[Paper Review] Pattern of indirect excitons in van der Waals heterostructure

Zhiwen Zhou, L. H. Fowler-Gerace+3 more|arXiv (Cornell University)|Feb 23, 2026

2D Materials and Applications0 citations

TL;DR

The authors observe a quasi-periodic triangular pattern of indirect excitons in a MoSe2/WSe2 heterostructure with a characteristic wavelength of ~2.6 μm, and discuss potential mechanisms behind this modulation.

ABSTRACT

We studied photoluminescence of spatially indirect excitons (IXs) in a MoSe$_2$/WSe$_2$ van der Waals heterostructure. We observed a quasi-periodic triangular pattern of IXs with the characteristic wavelength of the pattern $\sim$ 2.6 $μ$m.

Motivation & Objective

• Understand spatial modulation of indirect-exciton photoluminescence in MoSe2/WSe2 heterostructures.
• Characterize the pattern: wavelength, geometry, and robustness across density and temperature.
• Evaluate potential modulation mechanisms (Turing instability, attractive interactions, moiré effects, wrinkling).
• Relate exciton transport properties to observed luminescence patterns.
• Provide quantitative metrics to distinguish mechanisms (pattern wavelength, angle, coordination).

Proposed method

• Prepare MoSe2/WSe2 van der Waals heterostructure encapsulated in hBN with ~40 nm bottom and ~30 nm top layers.
• Maintain twist angle δθ = 1.1°, yielding a moiré period ≈ 17 nm.
• Excite with cw Ti:Sapphire laser at Eex = 1.689 eV, focused to ~2 μm spot.
• Collect indirect-exciton PL with an E ≤ 1.4 eV filter and 0.8 μm spatial-resolution CCD.
• Compute -ΔI(x,y) to highlight spatial modulation.
• Analyze local maxima via their positions to obtain wavelength (~2.6 μm), Fourier spectra, angular distributions (~60°), and Voronoi coordination.
• Examine density and temperature dependence of the pattern and IX transport as reported in related work.
• Compare observed pattern against various modulation mechanisms (Turing instability, attractive interactions, moiré and wrinkling).

Figure 1: IX pattern. (a) Schematic energy-band diagram for the heterostructure. The oval indicates an indirect exciton (IX) composed of an electron ( $-$ ) and a hole ( $+$ ). (b) A microscope image showing the layers of the heterostructure. Scale bar is 10 $\mu$ m. The red, green, cyan, and orange

Experimental results

Research questions

• RQ1 What is the characteristic wavelength and geometry of the indirect-exciton luminescence modulation in the MoSe2/WSe2 heterostructure?
• RQ2 Does the observed modulation originate from Turing-like quantum-degeneracy instabilities, interlayer interactions, moiré potentials, or mechanical wrinkling?
• RQ3 How do pattern features (wavelength, angle, coordination) vary with exciton density and temperature?
• RQ4 Is the modulation consistent with moiré or superlattice effects given the measured twist angle and moiré period?
• RQ5 What role do structural wrinkles or elastic instabilities play in establishing the observed pattern?

Key findings

• A quasi-periodic triangular pattern of indirect excitons with a wavelength of ~2.6 μm is observed.
• The pattern forms a distorted triangular lattice, with local maxima in -ΔI(x,y) forming a quasi-60° geometry.
• Voronoi analysis shows an average coordination number of six for cells not disrupted by edges, consistent with a triangular pattern.
• The modulation wavelength remains effectively constant across different densities and temperatures, indicating insensitivity to these parameters.
• Turing-instability and attractive-interaction mechanisms are unlikely explanations due to wavelength/density/temperature behavior; moiré period is far smaller than 2.6 μm; wrinkling is qualitatively consistent as a potential mechanism, given plausible micrometer-scale wrinkle wavelengths.
• IX long-range transport persists with little decay under certain conditions, coexisting with the modulation pattern.

Figure 2: Characteristics of IX pattern. (a) A histogram of the distances between the local maxima in $-\Delta I(x,y)$ . The characteristic wavelength $\lambda\sim 2.6$ $\mu$ m. (b) The Fourier transform of $-\Delta I(x,y)$ along the line connecting the local maxima. The broad peak on a noise backgr