Possible Wigner states in CrI3 heterostructures with graphene: A tight-binding model perspective

In this study, we present an effective tight-binding model for an accurate description of the lowest energy quadruplet of a conduction band in a ferromagnetic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>Cr</a:mi><a:msub><a:mi>X</a:mi><a:mn>3</a:mn></a:msub></a:mrow></a:math> monolayer, tuned to the complementary density functional theory simulations. This model, based on a minimum number of chromium orbitals, captures a distinctively flat dispersion in those bands but requires taking into account hoppings beyond nearest neighbors, revealing ligand-mediated electron pathways connecting remote chromium sites. Doping of states in the lowest conduction band of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>Cr</b:mi><b:msub><b:mi>X</b:mi><b:mn>3</b:mn></b:msub></b:mrow></b:math> requires charge transfer, which, according to recent studies [Tenasini , ; Tseng , ; Cardoso , , can occur in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mrow><c:mi>graphene</c:mi><c:mo>(</c:mo><c:mi mathvariant="normal">G</c:mi><c:mo>)</c:mo></c:mrow><c:mo>/</c:mo><c:mi>Cr</c:mi><c:msub><c:mi>X</c:mi><c:mn>3</c:mn></c:msub></c:mrow></c:math> heterostructures. Here, we use the detailed description of the lowest conduction band in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:msub><e:mi>CrI</e:mi><e:mn>3</e:mn></e:msub></e:math> to show that <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mi mathvariant="normal">G</f:mi><f:mo>/</f:mo><f:msub><f:mi>CrI</f:mi><f:mn>3</f:mn></f:msub><f:mo>/</f:mo><f:mi mathvariant="normal">G</f:mi></f:mrow></f:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mi mathvariant="normal">G</i:mi><i:mo>/</i:mo><i:msub><i:mi>CrI</i:mi><i:mn>3</i:mn></i:msub></i:mrow></i:math> are type-II heterostructures where light holes in graphene would coexist with heavy electrons in the magnetic layer, where the latter can be characterized by Wigner-Seitz radius <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:msub><k:mi>r</k:mi><k:mi>s</k:mi></k:msub><k:mo>∼</k:mo><k:mn>25</k:mn><k:mo>−</k:mo><k:mn>35</k:mn></k:mrow></k:math> (as estimated for hBN-encapsulated structures). Published by the American Physical Society 2024