Theory of Correlated Chern Insulators in Twisted Bilayer Graphene

Magic-angle twisted bilayer graphene is the best-studied physical platform featuring moiré potential-induced narrow bands with nontrivial topology and strong electronic correlations. Despite their significance, the Chern insulating states observed at a finite magnetic field—and extrapolating to a band filling <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>s</a:mi></a:math> at zero field—remain poorly understood. Unraveling their nature is among the most important open problems in the province of moiré materials. Here, we present the first comprehensive study of interacting electrons in finite magnetic field while varying the electron density, twist angle, and heterostrain. Within a panoply of correlated Chern phases emerging at a range of twist angles, we uncover a unified description for the ubiquitous sequence of states with the Chern number <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>t</c:mi></c:math> for <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mo stretchy="false">(</e:mo><e:mi>s</e:mi><e:mo>,</e:mo><e:mi>t</e:mi><e:mo stretchy="false">)</e:mo><e:mo>=</e:mo><e:mo>±</e:mo><e:mo stretchy="false">(</e:mo><e:mn>0</e:mn><e:mo>,</e:mo><e:mn>4</e:mn><e:mo stretchy="false">)</e:mo></e:math>, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mo>±</k:mo><k:mo stretchy="false">(</k:mo><k:mn>1</k:mn><k:mo>,</k:mo><k:mn>3</k:mn><k:mo stretchy="false">)</k:mo></k:math>, <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mo>±</o:mo><o:mo stretchy="false">(</o:mo><o:mn>2</o:mn><o:mo>,</o:mo><o:mn>2</o:mn><o:mo stretchy="false">)</o:mo></o:math>, and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mo>±</s:mo><s:mo stretchy="false">(</s:mo><s:mn>3</s:mn><s:mo>,</s:mo><s:mn>1</s:mn><s:mo stretchy="false">)</s:mo></s:math>. We also find correlated Chern insulators at unconventional sequences with <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>s</w:mi><w:mo>+</w:mo><w:mi>t</w:mi><w:mo>≠</w:mo><w:mo>±</w:mo><w:mn>4</w:mn></w:math>, as well as with fractional <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>s</y:mi></y:math>, and elucidate their nature.