朗道能级波函数干涉显示铁电量子霍尔相
Ferroelectric quantum Hall phase revealed by visualizing Landau level wavefunction interference
摘要：
在具有多个内部自由度的电子系统中，由于库仑相互作用，可以自发地形成新的对称性破缺态。多谷材料为这种状态的出现提供了特别丰富的背景，这些状态具有潜在的电子和光学应用。迄今为止，这些对称性破缺相的识别主要依赖于宏观输运或光学性质的检查。在这里，我们展示了一个强大的直接的方法，通过可视化的波函数的铋表面状态的扫描隧道显微镜。铋表面强的自旋-轨道耦合导致六个简并的泪珠状空穴袋。我们的光谱测量结果表明，这种简并完全解除在高磁场作为交换相互作用的结果，我们能够确定谷排序的性质，通过成像的对称性破缺朗道能级（LL）波函数。孤立缺陷附近单简并LL波函数的显著空间特征包含自旋织构谷之间的干涉的独特签名，其将电子基态识别为量子霍尔铁电体。我们的观察证实了最近的预测，即在强烈的各向异性谷系统的相互作用有利于占领一个单一的谷，引起紧急铁电性的铋的表面状态。
英文摘要：
Novel broken symmetry states can spontaneously form due to Coulomb interactions in electronic systems with multiple internal degrees of freedom. Multi-valley materials offer an especially rich setting for the emergence of such states, which have potential electronic and optical applications. To date, identification of these broken symmetry phases has mostly relied on the examination of macroscopic transport or optical properties. Here we demonstrate a powerful direct approach by visualizing the wave functions of bismuth surface states with a scanning tunneling microscope. Strong spin-orbit coupling on the surface of bismuth leads to six degenerate teardrop-shaped hole pockets. Our spectroscopic measurements reveal that this degeneracy is fully lifted at high magnetic field as a result of exchange interactions, and we are able to determine the nature of valley ordering by imaging the broken symmetry Landau level (LL) wave functions. The remarkable spatial features of singly degenerate LL wave functions near isolated defects contain unique signatures of interference between spin-textured valleys, which identify the electronic ground state as a quantum Hall ferroelectric. Our observations confirm the recent prediction that interactions in strongly anisotropic valley systems favor the occupation of a single valley, giving rise to emergent ferroelectricity in the surface state of bismuth.
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