Quantum hall ferromagnets
Quantum hall ferromagnets
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发表时间：
2016
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通讯作者：
Akshay Kumar
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作者：
Akshay Kumar
我们研究了与量子霍尔效应有关的几个量子相。我们最初的重点是一对量子霍尔铁磁体，其中量子霍尔有序同时发生与半导体谷指数相关的内部对称性的自发破缺。在我们的第一个例子- AlAs异质结构-中，我们研究了畴壁结构，随机场无序和偶极矩物理的作用。然后，在第二个例子——Si（111）中，我们证明了几个整数填充分数附近的对称性破缺涉及到被称为“有序无序”的热波动选择和由远离相应填充引起的Skyrme晶格的能量选择的组合，我们称之为“掺杂有序”的机制。在没有谷塞曼能量的情况下，我们还研究了这类系统在填充因子1附近的基态。我们证明了即使最低能量的带电激发是1 skyrmions，但最低能量的skyrmions晶格每单位细胞的电荷为bbb101。然后，我们将讨论范围扩大到包括具有多个陈氏数带的晶格系统。我们在分数阶陈氏绝缘体相中发现了量子霍尔铁磁体的类似物。与AlAs系统不同的是，这里的畴壁自然地带有间隙的电子激发。最后，我们得出了仅涉及拓扑的结果：我们表明，放置在氮化硼衬底上的ABC堆叠多层石墨烯具有局部贝里曲率非零的平坦带，但陈氏数为零。这允许访问具有非平凡量子距离度量的相互作用主导系统，但没有非零陈恩数的额外复杂性。
We study several quantum phases that are related to the quantum Hall effect. Our initial focus is on a pair of quantum Hall ferromagnets where the quantum Hall ordering occurs simultaneously with a spontaneous breaking of an internal symmetry associated with a semiconductor valley index. In our first example – AlAs heterostructures – we study domain wall structure, role of random-field disorder and dipole moment physics. Then in the second example – Si(111) – we show that symmetry breaking near several integer filling fractions involves a combination of selection by thermal fluctuations known as “order by disorder” and a selection by the energetics of Skyrme lattices induced by moving away from the commensurate fillings, a mechanism we term “order by doping”. We also study ground state of such systems near filling factor one in the absence of valley Zeeman energy. We show that even though the lowest energy charged excitations are charge one skyrmions, the lowest energy skyrmion lattice has charge >1 per unit cell. We then broaden our discussion to include lattice systems having multiple Chern number bands. We find analogs of quantum Hall ferromagnets in the menagerie of fractional Chern insulator phases. Unlike in the AlAs system, here the domain walls come naturally with gapped electronic excitations. We close with a result involving only topology: we show that ABC stacked multilayer graphene placed on boron nitride substrate has flat bands with non-zero local Berry curvature but zero Chern number. This allows access to an interaction dominated system with a non-trivial quantum distance metric but without the extra complication of a non-zero Chern number.