Programmable Quantum Anomalous Hall Insulator in Twisted Crystalline Flatbands

The isospin flavors in condensed matters can be continuously broken, forming various symmetry-broken quantum states. In moiré crystals, the competition between different isospin configurations can be effectively tuned by the twist angles and stacking orders. Here we report twisted double rhombohedral-trilayer-graphene as a new twisted crystalline flatband system showing rich moiré dependent topological phenomena. In devices with small twist angles, programmable Chern insulators with Chern number <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>C</a:mi> <a:mo>=</a:mo> <a:mn>3</a:mn> </a:mrow> </a:math> at integer moiré filling <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mi>v</c:mi> <c:mo>=</c:mo> <c:mn>1</c:mn> </c:mrow> </c:math> have been observed. We have further revealed an exotic hidden order which can quench the Chern insulator as well as multiple first-order transitions between different symmetry-broken phases. Interestly, in the device with a slightly larger twist angle, multiple Chern insulators with <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mrow> <e:mi>C</e:mi> <e:mo>=</e:mo> <e:mn>1</e:mn> </e:mrow> </e:math> at fractional moiré fillings including <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:mi>v</g:mi> <g:mo>=</g:mo> <g:mn>1</g:mn> <g:mo>/</g:mo> <g:mn>4</g:mn> </g:mrow> </g:math> , <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mrow> <i:mn>1</i:mn> <i:mo>/</i:mo> <i:mn>3</i:mn> </i:mrow> </i:math> , and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mrow> <k:mn>1</k:mn> <k:mo>/</k:mo> <k:mn>2</k:mn> </k:mrow> </k:math> have been observed, whereas the Chern insulator at <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mrow> <m:mi>v</m:mi> <m:mo>=</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> is absent. Our study demonstrated the twisted flatbands form rhombohedral-multilayer-graphene as a new platform to study tunable high Chern insulators as well as new devices for quantum storage and computation.