Recent experimental and theoretical works have revealed a strong analogy between (fractional) Chern insulators in multilayered moiré systems and (fractional) quantum Hall states, due to the emergence of a fictitious magnetic field in the former. We propose a simple interpretation of this magnetic field, attributing it to a real-space winding of the layer spinor in the electronic bands. Ideal Chern bands factorize into a lowest Landau level (LLL) and a spinor wave function. We generally demonstrate that the geometric phase arising from the skyrmionlike winding of the spinor compensates the LLL magnetic phase. The Skyrme texture persists in twisted bilayer graphene well beyond the chiral limit, under realistic corrugation condictions, making it an experimentally testable feature. We extend our findings for higher Chern numbers $\left|C\right|>1$, where we find $\left|C\right|$ color Landau levels carried by $\left|C\right|$ skyrmions. Their winding requires the number of layers $L$ to exceed the Chern number, $L\ge \left|C\right|+1$. Each skyrmion exhibits a Pontryagin winding index of $-1$. We verify our predictions at the first magic angle of twisted bilayer, trilayer, and monolayer-bilayer graphene.

Close

PrevNext

View figure in article

• Dirac fermions
• Geometric & topological phases
• Landau levels
• Non-Abelian gauge theories
• Graphene
• Twisted heterostructures