Insulating Nature of Strongly Correlated Massless Dirac Fermions in an Organic Crystal

Through resistivity measurements of an organic crystal hosting massless Dirac fermions with a charge-ordering instability, we reveal the effect of interactions among massless Dirac fermions on the charge transport. A low-temperature resistivity upturn appears robustly irrespective of the pressure and is enhanced while approaching the critical pressure of charge ordering, indicating that the insulating behavior originates from short-range Coulomb interactions. The observation of an apparently vanishing gap in the charge-ordered phase accords with the theoretical prediction of nontopological edge states.

Figure 1

Temperature dependence of the resistivity (a) and the corresponding Arrhenius plot (b) for $\alpha \text{−}(\mathrm{BEDT}\text{−}\mathrm{TTF}{)}_2{\mathrm{I}}_3$ under different pressures. The inset of (a) shows the crystal structure of $\alpha \text{−}(\mathrm{BEDT}\text{−}\mathrm{TTF}{)}_2{\mathrm{I}}_3$ viewed from the $c$ axis, namely, the $a\text{−}b$ in-plane structure, in the conducting state. The crystallographically inequivalent molecular sites $A$ ($A^{\prime }$), $B$, and $C$ comprise a unit cell as indicated by the square. The black crosses indicate the positions of the inversion centers.

Figure 2

(a) Pressure-temperature phase diagram. The different symbols indicate the charge-ordering temperatures $T_{\mathrm{CO}}$ determined from different crystals. For the definition of $T_{\mathrm{CO}}$, see the text. The solid line is a guide to the eye. $T_{\min }$ indicates the temperature at which the resistivity takes a minimum in the massless Dirac fermion state under pressures above 11 kbar. $T_{\mathrm{CO}}$ (red circles) and $T_{\min }$ are from the same sample. Regions I and II are discussed in the text. (b) Pressure dependence of the activation energy of the Arrhenius plot in Fig. 1. The filled and open red circles are from different surface places of the same crystal. The dashed line is a guide to the eye.

Figure 3

(a) Temperature dependence of the resistivity in the massless Dirac fermion state above 11 kbar. Sample 1 covers pressures up to 20 kbar (main panel). Sample 2 was measured at 25, 30, and 35 kbar, and sample 3 was used for the measurements at 40 kbar (inset). The bulk resistivity corresponding to the quantum sheet resistance, $C\times (h/e^2)=4.5\times {10}^{-3}\mathrm{\Omega }\mathrm{cm}$, is indicated, where $C=1.7\mathrm{nm}$ is the lattice constant along the $c$ axis 31] under a pressure of around 20 kbar. (b) Conductivity versus pressure for fixed temperatures above 11 kbar in the low-temperature region, where the resistivity upturn appears.