Unconventional Flat Chern Bands and 2<i>e</i> Charges in Skyrmionic Moiré Superlattices.

Abstract

The interplay of topological characteristics in real space and reciprocal space can lead to the emergence of unconventional topological phases. In this Letter, we implement a novel mechanism for generating higher-Chern flat bands on the basis of twisted bilayer graphene (TBG) coupled to topological magnetic structures in the form of the skyrmion lattice. In particular, we discover a scenario for generating |<i>C</i>| = 2 dispersionless electronic bands when the skyrmion periodicity and the moiré periodicity match. Following the Wilczek argument, the statistics of the charge-carrying excitations in this case is bosonic, characterized by electronic charge <i>Q</i> = 2<i>e</i>, which is even in units of electron charge <i>e</i>. The skyrmion coupling strength triggering the topological phase transition is realistic, with its lower bound estimated as 4 meV. The Hofstadter butterfly spectrum results in an unexpected quantum Hall conductance sequence <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>±</mo><mfrac><mrow><mn>2</mn><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mi>h</mi></mrow></mfrac><mo>,</mo><mo>±</mo><mfrac><mrow><mn>4</mn><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mi>h</mi></mrow></mfrac><mo>,</mo><mo>...</mo></math> for TBG with the skyrmion order.