Chern mosaic and ideal flat bands in equal-twist trilayer graphene

Abstract

We study trilayer graphene arranged in a staircase stacking configuration with equal consecutive twist angle. On top of the moiré crystalline pattern, a supermoiré long-wavelength modulation emerges that we treat adiabatically. For each valley, we find that the two central bands are topological with Chern numbers <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>C</a:mi><a:mo>=</a:mo><a:mo>±</a:mo><a:mn>1</a:mn></a:mrow></a:math> forming a Chern mosaic at the supermoiré scale. The Chern domains are centered around the high-symmetry stacking points ABA or BAB and they are separated by gapless lines connecting the AAA points where the spectrum is fully connected. In the chiral limit and at a magic angle of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>θ</b:mi><b:mo>∼</b:mo><b:mn>1</b:mn><b:mo>.</b:mo><b:msup><b:mn>69</b:mn><b:mo>∘</b:mo></b:msup></b:mrow></b:math>, we prove that the central bands are exactly flat with ideal quantum curvature at ABA and BAB. Furthermore, we decompose them analytically as a superposition of an intrinsic color-entangled state with <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mo>±</c:mo><c:mn>2</c:mn></c:mrow></c:math> and a Landau level state with Chern number <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mo>∓</d:mo><d:mn>1</d:mn></d:mrow></d:math>. To connect with experimental configurations, we also explore the nonchiral limit with finite corrugation and find that the topological Chern mosaic pattern is indeed robust and the central bands are still well separated from the remote bands. Published by the American Physical Society 2024

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