Quantum Hall effect in multilayered massless Dirac fermion systems with tilted cones

A massless Dirac fermion ststem was realized in $\alpha$-(BEDT-TTF)${}_2$I${}_3$ [BEDT-TTF=bis(ethylenedithio)tetrathiafulvalene] under high pressure. In contrast to graphene, this is the first bulk (multilayered) massless Dirac fermion material. Another important difference from graphene is that this system has highly tilted Dirac cones. In this case, conventional chiral symmetry is broken under a magnetic field. Here we experimentally addressed the following question: Is the Landau level structure of the system with tilted Dirac cones the same as that of graphene [conventional two-dimensional (2D) Dirac fermion system] under a magnetic field? The answer is yes. We succeeded in injecting holes into $\alpha$-(BEDT-TTF)${}_2$I${}_3$ under high pressure. The detection of Shubnikov–de Haas oscillations whose phase was modified by Berry's phase $\pi$ is direct evidence that this system is truly a 2D Dirac fermion system. In addition, we revealed the energy diagram of this device and characterized the multilayered quantum Hall effect.

Figure 1

(a) Crystal structure of $\alpha$-(BEDT-TTF)${}_2$I${}_3$ viewed from the $a$ axis. (b) Band structure of $\alpha$-(BEDT-TTF)${}_2$I${}_3$ under pressure. Note that the origins of the axes are taken at the position of the Dirac point. (c) Schematic diagram of this system. The thickness of the crystal measured with a step profiler was approximately 100 nm. (d) Optical image of a single crystal on a PEN substrate in the processed form. The crystal was cut by using a pulsed laser beam with a wavelength of 532 nm. The scale bar is approximately 0.2 mm. (e) Schematic energy diagram of the present device. The energy spectra (Dirac cones) for the layers are drawn.

Figure 2

Temperature dependence of resistivity in multilayered Dirac fermion systems $\alpha$-(BEDT-TTF)${}_2$I${}_3$ with PEN substrates. The inset shows $\Delta \rho =\rho -{\rho }_0$ against $T^2$, where ${\rho }_0$ is the resistivity at the limit of $T=0$.

Figure 3

(a) Magnetic field dependence of $R_{xx}$, $R_{xy}$, and $-(d^2{R}_{xx}/d{B}^2)$ under the pressure of approximately 1.7 GPa. We find magnetoresistance oscillations with two frequencies at magnetic fields below 1.5 T (black arrows) and above 2 T (red arrows). We denote the oscillation $-(d^2{R}_{xx}/d{B}^2)$ minima by arrows. Note that the minimum at 4.2 T indicates spin splitting of the $N=-2$ Landau level. The inset shows the result of fast Fourier transform (FFT) analysis. On the other hand, the plateaus observed in $R_{xy}$ at magnetic fields of approximately 3.5 and 5.5 T show that $R_{xx}$ minima are the hallmarks of the QHE. (b) Value of $B^{-1}$ for the SdH oscillation minima. In the case of Dirac fermion systems, the linear extrapolation of the data to $B^{-1}=0$ should be 1/2. For normal electrons, on the other hand, it is shifted to 0. (c) Angle dependence of $B_f$. (d) Distribution of doped carrier density in the layered direction. The line is the curve of $n\left(z\right)\propto {(L_n+L)}^{-2}$ with $L=1$.

Figure 4

(a) Landau index $N$ or filling factor for first layer $|{\nu }_{\mathrm{first}}|$ dependence of $-(d^2{R}_{xx}/d{B}^2)$ and ${\sigma }_{xy}$.

Figure 5

$R_{xy}$ and $R_{xx}$ for several current intensities at 0.5 K. The insets show $R_{xy}$ of the regions from 2 to 3 T and from 3 to 4 T. The high intensities of the currents blur the plateaus and resistance minima.

Figure 6

(a) Schematic energy diagram of the present device at 5.5 T. The Landau levels for the layers are drawn. The total filling factor (Chern number) ${\nu }_{\mathrm{total}}={\nu }_{\mathrm{first}}+{\nu }_{\mathrm{second}}+\Sigma {\nu }_{\mathrm{undoped}}=-6-2+0=-8$ is expected. (b) $L_n$ dependence of ${\sigma }_{xx}^{\mathrm{sheet}}{L}_n$. (c) $L_n$ dependence of ${\sigma }_{xy}^{\mathrm{sheet}}{L}_n$. Fitting lines indicate that ${\sigma }_{xx}^{\mathrm{sheet}}{L}_n\sim 0$ and ${\sigma }_{xy}^{\mathrm{sheet}}{L}_n\sim 8e^2/h$ at the limit of $L_n=2$. Thus, the QHE with ${\nu }_{\mathrm{total}}=-8$ is truly realized at the magnetic field of approximately 5.5 T.