Interband effects of magnetic field on Hall conductivity in the multilayered massless Dirac fermion system $\alpha$-(BEDT-TTF)${}_2$I${}_3$

We have discovered a two-dimensional zero-gap material with a layered structure in the organic conductor $\alpha$-(BEDT-TTF)${}_2$I${}_3$ under high hydrostatic pressure. In contrast to graphene, the electron-hole symmetry is not good except at the vicinity of the Dirac points. Thus, the temperature dependence of the chemical potential $\mu$ plays an important role in the transport in this system. The experimental formula of $\mu$ is revealed. We succeeded in detecting the interband effects of a magnetic field on the Hall conductivity when $\mu$ passes the Dirac point.

Figure 1

(a) Temperature dependence of $R_S$ for seven samples under a pressure of 1.8 GPa. The inset $R_S$ at temperatures below 10 K. (b) Temperature dependence of $R_S$ for sample 6. It was examined down to 80 mK. The inset shows the crystal structure of $\alpha$-(BEDT-TTF)${}_2$I${}_3$ viewed from the $a$ axis.

Figure 2

Temperature dependence of the Hall coefficient for (a) hole-doped-type and (b) electron-doped-type samples. Note that in this figure, the absolute value of $R_H$ is plotted. Thus, the dips in (b) indicate a change in the polarity. The inset in the upper part of (a) shows the configuration of the six electrical contacts. The schematic illustration of the Fermi levels for the hole-doped type and the electron-doped type are shown in the inset of the lower part of (a) and the inset of (b), respectively.

Figure 3

(a) Sheet electron density $n_S$ for five samples plotted against temperature at $R_H=0$. (b) $E_F$ was estimated from the relationship $n_S=E_F^2/\left(4\pi {\hslash }^2{v}_F^2\right)$ with $v_{\mathrm{F}}\sim 3.3\times {10}^4$ m/s. From this curve, the temperature dependence of $\mu$ is written approximately as $\mu /k_{\mathrm{B}}=E_F/k_B-AT$ with $A\sim 0.24$ when we assume $A$ is independent of $E_F$. (c) Temperature dependence of $\mu$ for $E_F=0$. Our experimental formula is quantitatively consistent with the theoretical curve of Kobayashi et al.[22] at temperatures below 100 K.

Figure 4

(a) Temperature dependence of the Hall conductivity for samples 1 and 7. (b) Chemical-potential dependence of the Hall conductivity for samples 1 and 7. Solid lines and dashed lines are the theoretical curves with and without the interband effects of the magnetic field by Kobayashi et al., respectively.[22]