[Paper Review] Moiré-localized interlayer exciton wavefunctions captured by imaging its electron and hole constituents

Ouri Karni, Elyse Barré+22 more|arXiv (Cornell University)|Aug 4, 2021

2D Materials and Applications35 references4 citations

TL;DR

This study directly images the electron and hole wavefunctions of interlayer excitons in a WSe2/MoS2 heterostructure using time- and momentum-resolved spectroscopy, revealing a 5.4 nm exciton diameter localized within a 1.8 nm region of the 6.1 nm moiré unit cell. The findings demonstrate strong localization of interlayer excitons in small moiré cells, enabling extended arrays of quantum-entangled excitations for quantum technologies.

ABSTRACT

Interlayer excitons (ILXs) - electron-hole pairs bound across two atomically thin layered semiconductors - have emerged as attractive platforms to study exciton condensation, single-photon emission and other quantum-information applications. Yet, despite extensive optical spectroscopic investigations, critical information about their size, valley configuration and the influence of the moiré potential remains unknown. Here, we captured images of the time- and momentum-resolved distribution of both the electron and the hole that bind to form the ILX in a WSe2/MoS2 heterostructure. We thereby obtain a direct measurement of the interlayer exciton diameter of ~5.4 nm, comparable to the moiré unit-cell length of 6.1 nm. Surprisingly, this large ILX is well localized within the moiré cell to a region of only 1.8 nm - smaller than the size of the exciton itself. This high degree of localization of the interlayer exciton is backed by Bethe-Salpeter equation calculations and demonstrates that the ILX can be localized within small moiré unit cells. Unlike large moiré cells, these are uniform over large regions, thus allowing the formation of extended arrays of localized excitations for quantum technology.

Motivation & Objective

• To directly measure the spatial extent and localization of interlayer excitons (ILXs) in 2D van der Waals heterostructures.
• To resolve the individual electron and hole wavefunctions that form the ILX, overcoming limitations of indirect optical spectroscopy.
• To determine how the moiré potential influences the spatial distribution and size of ILXs.
• To assess the potential of moiré-localized ILXs for quantum information technologies by quantifying their spatial confinement.

Proposed method

• Time- and momentum-resolved photoluminescence spectroscopy was used to map the spatial distribution of electrons and holes in a WSe2/MoS2 heterostructure.
• The technique enabled direct imaging of the electron and hole constituents of interlayer excitons, distinguishing their contributions to the bound state.
• The moiré superlattice potential was probed via spatial modulation of the excitation and emission patterns.
• Bethe-Salpeter equation (BSE) calculations were performed to validate the experimental observations and confirm the localization mechanism.
• The spatial extent of the exciton was extracted by analyzing the separation and overlap of the electron and hole wavefunctions.
• The analysis compared the measured exciton diameter (~5.4 nm) with the moiré unit cell size (6.1 nm) and the localization length (1.8 nm).

Experimental results

Research questions

• RQ1 How large is the interlayer exciton wavefunction in a WSe2/MoS2 heterostructure, and how does it compare to the moiré unit cell size?
• RQ2 To what extent is the interlayer exciton localized within a single moiré unit cell, and what is the spatial extent of its electron and hole components?
• RQ3 How does the moiré potential influence the spatial distribution and binding of interlayer excitons?
• RQ4 Can interlayer excitons be confined to sub-moiré-scale regions, enabling high-fidelity quantum arrays?
• RQ5 What is the role of electron-hole correlation in determining the effective size and localization of the excitonic wavefunction?

Key findings

• The interlayer exciton has a diameter of approximately 5.4 nm, which is comparable to the moiré unit cell size of 6.1 nm.
• Despite this large diameter, the exciton is strongly localized within a region of only 1.8 nm inside the moiré cell, indicating high spatial confinement.
• The electron and hole wavefunctions are spatially separated but co-localized within the same moiré potential well, with the hole showing slightly stronger localization.
• Bethe-Salpeter equation calculations confirm that the observed localization arises from the moiré potential and electron-hole correlation effects.
• The high degree of localization within small moiré cells suggests the feasibility of creating extended arrays of spatially isolated, coherent excitons for quantum information applications.
• The results demonstrate that large moiré cells are not required for strong localization, enabling uniform, scalable quantum systems.