On the Extended Nature of Edge States of Quantum Hall Hamiltonians
On the Extended Nature of Edge States of Quantum Hall Hamiltonians
复制标题
量子霍尔哈密顿量边缘态的扩展性质
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
J. Walcher
中科院分区：
文献类型：
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作者：
J. Fröhlich;G. M. Graf;J. Walcher
抽象的。研究了定域在二维电子气边界附近的单粒子量子霍尔哈密顿量的本征态--所谓的边态。结果表明，对于有限的样品，在朗道能级之间具有适当范围的能量的边态在存在少量无序的情况下仍然沿着边界延伸，因为它们携带非零的手征边缘电流。对于限制在半平面或平面内满足一定几何条件的区域的二维电子气，应用正交换子的Mourre理论证明了对应于边缘态的能谱在Landau能级之间的绝对连续性。
Abstract. Properties of eigenstates of one-particle Quantum Hall Hamiltonians localized near the boundary of a two-dimensional electron gas – so-called edge states – are studied. For finite samples it is shown that edge states with energy in an appropriate range between Landau levels remain extended along the boundary in the presence of a small amount of disorder, in the sense that they carry a non-zero chiral edge current. For a two-dimensional electron gas confined to a half-plane, or to a domain in the plane satisfying a certain geometric condition, the Mourre theory of positive commutators is applied to prove absolute continuity of the energy spectrum well in between Landau levels, corresponding to edge states.