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Weakly chiral networks and two-dimensional delocalized states in a weak magnetic field

机译：弱磁场中的弱手征网络和二维离域态

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We study numerically the localization properties of two-dimensional electrons in a weak perpendicular magnetic field. For this purpose we construct weakly chiral network models on the square and triangular lattices. The prime idea is to separate in space the regions with phase action of magnetic field, where it affects interference in course of multiple disorder scattering, and the regions with orbital action of magnetic field, where it bends electron trajectories. In our models, the disorder mixes counterpropagating channels on the links, while scattering matrices at the nodes describe exclusively the bending of electron trajectories. By artificially introducing a strong spread in the scattering strengths on the links (but keeping the average strength constant), we eliminate the interference and reduce the electron propagation over a network to a classical percolation problem. In this limit we establish the form of the disorder-magnetic field phase diagram. This diagram contains the regions with and without edge states, i.e., the regions with zero and quantized Hall conductivities. Taking into account that, for a given disorder, the scattering strength scales as inverse electron energy, we find agreement of our phase diagram with levitation scenario: energy separating the Anderson and quantum-Hall insulating phases floats up to infinity upon decreasing magnetic field. From numerical study, based on the analysis of quantum transmission of the network with random phases on the links, we conclude that the positions of the weak-field quantum-Hall transitions on the phase diagram are very close to our classical-percolation results. We checked that, in accord with the Pruisken theory, presence or absence of time-reversal symmetry on the links has no effect on the line of delocalization transitions. We also find that floating up of delocalized states in energy is accompanied by doubling of the critical exponent of the localization radius. We establish the origin of this doubling within classical-percolation analysis.
机译：我们从数值上研究了二维电子在弱垂直磁场中的定位特性。为此，我们在正方形和三角形晶格上构造了弱手性网络模型。最初的想法是在空间上将具有磁场相位作用的区域（在多重无序散射过程中会影响干扰的区域）与具有磁场轨道作用的区域（使电子轨道弯曲）分开。在我们的模型中，无序在链路上混合了反向传播的通道，而节点处的散射矩阵仅描述了电子轨迹的弯曲。通过在链路上人为地引入散射强度的强分布（但保持平均强度恒定），我们消除了干扰，并将电子在网络上的传播减少到经典的渗流问题。在此限制下，我们建立了无序磁场相位图的形式。该图包含具有和不具有边缘状态的区域，即具有零和量化的霍尔电导率的区域。考虑到对于给定的无序，散射强度按反电子能缩放，我们发现我们的相图与悬浮情况一致：随着磁场的减小，分离安德森相和量子霍尔绝缘相的能量上浮至无穷大。通过数值研究，在分析链路上具有随机相位的网络的量子传输的基础上，我们得出结论，相图上弱场量子-霍尔跃迁的位置与我们的经典渗流结果非常接近。我们根据普鲁伊斯肯（Pruisken）理论检查，链接上存在或不存在时间反转对称性对离域转变线没有影响。我们还发现，能量中离域态的上浮伴随着定位半径的临界指数加倍。我们在经典渗流分析中确定了这种加倍的起源。

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