Quantum Anomalous Hall Insulator of Composite Fermions

We show that a weak hexagonal periodic potential can transform a two-dimensional electron gas with an even-denominator magnetic filling factor into an quantum anomalous hall insulator of composite fermions, giving rise to the fractionally quantized Hall effect. The system provides a realization of the Haldane honeycomb-net model, albeit in a composite fermion system. We further propose a trial wave function for the state, and numerically evaluate its relative stability against the competing Hofstadter state. Possible sets of experimental parameters are proposed.

Figure 1

(a) The schematic structure of the proposed device: a 2DEG confined in a quantum well or heterostructure, with both a back gate and a top gate. The top gap is patterned with an antidot array of a triangular lattice. The back and top gate voltages $V_{\mathrm{BG}}$ and $V_{\mathrm{TG}}$ can be independently tuned to control the electron density and modulation strength of the periodic potential $V_0$. A magnetic field $\mathit{B}$ is applied perpendicularly to the 2DEG. (b) The spatial profile of the periodic potential.

Figure 2

(a) Electron spectrum at magnetic filling factor $1/2$ in the presence of the hexagonal periodic potential with $V_0=0.08{\epsilon }_a$ [${\epsilon }_a\equiv h^2/(2m_b{a}^2)$] and ${\nu }_e=1$, projected to the $k_x$ axis. $L=0(1)$ denotes the index of the original Landau level, which is split into subbands in the presence of the periodic potential. (b) Projected CF spectrum at the same parameters. Inset: CF $\mathrm{\Lambda }$-level dispersion along the $\mathrm{\Gamma }\text{−}K\text{−}M\text{−}\mathrm{\Gamma }$ direction in the hexagonal Brillouin zone. The spectra are calculated using the periodic boundary condition.

Figure 3

(a) The Haldane honeycomb-net model with the next-nearest hopping and staggered magnetic flux. The next-nearest hopping constant gains a phase factor $\varphi =-2\pi (2{\mathrm{\Phi }}_a+{\mathrm{\Phi }}_b)/{\varphi }_0$, where ${\mathrm{\Phi }}_{a(b)}$ is the magnetic flux through the plaquette $a$ ($b$). (b) The distribution of the staggered magnetic field of a CF insulating phase at $V_0=0.08{\epsilon }_a$, $p=1$, and ${\nu }_e=1$.

Figure 4

CF metal-insulator phase diagrams in $V_0\text{−}{\mu }_{\mathrm{CF}}$ for (a) $p=1$ and (b) $p=2$. The cyan zones are insulating phases with integer band fillings ${\nu }_e$ marked in diagrams. In the phase diagrams, we keep the magnetic filling factor ${\nu }_M=1/2p$ fixed when tuning ${\mu }_{\mathrm{CF}}$ to control the electron density by matching the magnetic field strength to the density ($B=2p{n}_e{\varphi }_0$). All the insulating phases shown in the phase diagrams have a Chern number $\mathcal{C}=-1$.