To determine how electronic correlations open a gap in two-dimensional massless Dirac electrons in the organic compounds $\alpha$-(BEDT-TTF)$_2$I$_3$ [$\alpha$-(ET)$_2$I$_3$] and $\alpha$-(BEDT-TSeF)$_2$I$_3$ [$\alpha$-(BETS)$_2$I$_3$], we derive and analyze $ab$ $initio$ low-energy effective Hamiltonians for these two compounds. We find that the horizontal strip charge ordering opens a gap in the massless Dirac electrons in $\alpha$-(ET)$_2$I$_3$, while an insulating phase without explicit symmetry breaking appears in $\alpha$-(BETS)$_2$I$_3$. We clarify that the combination of the anisotropic transfer integrals and the electronic correlations induces a dimensional reduction in the spin correlations, i.e., one-dimensional spin correlations develop in $\alpha$-(BETS)$_2$I$_3$. We show that the one-dimensional spin correlations open a gap in the massless Dirac electrons. Our finding paves the way for opening gaps for massless Dirac electrons using strong electronic correlations.

中文翻译：

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有机化合物中相关狄拉克电子的开隙机制$α$-(BEDT-TTF)$_2$I$_3$和$α$-(BEDT-ESeF)$_2$I$_3$

确定电子相关性如何在有机化合物中打开二维无质量狄拉克电子的间隙 $\alpha$-(BEDT-TTF)$_2$I$_3$ [$\alpha$-(ET)$_2$I$ _3$] 和 $\alpha$-(BEDT-TSeF)$_2$I$_3$ [$\alpha$-(BETS)$_2$I$_3$]，我们推导出和分析 $ab$ $initio$ 低-这两种化合物的能量有效哈密顿量。我们发现水平条带电荷排序在 $\alpha$-(ET)$_2$I$_3$ 中的无质量狄拉克电子中打开了一个间隙，而在 $\alpha$-(BETS )$_2$I$_3$。我们阐明了各向异性传递积分和电子相关性的组合导致自旋相关性的维度减少，即一维自旋相关性在$\alpha$-(BETS)$_2$I$_3$ 中发展。我们表明，一维自旋相关在无质量的狄拉克电子中打开了一个间隙。我们的发现为使用强电子相关性打开无质量狄拉克电子的间隙铺平了道路。