Valley Isospin Controlled Fractional Quantum Hall States in Bilayer Graphene
Valley Isospin Controlled Fractional Quantum Hall States in Bilayer Graphene
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DOI：
10.1103/physrevx.12.031019
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发表时间：
2021-05
影响因子：
12.5
通讯作者：
Ke Huang;Hailong Fu;D. R. Hickey;N. Alem;Xi Lin;Kenji Watanabe;T. Taniguchi;Jun Zhu
中科院分区：
文献类型：
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作者：
Ke Huang;Hailong Fu;D. R. Hickey;N. Alem;Xi Lin;Kenji Watanabe;T. Taniguchi;Jun Zhu
一个二维的电子系统放置在磁场中发展朗道能级，其中强库仑相互作用导致多体关联基态的出现。类似于电子自旋的量子数使得能够理解和控制复杂的基态秩序和集体激发。由于其自旋，谷和轨道自由度，Bernal堆叠的双层石墨烯提供了一个丰富的平台，以追求相关的现象在两个维度。在这项工作中，我们制造了双栅Bernal堆叠的双层石墨烯器件，并使用垂直电场对其谷同位旋自由度进行了前所未有的精细控制。更高的样本质量使我们能够探测在以前的研究中被无序所掩盖的制度。我们提出了一个新的偶数分母分数量子霍尔态在填充因子{\nu} = 5/2的证据。发现5/2态在消失谷塞曼分裂的极限下是自发谷极化的，这与关于摩尔-里德态的自旋极化的理论预测一致。在偶分母分数量子霍尔态附近，我们观察到摩尔-里德Pfiran波函数在{\nu}= 3/2，7/2和-1/2处的预测莱文-哈尔佩林子态和反Pfiran波函数在{\nu}= 5/2处的预测莱文-哈尔佩林子态的出现。这些观察结果表明双层石墨烯中的粒子-空穴对称性被打破。我们构建了一个全面的谷极化相图的Jain序列分数态周围的填充因子3/2。这些结果用双组分复合费米子模型得到了很好的解释，进一步证明了双层石墨烯谷区同位旋的SU（2）性质。我们的实验为今后在双层石墨烯中操纵谷同位旋以设计奇异拓扑秩序和量子信息过程铺平了道路。
A two-dimensional electron system placed in a magnetic field develops Landau levels, where strong Coulomb interactions lead to the appearance of many-body correlated ground states. Quantum numbers similar to the electron spin enable the understanding and control of complex ground state order and collective excitations. Owing to its spin, valley and orbital degrees of freedom, Bernal-stacked bilayer graphene offers a rich platform to pursue correlated phenomena in two dimensions. In this work, we fabricate dual-gated Bernal-stacked bilayer graphene devices and demonstrate unprecedented fine control over its valley isospin degrees of freedom using a perpendicular electric field. Higher sample quality enables us to probe regimes obscured by disorder in previous studies. We present evidence for a new even-denominator fractional quantum Hall state at filling factor {\nu} = 5/2. The 5/2 state is found to be spontaneously valley polarized in the limit of vanishing valley Zeeman splitting, consistent with a theoretical prediction made regarding the spin polarization of the Moore-Read state. In the vicinity of the even-denominator fractional quantum Hall states, we observe the appearance of the predicted Levin-Halperin daughter states of the Moore-Read Pfaffian wave function at {\nu}= 3/2, 7/2, and -1/2 and of the anti-Pfaffian at {\nu}= 5/2. These observations suggest the breaking of particle-hole symmetry in bilayer graphene. We construct a comprehensive valley polarization phase diagram for the Jain sequence fractional states surrounding filling factor 3/2. These results are well explained by a two-component composite fermion model, further demonstrating the SU(2) nature of the valley isospin in bilayer graphene. Our experiment paves the path for future efforts of manipulating the valley isospin in bilayer graphene to engineer exotic topological orders and quantum information processes.