Gate and carriers tunable valley imbalance in topological proximitized rhombohedral trilayer graphene

We investigated the electronic structure, Fermi surface topology and the emergence of valley imbalance in rhombohedral trilayer graphene induced by the topological proximity and the electric fields. We show that, a strong proximity strength isolates the unperturbed low energy bands at the charge neutrality and the isolated topological bands show metallic nature under the influence of applied electric fields. Our calculations indicate that valley-resolved metallic states with a finite Chern number|C|=3can appear near charge neutrality for appropriate electric fields and second-nearest-neighbor strengths. The Fermi surface topology of these metallic bands greatly influenced by the applied electric fields and carrier doping. The valley imbalance lead to the dominant carriers of eithere-orh+Fermi surface pockets and the choice of carriers is subjected to the direction of electric fields. The gate-tunable and carrier-induced valley imbalance in topologically proximated RTG may have potential applications toward the realization of superconductivity.