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Direct measurement of discrete valley and orbital quantum numbers in bilayer graphene

机译:直接测量双层石墨烯中的离散谷和轨道量子数

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摘要

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.
机译:双层石墨烯的高磁场电子结构通过自旋,谷底同位旋和偶然的轨道简并性得到增强,从而导致对称状态破坏的复杂相图。在这里,我们提出了一种用于测量层分辨电荷密度的技术,通过该技术,我们可以直接确定零能朗道能级内的波谷和轨道极化。层极化在不同谷,自旋和轨道顺序的状态之间的32个电场调谐的相变中以不连续的步长演化,其中包括由偏斜层间跳变稳定的先前未观察到的轨道极化状态。我们将数据拟合到一个模型,该模型同时捕获了单粒子和相互作用引起的各向异性,从而提供了有关电子系统的完整图片。由此产生的对称性突破路线图为分数量子霍尔态的确定性工程铺平了道路,而我们的层解析技术可以轻松扩展到其他二维材料,其中层极化映射到谷值或自旋量子数。

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