Gap opening mechanism for correlated Dirac electrons in organic compounds α−(BEDT−TTF)2I3 and α−(BEDT−TSeF)2I3

To determine how electron correlations open a gap in two-dimensional massless Dirac electrons in the organic compounds $\ensuremath{\alpha}\text{\ensuremath{-}}{(\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}₂{\mathrm{I}}₃$ [$\ensuremath{\alpha}\text{\ensuremath{-}}{(\mathrm{ET})}₂{\mathrm{I}}₃$] and $\ensuremath{\alpha}\text{\ensuremath{-}}{(\text{BEDT-}\mathrm{TSeF})}₂{\mathrm{I}}₃$ [$\ensuremath{\alpha}\ensuremath{-}{(\mathrm{BETS})}₂{\mathrm{I}}₃$], 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 $\ensuremath{\alpha}\text{\ensuremath{-}}{(\mathrm{ET})}₂{\mathrm{I}}₃$, while an insulating phase without explicit symmetry breaking appears in $\ensuremath{\alpha}\ensuremath{-}{(\mathrm{BETS})}₂{\mathrm{I}}₃$. 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 $\ensuremath{\alpha}\ensuremath{-}{(\mathrm{BETS})}₂{\mathrm{I}}₃$. 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.