【纯计算】一维范德华异质结的曲率对能带影响几何？

能带对齐作为半导体研究的核心概念，对理解晶体管和量子阱激光器等各类半导体器件的原理起着关键作用。2020 年，科研人员使用化学气相沉积在单壁碳纳米管和氮化硼纳米管上生长出直径小至 3.9 纳米的单壁单晶二硫化钼纳米管。这些化学组成不同的同轴纳米管形成一类全新的异质结构，即一维范德华异质结。

Fig. 1 One-dimensional (1D) van der Waals (vdW) heterostructures and diameter-dependent band-edge levels of MoS2 and WS2 nanotubes.

阐明同轴纳米管之间的能带对齐是一维范德华异质结物理性质与器件研究的关键一步。然而，纳米管的曲率如何影响一维范德华异质结中的能带对齐，在此之前尚不清楚。

Fig. 2 Diameter-dependent band-edge levels of MoSe2, WSe2 and MoTe2 nanotubes.

来自中国西湖大学工学院的李文彬教授团队通过系统的第一性原理计算表明，对于TMDC一维范德华异质结，曲率可以导致能带对齐类型发生转变。

Fig. 3 Effect of curvature-induced flexoelectricity on the band-edge levels of MoSe2 nanotubes.

他们发现，随着纳米管管径的减小和曲率的上升，单个TMDC 纳米管的半导体导带底能级呈现出快速且单调的降低，而价带顶能级先下降再上升。

Fig. 4 Effect of circumferential tensile strain on the band-edge levels of MoSe2 nanotubes.

这些特性可以根据曲率诱导的挠曲电和相应的静电势效应，以及 TMDC 纳米管中固有的周向拉伸应变和弯曲应变来充分解释。当TMDC纳米管形成同轴范德华异质结时，挠曲电电势差导致的管间耦合效应，协同受管径调控的带边能级变化，可使具有较大管径的MoSe₂@WS₂、MoTe₂@MoSe₂ 和 MoTe₂@WS₂ 一维范德华异质结发生从 II 型到 I 型能带对齐类型的转变。

Fig. 5 Band alignment in 1D vdW heterostructures consisting of WS2 nanotubes nested in MoS2 nanotubes.

李文彬教授团队的这一成果为理解一维范德华异质结中的能带对齐奠定了重要基础，并为合理设计TMDC一维范德华异质结铺平了道路。相关论文近期发布于npj Computational Materials 9: 92 (2023)。手机阅读原文，请点击本文底部左下角“阅读原文”，进入后亦可下载全文PDF文件。

Fig. 6 1D vdW heterostructures that exhibit Type I band alignment at large tube diameters. 

Editorial Summary

1D van der Waals heterostuctures: Band alignment controlled by the curvature

Band alignment is a core concept in the study of semiconductors, explaining a wide range of phenomena underlying applications such as transistors and quantum well lasers. In 2020, researchers used chemical vapor deposition to successfully grow single-walled, single-crystal MoS₂ nanotubes with diameters as small as 3.9 nm on single-walled carbon nanotubes and boron-nitride nanotubes. These coaxial nanotubes with different chemical compositions form a new class of heterostructures, namely one-dimensional (1D) van der Waals (vdW) heterostructures. Elucidating the band alignment between coaxial nanotubes is a key step in exploring the physical properties and device applications of such 1D vdW heterostructures. However, the effect of curvature on the band alignment of 1D vdW heterostructures remained unclear. This study provides a comprehensive theoretical framework to understand the curvature-dependent band alignment in 1D vdW heterostructures of transition metal dichalcogenides (TMDCs).

Through comprehensive first-principles calculations, a team led by Prof. Wenbin Li from the School of Engineering, Westlake University, China, reveals that the effect of curvature can lead to a transition in the band-alignment type in 1D vdW heterostructures of TMDCs. They find that, as the diameter of a TMDC nanotube decreases, the conduction band minimum exhibits a rapid and monotonic decrease, whereas the valence band maximum exhibits an initial decrease before increasing. These properties can be fully explained in terms of curvature-induced flexoelectricity and the associated electrostatic potential effect, as well as the intrinsic circumferential tensile strain and bending strain within the TMDC nanotubes. They predict that in 1D vdW heterostructures of coaxial TMDC nanotubes, the concerted effect of diameter-dependent band-edge levels and intertube coupling via flexovoltage can lead to a transition of intertube band alignment from Type II to Type I in large-diameter MoSe₂@WS₂, MoTe₂@MoSe₂, and MoTe₂@WS₂heterostructures. This study lays down an important foundation for understanding the band alignment in 1D vdW heterostructures and paves the way for rational design of TMDC-based 1D vdW heterostructures. The article was recently published in npj Computational Materials 9,: 92 (2023).

原文Abstract及其翻译

Curvature-controlled band alignment transition in 1D van der Waals heterostructures (一维范德华异质结中曲率控制的能带对齐类型转变)

Shu Zhao, Chunxia Yang, Ziye Zhu, Xiaoping Yao & Wenbin Li

Abstract The effect of curvature on the band alignment of one-dimensional (1D) van der Waals (vdW) transition metal dichalcogenide (TMDC) heterostructures is studied by comprehensive first-principles calculations. We find that, as the diameter of a TMDC nanotube decreases, the combined effect of curvature-induced flexoelectricity and circumferential tensile strain causes a rapid lowering of the conduction band minimum, whereas the valence band maximum exhibits an initial lowering before rising. As individual TMDC nanotubes form coaxial heterostructures, the concerted effect of diameter-dependent band-edge levels and intertube coupling via flexovoltage can result in a transition of intertube band alignment from Type II to Type I in multiple heterostructural systems, including large-diameter MoSe₂@WS₂, MoTe₂@MoSe₂, and MoTe₂@WS₂ heterostructures. These results lay down a foundation for the rational design of 1D vdW heterostructures.

摘要通过第一性原理计算，本文研究了曲率对过渡金属二硫化物 (TMDC) 一维范德华异质结中能带对齐的影响。我们发现，随着纳米管管径的减小，在曲率诱导的挠曲电效应和周向拉伸应变的共同作用下，TMDC纳米管的导带底能级快速下降，而价带顶能级则先降低再上升。当不同TMDC纳米管形成嵌套的同轴异质结时，与管径相关的带边能级变化，叠加通过挠曲电电势差进行的管间耦合，可协同导致管间能带对齐类型在多个异质结系统中从 II 型转变为 I 型，包括大管径的MoSe₂@WS₂、MoTe₂@MoSe₂和 MoTe₂@WS₂ 异质结。这些结果为一维范德华异质结的理性设计奠定了基础。