Topological Semimetals Predicted from First-principles Calculations
Hongming Weng, Xi Dai, Zhong Fang
备注：
A summary on Topological Semimetal, including three members and their relationship. Totally 58 pages and 26 figures. Manuscript finished at the beginning of January 2016
本文综述了我们对三种拓扑半金属的理论预言，即Dirac半金属、Weyl半金属和节点线半金属。TSM是量子物质的一种新态，它不同于拓扑绝缘体。它们的特点是费米面的拓扑稳定性，无论它是否包围带交叉点，即，狄拉克锥状能量节点，或不是。它们之间的区别在于节点的简并度和动量空间分布。实现这些有趣的拓扑量子态对基础科学和未来的应用都是非常具有挑战性的。2012年和2013年，理论上预测Na $_3$ Bi和Cd $_3$ As $_2$分别为DSM。他们在2014年的实验验证点燃了对TSM的热点和密集的研究。随后的理论预言激发了第二波TaAs族的WSM，并在这一年里有许多实验工作问世。2014年，一种碳的三维晶体被提出为NLSM，这是由于可忽略的自旋轨道耦合以及时间反演和反转对称性的共存。虽然NLSM的最终实验证实仍然缺失，但已经有几个理论建议，包括我们的Cu $_3$ PdN。在最后一部分，我们总结了TSM家族及其相互关系。
英文摘要：
We have given a summary on our theoretical predictions of three kinds of topological semimetals (TSMs), namely, Dirac semimetal (DSM), Weyl semimetal (WSM) and Node-Line Semimetal (NLSM). TSMs are new states of quantum matters, which are different with topological insulators. They are characterized by the topological stability of Fermi surface, whether it encloses band crossing point, i.e., Dirac cone like energy node, or not. They are distinguished from each other by the degeneracy and momentum space distribution of the nodal points. To realize these intriguing topological quantum states is quite challenging and crucial to both fundamental science and future application. In 2012 and 2013, Na$_3$Bi and Cd$_3$As$_2$ were theoretically predicted to be DSM, respectively. Their experimental verifications in 2014 have ignited the hot and intensive studies on TSMs. The following theoretical prediction of nonmagnetic WSM in TaAs family stimulated a second wave and many experimental works have come out in this year. In 2014, a kind of three dimensional crystal of carbon has been proposed to be NLSM due to negligible spin-orbit coupling and coexistence of time-reversal and inversion symmetry. Though the final experimental confirmation of NLSM is still missing, there have been several theoretical proposals, including Cu$_3$PdN from us. In the final part, we have summarized the whole family of TSMs and their relationship.
We review recent theoretical progress in the understanding and prediction of novel topological semimetals. Topological semimetals define a class of gapless electronic phases exhibiting topologically stable crossings of energy bands. Different types of topological semimetals can be distinguished based on the degeneracy of the band crossings, their codimension (e.g., point or line nodes), as well as the crystal space group symmetries on which the protection of stable band crossings relies. The dispersion near the band crossing is a further discriminating characteristic. These properties give ris…
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