Competing Zero-Field Chern Insulators in Superconducting Twisted Bilayer Graphene

The discovery of magic angle twisted bilayer graphene has unveiled a rich variety of superconducting, magnetic, and topologically nontrivial phases. Here, we show that the zero-field states at odd integer filling factors in $h$-BN nonaligned devices are consistent with symmetry broken Chern insulators, as is evidenced by the observation of the anomalous Hall effect near moiré cell filling factor $\nu =+1$. The corresponding Chern insulator has a Chern number $C=\pm 1$ and a relatively high Curie temperature of $T_c\approx 4.5\mathrm{K}$. In a perpendicular magnetic field above $B>0.5\mathrm{T}$ we observe a transition of the $\nu =+1$ Chern insulator from Chern number $C=\pm 1$ to $C=3$, characterized by a quantized Hall plateau with $R_{yx}=h/3e^2$. These observations demonstrate that interaction-induced symmetry breaking leads to zero-field ground states that include almost degenerate and closely competing Chern insulators, and that states with larger Chern numbers couple most strongly to the $B$ field. In addition, the device reveals strong superconducting phases with critical temperatures of up to $T_c\approx 3.5\mathrm{K}$. By providing the first demonstration of a system that allows gate-induced transitions between magnetic and superconducting phases, our observations mark a major milestone in the creation of a new generation of quantum electronics.

Figure 1

(a) Optical image and transport measurement setup of the MATBG device. (b) Top: color map $R_{xx}$ vs $n$ and $T$ shows the coexistence of SC, CI, and CCI states. BI denotes band insulators. Bottom: $R_{xx}$ and $R_{yx}$ vs $n$ line traces at 20 mT show gate induced transitions between the SC and CCI states, with the inset showing the zero-resistance state of the SC. (c) $R_{xx}$ vs $T$ of the SC at optimal doping $\nu =-2.16$, shows a $T_c=3.5\mathrm{K}$ (50% of normal resistance). (d) $d{V}_{xx}/dI$ vs $I$ vs $B$ in the SC state. (e) $R_{yx}$ and $R_{xx}$ vs $B$ taken for increasing and decreasing $B$ at $\nu =+0.84$. Hysteresis loops indicate an incipient Chern insulator $|C|=1$ with (f) showing its temperature dependence with a $T_C\sim 4.5\mathrm{K}$.

Figure 2

(a),(b) $R_{xx}$ and $R_{yx}$ vs $n$ and $B$. The phase space exhibits a zero-field CCI with $C=-1$ (green line) and a set of high-field CCI with $C=\pm 1$, $\pm 2$, and $\pm 3$ (blue lines). We observe the full set of Chern insulators emanating from partial fillings of the superlattice unit cell $(\nu ,C)=(\pm 1,\pm 3)$, $(\pm 2,\pm 2)$, $(\pm 3,\pm 1)$. (c) Schematic image of (a),(b). Solid lines mark well developed CCIs, whereas dashed lines show other quantum Hall states.

Figure 3

Phase diagram of MATBG in a $B$ field. Large $B$ field favors states with the largest Chern number, which exhibit the maximum valley polarization allowed by the filling. At low $B$, the system undergoes phase transitions from the high-field ground states. While for $\nu =0$ and $\pm 2$, the many-body states are CCIs with $C=0$ which exhibit intervalley coherence, at $\nu =\pm 3$, there is strong competition between a $C=\pm 1$ and several $C=0$ translational or rotational symmetry broken states. Experimentally, no CCI is obtained at this filling, indicating that the CDW or nematic states win. At filling $\nu =\pm 2$, the ground state switches from $|C|=2$ in high field to $C=0$ at low field, in agreement with experiment. Nontrivially, at $\nu =\pm 1$, the ground state switches from $|C|=3$ in high field to $|C|=1$ in low field. Dark blue lines above $B_1$ show valley polarized CCI states. PIVC denotes partially intervalley coherent and IVC—intervalley coherent states.

Figure 4

(a) $R_{yx}$ vs $B$ taken along the green line in (b). (b) $R_{yx}$ vs $n$ and $B$ close to $\nu =+1$. A CCI zero-field CCI with $C=-1$ and a high-field CCI with $C=3$ (white line). (c) $R_{yx}$ and $R_{xx}$ vs $n$ taken at $B=2.5\mathrm{T}$ shows fully quantized $h/3e^2$ plateau. (d) AHE resistance $\mathrm{\Delta }{R}_{yx}/2$ vs $n$ and $B$ where green and blue symbols show coercive field values. (e) $R_{yx}$ vs $B$ line traces taken at corresponding $n$ in (d). (f),(g) Schematics of the $C=-1$ and $C=+3$ states at filling $\nu =+1$. For $C=-1$, we propose a partially intervalley coherent state, while for $C=+3$ a valley polarized state.