${\mathrm{Bi}}_2{\mathrm{Se}}_3$, a layered three-dimensional (3D) material, exhibits topological insulating properties due to the presence of surface states and a bandgap of 0.3 eV in the bulk. We study the effect of hydrostatic pressure $P$ and doping with rare earth elements on the topological aspect of this material in bulk from a first principles perspective. Our study shows that under a moderate pressure of $P>7.9\mathrm{GPa}$, the bulk electronic properties show a transition from an insulating to a Weyl semi-metal state due to band inversion. This electronic topological transition may be correlated to a structural change from a layered van der Waals material to a 3D system observed at $P=7.9\mathrm{GPa}$. At large $P$, the density of states have a significant value at the Fermi energy. Intercalating Gd with a small doping fraction between ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ layers drives the system to a metallic anti-ferromagnetic state, with Weyl nodes below the Fermi energy. At the Weyl nodes, time reversal symmetry is broken due to the finite local field induced by large magnetic moments on Gd atoms. However, substituting Bi with Gd induces anti-ferromagnetic order with an increased direct bandgap. Our study provides novel approaches to tune topological transitions, particularly in capturing the elusive Weyl semimetal states, in 3D topological materials.

中文翻译：

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Bi2Se3本体中向Weyl态的拓扑转变：静水压力和掺杂的影响

${\mathrm{双}}_{\mathrm{2个}}{\mathrm{硒}}_3$，是一种分层的三维（3D）材料，由于存在表面状态和整体中的带隙为0.3 eV，因此具有拓扑绝缘特性。我们研究静水压力的影响$P$从第一原理的角度出发，在该材料的拓扑结构方面对稀土元素进行掺杂。我们的研究表明，在中等压力下$P>7.9\mathrm{GPa}$，体电子性质由于能带反转而显示出从绝缘态到Weyl半金属态的转变。这种电子拓扑转变可能与从层状范德华材料到3D系统的结构变化相关，在$P=7.9\mathrm{GPa}$。大体上$P$，状态密度在费米能量处具有重要的价值。掺入Gd的掺杂比例小${\mathrm{双}}_{\mathrm{2个}}{\mathrm{硒}}_3$层驱动系统进入金属反铁磁状态，Weyl节点低于费米能量。在Weyl节点上，由于Gd原子上的大磁矩引起的有限局部磁场，打破了时间反转对称性。但是，用Gd取代Bi会导致反铁磁有序，直接带隙增加。我们的研究提供了新颖的方法来调整拓扑转换，尤其是在3D拓扑材料中捕获难以捉摸的Weyl半金属态。