论文标题
标量潜在诱发拓扑过渡的微观起源和标量霍尔效应
Microscopic origin of scalar potential induced topological transition in massive Dirac fermions and scalar Hall effect
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
We present a systematic study of scalar potential induced topological transition in massive Dirac fermions. We show how a distribution of scalar potential can manipulate the signature of the gap or the mass, as well as the dispersion leading to a band inversion. This is mediated by the Klein tunnelling as well as inverse Klein tunnelling which makes it inherently different from the mechanism leading to topological Anderson insulator. In one dimension it can lead to the formation of edge localisation. In two dimensions this can give rise to the quantised Hall effect. Unlike conventional Hall effects, this is induced by a scalar interaction and intrinsic in nature. Therefore we call it a scalar Hall effect. This can facilitate a direct manipulation of topological invariants, e.g. the Chern number, as well as the manipulation of the edge states locally in a trivial insulator and thus opens new possibilities for tuning physical observables which originate from the nontrivial topology.
