论文标题
扭曲的双层石墨烯中平坦频段的3/2魔法量化规则以及与量子厅效应的关系
3/2 magic-angle quantization rule of flat bands in twisted bilayer graphene and relationship with the Quantum Hall effect
论文作者
论文摘要
扭曲的石墨烯双层中的平面电子模式负责超导和其他高度相关的电子电子相。尽管有些提示是量子厅效应与零平风模式之间可能存在的联系，但尚不清楚这种连接是如何出现的。在这里，使用手性模型汉密尔顿研究了扭曲的双层石墨烯中的电子行为。结果，事实证明，对于高阶魔法角，零平面模式与分散剂$σ^2 = 1/3α$相连，其中$α$是结合扭角和能量尺度的耦合参数。然后证明，汉密尔顿的平方是$ 2 \ times 2 $矩阵操作员，事实证明与二维量子谐波振荡器相当。石墨烯的两部分晶格之间的层间电流是用角动量项鉴定出来的，而限制电位是有效的二次潜力。从那里证明了高阶魔术角的限制量化规则，即$α_{m+1}-α_{m} = 3/2 $，其中$ m $是角度的顺序。所有这些结果与数值计算非常吻合。
Flat band electronic modes in twisted graphene bilayers are responsible for superconducting and other highly correlated electron-electron phases. Although some hints were known of a possible connection between the quantum Hall effect and zero flat band modes, it was not clear how such connection appears. Here the electronic behavior in twisted bilayer graphene is studied using the chiral model Hamiltonian. As a result, it is proved that for high-order magic angles, the zero flat band modes converge into coherent Landau states with a dispersion $σ^2=1/3α$, where $α$ is a coupling parameter that incorporates the twist angle and energetic scales. Then it is proved that the square of the hamiltonian, which is a $2\times 2$ matrix operator, turns out to be equivalent to a two-dimensional quantum harmonic oscillator. The interlayer currents between graphene's bipartite lattices are identified with the angular momentum term while the confinement potential is an effective quadratic potential. From there it is proved a limiting quantization rule for high-order magic angles, i.e., $α_{m+1}-α_{m}=3/2$ where $m$ is the order of the angle. All these results are in very good agreement with numerical calculations.
