Ambient-pressure Dirac electron system in the quasi-two-dimensional molecular conductor $\alpha \text{−}{\left(\mathrm{BETS}\right)}_2{\mathrm{I}}_3$

We investigated the precise crystal structures and electronic states of a quasi-two-dimensional molecular conductor $\alpha \text{−}{\left(\mathrm{BETS}\right)}_2{\mathrm{I}}_3$ at ambient pressure. The electronic resistivity of this molecular solid shows metal-to-insulator (MI) crossover behavior at $T_{\mathrm{MI}}=50\mathrm{K}$. Our x-ray diffraction and ${}^{13}\mathrm{C}$ nuclear magnetic resonance experiments revealed that $\alpha \text{−}{\left(\mathrm{BETS}\right)}_2{\mathrm{I}}_3$ maintains the inversion symmetry below $T_{\mathrm{MI}}$. First-principles calculations found a pair of anisotropic Dirac cones at a general $k$ point, with the degenerate contact points at the Fermi level. The origin of the insulating state in this system is a small energy gap of $\sim 2\mathrm{meV}$ opened by the spin-orbit interaction. The $Z_2$ topological invariants indicate that this system is a weak topological insulator. Our results suggest that $\alpha \text{−}{\left(\mathrm{BETS}\right)}_2{\mathrm{I}}_3$ is a promising material for studying the bulk Dirac electron system in two dimensions.

Figure 1

Crystal structure of $\alpha \text{−}{\left(\mathrm{BETS}\right)}_2{\mathrm{I}}_3$ in (a) bc plane and (b) ab plane. (c) ${}^{13}\mathrm{C}$ NMR spectra for $\alpha \text{−}{\left(\mathrm{BETS}\right)}_2{\mathrm{I}}_3$ at 100 and 30 K. An external field of 7 T was applied parallel to the $c$ axis. Zero frequency corresponds to the zero Knight shift frequency.

Figure 2

(a), (b) Molecular structures of ET and BETS, respectively. (c) Temperature dependence of the charge amount Q in ET [70] in $\alpha \text{−}{\left(\mathrm{ET}\right)}_2{\mathrm{I}}_3$. (d), (e) Temperature dependence of the δ value in BETS and ET in $\alpha \text{−}{\left(\mathrm{BETS}\right)}_2{\mathrm{I}}_3$ and $\alpha \text{−}{\left(\mathrm{ET}\right)}_2{\mathrm{I}}_3$, respectively. The δ value $[\delta =(b+c)-(a+d\left)\right]$ corresponds to the difference in length between the C=C and C–S bonds in the molecule.

Figure 3

Valence electron density distribution of molecule A in $\alpha \text{−}{\left(\mathrm{ET}\right)}_2{\mathrm{I}}_3$ at (a) 150 K and (c) 30 K, and in $\alpha \text{−}{\left(\mathrm{BETS}\right)}_2{\mathrm{I}}_3$ at (b) 80 K and (d) 30 K, obtained by the core differential Fourier synthesis analysis from the x-ray diffraction data in the limit $0{\AA }^{-1}\le sin\theta /\lambda \le 0.5{\AA }^{-1}$.

Figure 4

(a) Band structure calculated from first-principles density functional theory and (b) local density of states (LDOS) of $\alpha \text{−}{\left(\mathrm{BETS}\right)}_2{\mathrm{I}}_3$ in the low-temperature phase (30 K) (without the spin-orbit coupling effect calculated with the FLAPW method). The dashed horizontal line shows the Fermi energy $E_F$. Green, red, and blue solid curves indicate the LDOS of molecules A, B, and C, respectively. (c) Band dispersion is seen from two directions close to the Dirac cone on the $k=\left(k_x,k_y,0\right)$ plane; a pair of Dirac points is located at $k=\left(\pm 0.2958,\mp 0.3392,0\right)$.

Figure 5

Band dispersion of $\alpha \text{−}{\left(\mathrm{BETS}\right)}_2{\mathrm{I}}_3$ along the X (–0.5, 0, 0), (–0.2995, $y$, 0), and M(=S) (–0.5, 0.5, 0) lines (a) without and (b) with spin-orbit coupling near the Fermi energy $E_F$, calculated using the quantum espresso code. The zero energies in (a), (b) are set to be at the chemical potential and the top of the valence bands, respectively.

Figure 6

(a) Total density of states (DOSs) close to the Dirac cones in $\alpha \text{−}{\left(\mathrm{BETS}\right)}_2{\mathrm{I}}_3$ at ambient pressure, when spin-orbit coupling is included. The solid (black) and dashed (green) curves show the DOSs at 30 and 80 K, respectively. The gray shaded region lying above the energy zero (chemical potential) represents the band gap (∼2 meV) in the 30 K structure. (b) DOS for the ambient-pressure structure at 30 K [including the same data as the solid curve in (a) but plotted on a different scale]. (c) DOS for the experimental structure under a pressure of 0.7 GPa [24]. (d) DOS of $\alpha \text{−}{\left(\mathrm{ET}\right)}_2{\mathrm{I}}_3$ for 150 K (above the charge-ordering transition temperature). The zero energies in (a), (b), (d) are set to the tops of the valence bands; the zero energy in (c) is the Fermi energy $E_F$.