There has been growing interest in investigating properties of elementary particles predicted by the standard model. Examples of such studies include exploring their low-energy analogs in a condensed-matter system, where they arise as collective states or quasiparticles. Here we show that a toolbox for systematically engineering the emergent elementary fermions, i.e., Dirac, Weyl, and Majorana fermions, can be built in a single atomic system composed of a spinless magnetic dipolar Fermi gas in a three-dimensional optical lattice. The designed direction-dependent dipole-dipole interaction leads to both the basic building block, i.e., in-plane $p+ip$ superfluid pairing instability, and the manipulating tool, i.e., out-of-plane Peierls instability. It is shown that the Peierls instability provides a natural way of tuning the topological nature of $p+ip$ superfluids and can transform the fermion's nature between distinct emergent particles. Our scheme should contribute to the search for elementary particles through manipulating the topology.

中文翻译：

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三维光学晶格中具有偶极费米气体的基本费米子工具箱

人们对研究由标准模型预测的基本粒子的性质越来越感兴趣。此类研究的例子包括在凝聚态系统中探索它们的低能量类似物，在那里它们以集体态或准粒子的形式出现。在这里，我们展示了一个用于系统地设计涌现基本费米子（即狄拉克、外尔和马约拉纳费米子）的工具箱，可以构建在由三维光学晶格中的无自旋磁偶极费米气体组成的单个原子系统中。设计的与方向相关的偶极-偶极相互作用导致基本构建块，即平面内$磷+\mathrm{一世}磷$超流体配对不稳定性和操纵工具，即平面外 Peierls 不稳定性。结果表明，Peierls 不稳定性提供了一种调整拓扑性质的自然方式$磷+\mathrm{一世}磷$超流体，可以在不同的涌现粒子之间转换费米子的性质。我们的方案应该有助于通过操纵拓扑来寻找基本粒子。