一维Dirac系统零模的质量分类和操纵
Mass classification and manipulation of zero modes in one-dimensional Dirac systems
摘要：
我们提出了一个详细的质量分类的所有可能的零能量模式在一维狄拉克系统。通过在狄拉克哈密顿量中引入线性质量项，我们发现拓扑保护的零能模具有质量-动量对偶性。基于对偶性，我们将2 * 2子空间中的三种基本零能模分别分类为：子格子中的孤子，Nambu子空间中的Majorana零模和自旋子空间中的磁零能模.在质量竞争机制下，在8 * 8内部空间及其4 * 4子空间中，通过提升Kramers简并度，出现了孤立的零能模。我们还提出了操纵狄拉克哈密顿量可能的质量的实验方法。我们的分类方案可以很容易地扩展到2D或3D系统，并适用于其他领域的拓扑保护状态的调查。
英文摘要：
We present a detailed mass classification of all possible zero-energy modes in one-dimensional Dirac systems. By introducing a linear mass term into the Dirac Hamiltonian, we find that the topologically protected zero-energy modes have the mass-momentum duality. Based on the duality, we classify three fundamental zero-energy modes in 2 * 2 subspaces respectively: solitons in sublattice subspace, Majorana zero modes in Nambu subspace, and magnetic zero-energy modes in spin subspace. Within the mechanism of mass competition, isolated zero-energy modes emerge by lifting Kramers degeneracy in the combined 8 * 8 inner space and its 4 * 4 subspaces. We also propose experimental methods of manipulating possible masses in Dirac Hamiltonians. Our classification scheme could easily be extended to 2D or 3D systems and applied to investigate topologically protected states in other fields.
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