论文标题
磁场中的蜂窝结构
Honeycomb structures in magnetic fields
论文作者
论文摘要
我们考虑降低磁场中蜂窝状晶格的维度模型，并报告有关状态的光谱，密度，自相似性和金属/绝缘子转变的结果。我们进行了光谱分析，通过该分析，我们发现了通过蜂窝的非理性磁通磁通量的分形插管光谱，证明了每个理性通量的零能量狄拉克锥，获得锥形点附近状态密度的明确膨胀，并显示出在安德森（Anderson）体内疾病下的迁移率的存在。我们的结果提供了对De Haas-Van Alphen和量子厅效应的精确描述，并提供了有关运输特性的定量估计。特别是，我们的发现通过超越完美的锥体近似来解释实验观察到的不对称现象。
We consider reduced-dimensionality models of honeycomb lattices in magnetic fields and report results about the spectrum, the density of states, self-similarity, and metal/insulator transitions under disorder. We perform a spectral analysis by which we discover a fractal Cantor spectrum for irrational magnetic flux through a honeycomb, prove the existence of zero energy Dirac cones for each rational flux, obtain an explicit expansion of the density of states near the conical points, and show the existence of mobility edges under Anderson-type disorder. Our results give a precise description of de Haas-van Alphen and Quantum Hall effects, and provide quantitative estimates on transport properties. In particular, our findings explain experimentally observed asymmetry phenomena by going beyond the perfect cone approximation.
