Direct measurement of discrete valley and orbital quantum numbers in bilayer graphene.
Direct measurement of discrete valley and orbital quantum numbers in bilayer graphene.
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DOI：
10.1038/s41467-017-00824-w
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发表时间：
2017-10-16
影响因子：
16.6
通讯作者：
Young AF
中科院分区：
文献类型：
--
作者：
Hunt BM;Li JIA;Zibrov AA;Wang L;Taniguchi T;Watanabe K;Hone J;Dean CR;Zaletel M;Ashoori RC;Young AF
自旋、谷同位旋和意外的轨道简并增强了双层石墨烯的高磁场电子结构，导致了一个复杂的对称性破缺态相图。在这里，我们提出了一种测量层分辨电荷密度的技术，从中我们可以直接确定零能量朗道能级内的谷和轨道极化。层极化在32个不同谷态、自旋态和轨道序态之间的电场调谐相变中以离散的步骤演变，包括以前未观察到的由倾斜层间跳变稳定的轨道极化态。我们将数据拟合到一个模型中，该模型捕获了单粒子和相互作用诱导的各向异性，提供了这个相关电子系统的完整图像。由此产生的对称破缺路线图为分数量子霍尔态的确定性工程铺平了道路，而我们的层分解技术很容易扩展到其他二维材料，其中层极化映射到谷或自旋量子数。双层石墨烯在高磁场下的相图一直是一个悬而未决的问题，可能存在多个内部量子自由度之间的顺序。在这里，Hunt等人报告了谷和轨道阶的测量，使他们能够直接重建相图。
The high magnetic field electronic structure of bilayer graphene is enhanced by the spin, valley isospin, and an accidental orbital degeneracy, leading to a complex phase diagram of broken symmetry states. Here, we present a technique for measuring the layer-resolved charge density, from which we directly determine the valley and orbital polarization within the zero energy Landau level. Layer polarization evolves in discrete steps across 32 electric field-tuned phase transitions between states of different valley, spin, and orbital order, including previously unobserved orbitally polarized states stabilized by skew interlayer hopping. We fit our data to a model that captures both single-particle and interaction-induced anisotropies, providing a complete picture of this correlated electron system. The resulting roadmap to symmetry breaking paves the way for deterministic engineering of fractional quantum Hall states, while our layer-resolved technique is readily extendable to other two-dimensional materials where layer polarization maps to the valley or spin quantum numbers. The phase diagram of bilayer graphene at high magnetic fields has been an outstanding question, with orders possibly between multiple internal quantum degrees of freedom. Here, Hunt et al. report the measurement of the valley and orbital order, allowing them to directly reconstruct the phase diagram.
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