Abstract
In flat bands of two-dimensional materials, the mass of charge carriers increases dramatically and the Coulomb energy of the charge carriers can be much larger than the quenched kinetic energy. When the flat band is partially filled, electron-electron interactions can drive electrons to form exotic correlated phases, such as quantum Hall ferromagnetism, fractional quantum Hall effect, superconductivity, and quantum anomalous Hall effect. Therefore, flat bands in two-dimensional materials have attracted much attention very recently. In the past few years, the strongly correlated phenomena in flat bands have become a hot topic in community of condensed matter physics. There are several different methods, such as using a perpendicular magnetic field, introducing strained structures, and introducing a twist angle, to realize the flat bands in two-dimensional materials. In this review article, we summarize the methods to realize flat bands in two-dimensional systems and introduce the related novel electronic states when the flat band is partially filled.
Highlights
In flat bands of two-dimensional materials, the mass of charge carriers increases dramatically and the Coulomb energy of the charge carriers can be much larger than the quenched kinetic energy
In the past few years, the strongly correlated phenomena in flat bands have become a hot topic in community of condensed matter physics
We summarize the methods to realize flat bands in two-dimensional systems and introduce the related novel electronic states when the flat band is partially filled
Summary
三层石墨烯的自然形态具有两种堆垛构型 [55]: ABA 堆垛, 最顶层的原子位于底层原子的顶部, 表 现出镜像对称性; ABC 堆垛, 其中顶层的一个子格 位于底层六边形中心的上方, 表现为反转对称, 但 缺乏镜像对称 (图 2(c) 左图 [56]). 尽管 ABC 堆垛三 层石墨烯 (ABC-TLG) 相较于 ABA 堆垛三层石墨 烯 (ABA-TLG) 更不稳定, 但 ABC-TLG 在低能带 处电子的能量色散关系成立方的依赖关系, 具有极 大的电子态密度 [57,58], 在电中性点处能自发地形成 平带 [54] (图 2(c) 右图 [56]). 2015 年, Xu 等 [59] 利用 STM 对 ABC-TLG 的电子态密度进行了直接的探 测, 结果显示在费米能级附近出现了一个很强的电 子态密度峰, 表明此处的能带结构十分平坦, 这一 实验结果同理论预期是一致的. 三层石墨烯的自然形态具有两种堆垛构型 [55]: ABA 堆垛, 最顶层的原子位于底层原子的顶部, 表 现出镜像对称性; ABC 堆垛, 其中顶层的一个子格 位于底层六边形中心的上方, 表现为反转对称, 但 缺乏镜像对称 (图 2(c) 左图 [56]). 尽管 ABC 堆垛三 层石墨烯 (ABC-TLG) 相较于 ABA 堆垛三层石墨 烯 (ABA-TLG) 更不稳定, 但 ABC-TLG 在低能带 处电子的能量色散关系成立方的依赖关系, 具有极 大的电子态密度 [57,58], 在电中性点处能自发地形成 平带 [54] (图 2(c) 右图 [56]). 2015 年, Xu 等 [59] 利用 STM 对 ABC-TLG 的电子态密度进行了直接的探 测, 结果显示在费米能级附近出现了一个很强的电 子态密度峰, 表明此处的能带结构十分平坦, 这一 实验结果同理论预期是一致的. 此外, ABC-TLG 中 l = 3 的手征费米子, 决定了 其可以出现更多新奇的电子态 [60,61]. 目前, 理论和 实验都已证实 ABC-TLG 具备不同于单层、双层 石墨烯以及 ABA-TLG 的电学和光学性质 [56,62−66], 存在巨大的研究潜力, 这也使得 ABC-TLG 在近 年来引起了科学家们的广泛关注
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