Isospin polarized Chern insulator state of <i>C</i> = 4 in twisted double bilayer graphene

Abstract

A flat band with nearly zero dispersion can be created by twisting the relative orientation of van der Waals materials , leading to a series of strongly correlated states, such as unconventional superconductivity, correlated insulating state, and orbital magnetism. The bandwidth and topological property of electronic band structure in a twisted double bilayer graphene are tunable by an external displacement field. This system can be an excellent quantum simulator to study the interplay between topological phase transition and strong electron correlation. Theoretical calculation shows that the <inline-formula><tex-math id="M4">\begin{document}$ {C}_{2x} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230497_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230497_M4.png"/></alternatives></inline-formula> symmetry in twisted double bilayer graphene (TDBG) can be broken by an electric displacement field, leading the lowest conduction and valence band near charge neutrality to obtain a finite Chern number. The topological properties of the band and the symmetry breaking driven by the strong interaction make it possible to realize and regulate the old insulation state at low magnetic fields. Hence Chern insulator may emerge from this topological non-trivial flat band under strong electron interaction. Here, we observe Chern insulator state with Chern number 4 at filling factor <inline-formula><tex-math id="M5">\begin{document}$ \nu =1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230497_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230497_M5.png"/></alternatives></inline-formula> under a small magnetic field on twisted double bilayer graphene with twist angle 1.48<sup>. </sup>. Moreover, the longitudinal resistance shows a peak under a parallel magnetic field and increases with temperature or field rising, which is similar to the Pomeranchuk effect in <sup>3</sup>He. This phenomenon indicates that Chern insulator at <inline-formula><tex-math id="M6">\begin{document}$ \nu =1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230497_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230497_M6.png"/></alternatives></inline-formula> may originate from isospin polarization.