h, Band-structure schematic indicating direct excitons (A$_{1s}$,B$_{1s}$) and indirect intralayer excitons ($\Gamma - K,\Lambda$). i, Registry-resolved SPI $\mathrm{PR}(E)$ spectra averaged over pixels assigned to each stacking. j, Zoom-in on the A$_{1s}$/B$_{1s}$ energy region showing strong enhancement at $R_{M}^{M}$ and suppression at 3R sites. k, Zoom-in on the indirect excitons showing the opposite site selectivity: enhanced $\Gamma- K$ ($\sim1.46~\mathrm{eV}$) and $i$ ($1.6\text{-}1.7~\mathrm{eV}$) features at 3R and strong suppression at $R_{M}^{M}$. All spectra are recorded at room temperature.
• Figure 1: pc-AFM setup and benchmarking.a, Schematic of the pc-AFM experiment combining c-AFM with monochromatic back-illumination. b,c, and d, PPS spectra of monolayer MoS$_2$, WS$_2$ and MoSe$_2$, respectively. e, PPS spectra of monolayer MoS$_2$ acquired with two different tips (Pt (Rocky Mountain nano 12pt400b) vs doped diamond), showing the spectral convolution by the larger tip (Pt). f, PPS spectra of monolayer MoS$_2$ acquired for different sample biases, no noticeable differences are observed in the spectra. g, The A$_{1s}$/B$_{1s}$ exciton energy positions as a function of MoS$_2$ thickness. h, PPS spectra on monolayer MoSe$_2$ acquired as a function of the tip-induced force.
• Figure 2: Real-space, registry-selective exciton confinement in the moiré superlattice.a, Dark current image resolving the moiré lattice, the arrows mark scan trajectories used for line spectroscopy. b,c$\mathrm{PR}(E)$ linespectroscopies along the blue and white paths in a, showing periodic enhancement of the direct A$_{1s}$ and B$_{1s}$ excitons and their Rydberg states near $2.2~\mathrm{eV}$ at $R_{M}^{M}$ nodes, and revealing features at $\sim1.46~\mathrm{eV}$ ($\Gamma- K$, interlayer) and $1.6\text{-}1.7~\mathrm{eV}$ ($i$, intralayer) that localize at 3R domains and anticorrelate with the A$_{1s}$/B$_{1s}$ contrast. d, Energy-selected PR maps off resonance as well as at A$_{1s}$, B$_{1s}$, $\Gamma- K$, and $i$ transitions, demonstrating registry-locked localization and small site-dependent energy shifts.
• Figure 2: Reproducibility of registry-resolved photoresponse.a-d, Additional SPI data acquired at different sample locations showing the same registry-selective confinement of A$_{1s}$/B$_{1s}$ and indirect excitons as in the main text (blue marks spectra corresponding to the $R_{M}^{M}$ sites and red to 3R sites. e, PR(E) maps acquired away from the neutral excitons and at the energies of the A$_{1s}$ and B$_{1s}$ excitons, revealing the moiré modulation, in another location of the sample. f, Averaged ln(I)-V spectrum acquired on the twisted bilayer MoS$_2$ and fitted both polarities with the thermionic-emission model. g, Current images extracted from grid I-V measurements on the moiré. h, Maps of the calculated (effective) Schottky barrier heights for both the positive and negative polarity based on the thermionic emission model used to fit the curve in panel f, demonstrating a barrier homogeneity. i, Effective barrier height as a function of photon energy, showing a slight but spatially uniform increase.
• Figure 3: Exciton bandstructure and wavefunction localization. $K-K$ Exciton moiré band structure of twisted bilayer MoS$_2$. Band structure for a, uncoupled and b, coupled $2^\circ$ twisted MoS$_2$ bilayers. c, Excitonic wavefunction at the $\gamma$ point for the lowest-energy moiré band in b. The colormap indicates the exciton wavefunction magnitude.