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

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• Charge density waves
• Dirac fermions
• Magnetic order
• Molecular solids
• Organic compounds
• Strongly correlated systems