倾斜磁场作用下半导体超晶格的分岔与混沌
Bifurcations and chaos in semiconductor superlattices with a tilted magnetic field
摘要：
研究了在外加偏压和相对于超晶格轴倾斜的磁场作用下，耗散效应对半导体超晶格中电子输运的影响.在以前的工作中，我们发现尽管外加磁场是静止的，但它们的行为类似于THz平面波，在最低的微带内强烈耦合了电子的Bloch运动和回旋运动.因此，电子表现出一种独特类型的哈密顿混沌，这在相空间中产生了一个复杂的导电通道网（随机网络），导致在施加电压的临界值下电流的共振增加。这种相空间图案化提供了用于控制电阻的敏感机制。在本文中，我们研究的电子动力学的耗散的影响，通过修改的半经典运动方程，包括一个线性阻尼项。我们证明，即使在耗散的存在下，确定性混沌起着重要的作用，在电子输运过程。我们确定机制的发病混沌和探讨相关的序列中的电子轨迹的分叉。当布洛赫频率和回旋频率相当时，系统中会出现复杂的多稳态现象。特别是，对于固定值的控制参数几个不同的稳定制度可以共存，每个对应于不同的初始条件。我们表明，这种多稳态有明确的，实验上可观察到的，签名的电子输运特性。
英文摘要：
We study the effects of dissipation on electron transport in a semiconductor superlattice with an applied bias voltage and a magnetic field that is tilted relative to the superlattice axis.In previous work, we showed that although the applied fields are stationary,they act like a THz plane wave, which strongly couples the Bloch and cyclotron motion of electrons within the lowest miniband. As a consequence,the electrons exhibit a unique type of Hamiltonian chaos, which creates an intricate mesh of conduction channels (a stochastic web) in phase space, leading to a large resonant increase in the current flow at critical values of the applied voltage. This phase-space patterning provides a sensitive mechanism for controlling electrical resistance. In this paper, we investigate the effects of dissipation on the electron dynamics by modifying the semiclassical equations of motion to include a linear damping term. We demonstrate that even in the presence of dissipation,deterministic chaos plays an important role in the electron transport process. We identify mechanisms for the onset of chaos and explore the associated sequence of bifurcations in the electron trajectories. When the Bloch and cyclotron frequencies are commensurate, complex multistability phenomena occur in the system. In particular, for fixed values of the control parameters several distinct stable regimes can coexist, each corresponding to different initial conditions. We show that this multistability has clear, experimentally-observable, signatures in the electron transport characteristics.
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