Effects of band gap on the magic-angle of twisted bilayer graphene

Guodong Yu, Lanting Feng
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Abstract

Band flattening has been observed in various materials with twisted bilayer structures, such as graphene, MoS2, and hexagonal boron nitride (hBN). However, the unique phenomenon of magic-angle has only been reported in the twisted bilayer graphene (tBG) and not in the twisted bilayer semiconductors or insulators. We aim to investigate the impact of gap opening and interlayer coupling strength on the magic-angle in the tBG. Our results based on the continuum model Hamiltonian with mass term indicate that the presence of a band gap hinders the occurrence of the magic-angle, but strengthening the interlayer coupling tends to restore it. By introducing layer asymmetry, such as interlayer bias or mass difference between layers, the flat bands become more dispersive. Furthermore, we have explored the influence of the Moire's potential due to the hBN substrate by calculating the quasi-band-structure of the hetero-structure tBG/hBN. Our findings indicate that the conclusions drawn from using the mass term remain valid despite the presence of the Moire's potential due to the hBN substrate.
带隙对扭曲双层石墨烯魔角的影响
在石墨烯、MoS2 和六方氮化硼(hBN)等各种具有扭曲双层结构的材料中都观察到了带平坦化现象。然而,只有在扭曲双层石墨烯(tBG)中出现过独特的魔角现象,而在扭曲双层半导体或绝缘体中却未见报道。我们的目的是研究间隙开口和层间耦合强度对 tBG 中魔幻角度的影响。我们基于带质量项的连续模型哈密顿的研究结果表明,带隙的存在会阻碍魔角的出现,但加强层间耦合往往会恢复魔角。通过引入层不对称,如层间偏差或层间质量差,平坦带变得更加分散。此外,我们还通过计算异质结构 tBG/hBN 的准带结构,探讨了由于 hBN 衬底而产生的摩尔势的影响。我们的研究结果表明,尽管存在因 hBN 衬底而产生的摩尔势,但使用质量项得出的结论仍然有效。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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