Randeria Mallika T, Agarwal Kartiek, Feldman Benjamin E, Ding Hao, Ji Huiwen, Cava R J, Sondhi S L, Parameswaran Siddharth A, Yazdani Ali
Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA.
Department of Electrical Engineering, Princeton University, Princeton, NJ, USA.
Nature. 2019 Feb;566(7744):363-367. doi: 10.1038/s41586-019-0913-0. Epub 2019 Feb 6.
Symmetry and topology are central to understanding quantum Hall ferromagnets (QHFMs), two-dimensional electronic phases with spontaneously broken spin or pseudospin symmetry whose wavefunctions also have topological properties. Domain walls between distinct broken-symmetry QHFM phases are predicted to host gapless one-dimensional modes-that is, quantum channels that emerge because of a topological change in the underlying electronic wavefunctions at such interfaces. Although various QHFMs have been identified in different materials, interacting electronic modes at these domain walls have not been probed. Here we use a scanning tunnelling microscope to directly visualize the spontaneous formation of boundary modes at domain walls between QHFM phases with different valley polarization (that is, the occupation of equal-energy but quantum mechanically distinct valleys in the electronic structure) on the surface of bismuth. Spectroscopy shows that these modes occur within a topological energy gap, which closes and reopens as the valley polarization switches across the domain wall. By changing the valley flavour and the number of modes at the domain wall, we can realize different regimes in which the valley-polarized channels are either metallic or develop a spectroscopic gap. This behaviour is a consequence of Coulomb interactions constrained by the valley flavour, which determines whether electrons in the topological modes can backscatter, making these channels a unique class of interacting one-dimensional quantum wires. QHFM domain walls can be realized in different classes of two-dimensional materials, providing the opportunity to explore a rich phase space of interactions in these quantum wires.
对称性和拓扑结构是理解量子霍尔铁磁体（QHFMs）的核心，量子霍尔铁磁体是二维电子相，其自旋或赝自旋对称性自发破缺，且波函数也具有拓扑性质。不同的破缺对称QHFM相之间的畴壁预计会存在无隙一维模式，即由于此类界面处底层电子波函数的拓扑变化而出现的量子通道。尽管在不同材料中已识别出各种QHFMs，但这些畴壁处的相互作用电子模式尚未得到探测。在此，我们使用扫描隧道显微镜直接观察铋表面具有不同谷极化（即电子结构中能量相等但量子力学上不同的谷的占据情况）的QHFM相之间的畴壁处边界模式的自发形成。光谱学表明，这些模式出现在拓扑能隙内，当谷极化穿过畴壁时，能隙会关闭并重新打开。通过改变畴壁处的谷类型和模式数量，我们可以实现不同的状态，其中谷极化通道要么是金属性的，要么会形成光谱能隙。这种行为是由谷类型所约束的库仑相互作用的结果，谷类型决定了拓扑模式中的电子是否能够背散射，使得这些通道成为一类独特的相互作用一维量子线。QHFM畴壁可以在不同类别的二维材料中实现，这为探索这些量子线中丰富的相互作用相空间提供了机会。
