Engineering Flat Bands in Twisted-Bilayer Graphene away from the Magic Angle with Chiral Optical Cavities

Twisted bilayer graphene (TBG) is a recently discovered two-dimensional superlattice structure which exhibits strongly correlated quantum many-body physics, including strange metallic behavior and unconventional superconductivity. Most of TBG exotic properties are connected to the emergence of a pair of isolated and topological flat electronic bands at the so-called magic angle, $\theta \approx 1.05°$, which are nevertheless very fragile. In this work, we show that, by employing chiral optical cavities, the topological flat bands can be stabilized away from the magic angle in an interval of approximately $0.8°<\theta <1.3°$. As highlighted by a simplified theoretical model, time reversal symmetry breaking (TRSB), induced by the chiral nature of the cavity, plays a fundamental role in flattening the isolated bands and gapping out the rest of the spectrum. Additionally, TRSB suppresses the Berry curvature and induces a topological phase transition, with a gap closing at the $\mathrm{\Gamma }$ point, towards a band structure with two isolated flat bands with Chern number equal to 0. The efficiency of the cavity is discussed as a function of the twisting angle, the light-matter coupling and the optical cavity characteristic frequency. Our results demonstrate the possibility of engineering flat bands in TBG using optical devices, extending the onset of strongly correlated topological electronic phases in moiré superlattices to a wider range in the twisting angle.

Figure 1

Top panel. A cartoon of the optical setup considered in this work. Two skewed sheets of graphene are stacked on top of each other with a twisting angle $\theta$ creating a characteristic moiré pattern. They are then put inside a chiral optical cavity with a light-matter coupling $g$ and a characteristic frequency ${\omega }_c$. Bottom panel. The dominant Feynman diagram describing light-matter interactions in the optical chiral cavity and giving rise to the self-energy ${\mathrm{\Sigma }}_0(\epsilon ,\mathbf{q})$.

Figure 2

The spectral function $A(\epsilon ,q)$ showing the band structure of TBG with different light-matter coupling strength $g$ and twisting angle $\theta$. (a): $\theta =0.8°$, $\tilde{g}=0$; (b): $\theta =0.8°$, $\tilde{g}=2$; (c): $\theta =1.5°$, $\tilde{g}=0$; (d): $\theta =1.5°$, $\tilde{g}=2.5$. The optical cavity characteristic frequency is fixed to ${\omega }_c=0.3\mathrm{eV}$.

Figure 3

The band structure of TBG at $\theta =1.5°$ obtained from the deformed Hamiltonian in Eq. (10). Panels (a),(b),(c),(d), respectively, correspond to an increasing value for the time reversal breaking parameter $\tau =0$, 0.05, 0.15, 0.2. The color scheme on top of the electronic bands in panels indicates the value of the reduced Berry curvature, and the integer numbers the Chern number of the lowest bands.

Figure 4

The value of the energy bandwidth $\mathrm{\Delta }\epsilon (\tilde{g},\theta )$ for different $\tilde{g}$ and $\theta$. Darker color corresponds to a flatter band. The black solid lines indicate a few constant $\mathrm{\Delta }\epsilon$ values as reference. The optical cavity frequency is set to ${\omega }_c=0.3\mathrm{eV}$.