二維材料層間晶格不匹配產生的莫爾圖案為新型電子和激子物理提供了一個嶄新平臺。特別具有類型-II能帶對齊的過渡金屬二硫化物（TMD）轉角異質結構，由于轉角引起的莫爾勢導致了激子定域變化，從而呈現出了有趣的光學特性。

層間轉角角度決定了莫爾布里淵區（MBZ）與單層晶胞布里淵區（UBZs）之間的關聯，引發了相關的莫爾勢。這導致了在UBZs中具有不同動量態之間的光允許電子–空穴躍遷，這可能與吸收過程中激子的精細結構有關。為了對激子結構與轉角角度之間關系進行全面理解，需要對轉角結構中的激子進行基于GW-BSE的多體微擾理論分析。

來自印度科學研究所物理系凝聚態理論中心的Sudipta Kundu等，提出了一種使用GW-BSE研究TMD異質結中雙層轉角角度對激子性質和光學選擇規則影響的方法。作者在一個相對旋轉角度為16°的轉角MoS₂/MoSe₂異質結構上演示了其方法，該結構允許在UBZs中不同高對稱點之間發生躍遷，由原子重構和層間不匹配確定。通過分析，作者揭示了一種獨特的動量混合激子性質，其狀態由層間和層內電子–空穴激發組成。 

這些結果指出了動量直接激子和光學活躍激子的一般性質，其混合了層UBZs中的不同點，并且在較小的角度下同樣有效。這一結果表明，激子性質和光譜特征與轉角的TMD異質結構的底層結構之間存在直接的關系，可為通過選擇層間轉角角度來調節激子性質提供了潛在可能性。該文最近發布于npj Computational Materials 9: 186 (2023). 

Editorial Summary

Moiré patterns generated due to a lattice mismatch between layers of two-dimensional materials serve as an emerging platform for novel correlated electronic and excitonic physics. In particular, twisted heterostructures of transition metal dichalcogenides (TMDs) with a type-II band alignment hold intriguing optical properties due to the varying exciton localization associated with the twist-induced moiré potential. The interlayer twist angle dictates the relation between the moiré Brillouin Zone (MBZ) and the unit-cell Brillouin Zones (UBZs) of the separate layers, inducing an associated moiré potential. This leads to optically-allowed electron-hole transitions between states of different momenta in the UBZs, which can be associated with the exciton fine structure in absorption. A full GW-BSE based many-body theory analysis of excitons in the twisted structure is required for a general ab initio understanding of the relation between the twist angle and the exciton structure.

Sudipta Kundu et al. from the Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, presented an approach to study the effect of twist angle on the exciton nature and optical selection rules in TMD hetero-bilayers by using GW-BSE. They demonstrated their approach on a twisted MoS₂/MoSe₂heterostructure with a relative rotation angle of 16°, which allows transitions between distinct high-symmetry points in the UBZs, determined by the atomic reconstruction and interlayer mismatch. Analyses reveal a unique momentum-mixed excitonic nature, with states that are comprised of both inter- and intra-layer electron-hole excitations. These results point to a general property of momentum-direct and optically-active excitons that mix different points in the layer UBZs, and is valid at smaller angles as well. Their findings suggest a direct relation between exciton nature and spectral features to the underlying structure in twisted TMD heterostructures, offering potential tunability of excitonic properties upon the choice of interlayer twist angle. This article was recently published in npj Computational Materials 9: 186 (2023).

原文Abstract及其翻譯

Exciton fine structure in twisted transition metal dichalcogenide heterostructures （轉角過渡金屬硫化物異質結構中的激子精細結構）

Sudipta Kundu, Tomer Amit, H. R. Krishnamurthy, Manish Jain & Sivan Refaely-Abramson 

Abstract Moiré superlattices of transition metal dichalcogenide (TMD) heterostructures give rise to rich excitonic phenomena associated with the interlayer twist angle. Theoretical calculations of excitons in such systems are typically based on model moiré potentials that mitigate the computational cost. However, predictive understanding of the electron-hole coupling dominating the excitations is crucial to realize the twist-induced modifications of the optical selection rules. In this work, we use many-body perturbation theory to evaluate the relation between twist angle and exciton properties in TMD heterostructures. We present an approach for unfolding excitonic states from the moiré Brillouin zone onto the separate-layer ones. Applying this method to a large-angle twisted MoS₂/MoSe₂ bilayer, we find that the optical spectrum is dominated by mixed electron–hole transitions with different momenta in the separate monolayers, leading to unexpected hybridization between interlayer and intralayer excitons. Our findings offer a design pathway for exciton layer-localization in TMD heterostructures.

摘要過渡金屬硫化物（TMD）異質結構的莫爾超晶格引起了與層間轉角相關豐富的激子現象。此類系統中激子的理論計算通常基于模型莫爾勢，從而降低計算成本。然而，對主導激發的電子–空穴耦合的預測性理解，對于實現光學選擇規則扭轉引起的修改至關重要。在本工作中，我們使用多體微擾理論評估了TMD異質結構中的轉角和激子性質之間的關系。我們提出了一種從莫爾布里淵區展開激子態到單獨層的方法。將這種方法應用于大角度扭曲的MoS₂/MoSe₂雙層，我們發現，光譜主要由在單獨單層中具有不同動量的混合電子–空穴躍遷主導，導致層間和層內激子之間的意外雜化。我們的發現為TMD異質結構中的激子層定位提供了設計途徑。