论文标题
库仑相互作用下高阶拓扑绝缘子的命运
Fate of higher-order topological insulator under Coulomb interaction
论文作者
论文摘要
在本文中，我们研究了远程库仑相互作用对重新归一化组理论的三维二阶绝缘体（TI）的影响。我们发现分析方法和最近的字母物理学结论。莱特牧师。 {\ bf 127}，176601（2021）是不可靠的。这封信中有两个问题。首先，由RG流$ m \ rightarrow \ infty $和$ d \ rightarrow0 $描述的特征不能用作从二阶Ti到Ti的过渡标准，因为这种特征基本上不能由Coulomb互动引起，而仅是由Fermion依据贡献Fermion Action的造成的结果。确实，即使在免费的二阶Ti中，也可以满足此特征。其次，$ b $的流量不引起注意，这非常重要，应该认真研究。在本文中，我们仔细分析了由库仑相互作用引起的模型参数流的校正。我们发现，$ M $的迹象会更改，但如果初始库仑强度足够大，则符合$ b $的符号将持有，而$ m $的符号则持有，但如果最初的库仑强度占据较小的值，则$ b $的符号会更改。这些结果表明，二阶Ti不仅在较强的库仑相互作用下，而且在弱库仑相互作用下不稳定。我们还通过重新归一化组理论研究了二阶Ti中疾病散射的影响。根据物理的标准。莱特牧师。 {\ bf 127}，176601（2021），弱混乱将二阶Ti驱动到Ti。但是，我们发现二阶Ti对弱混乱症具有鲁棒性，因为弱障碍不会对二阶Ti进行定性修改。该结果与基于其他方法的最新研究一致。还研究了二阶Ti中库仑相互作用和疾病的相互作用。
In this article, we study the influence of long-range Coulomb interaction on three-dimensional second-order topological insulator (TI) by renormalization group theory. We find that both the analysis method and conclusions in the recent Letter Phys. Rev. Lett. {\bf 127}, 176601 (2021) are unreliable. There are two problems in this Letter. Firstly, the characteristic described by the RG flows $m\rightarrow\infty$ and $D\rightarrow0$ can not be used as the criterion for transition from second-order TI to TI, since this characteristic could be essentially not induced by Coulomb interaction but only results from the trivial power counting contribution of fermion action. Indeed, this characteristic is satisfied even for free second-order TI. Second, the flow of $B$ is not paid attention, which is very important and should be seriously studied. In this article, we analyze carefully the corrections for the flows of the model parameters induced by Coulomb interaction. We find that the sign of $m$ changes but the sign of $B$ holds if the initial Coulomb strength is large enough, while the sign of $m$ holds but the sign of $B$ changes if the initial Coulomb strength takes small values. These results indicate that second-order TI is unstable to trivial band insulator not only under strong Coulomb interaction but also under weak Coulomb interaction. We also study the effects of disorder scattering in second-order TI by renormalization group theory. According to the criterion in Phys. Rev. Lett. {\bf 127}, 176601 (2021), weak disorder drives second-order TI to TI. However, we find that second-order TI is robust against weak disorder, since weak disorder does not give qualitative modification for second-order TI. This result is consistent with recent studies based on other methods. Interplay of Coulomb interaction and disorder in second-order TI is also investigated.
