Gate and Carriers tunable Valley Imbalance in Topological Proximitized Rhombohedral Trilayer Graphene

TL;DR

This work demonstrates that topological proximity to a Haldane layer in rhombohedral trilayer graphene can induce valley-imbalanced, metallic states near charge neutrality and engineer nontrivial band topology. By employing a tight-binding framework that includes RTG, a Haldane layer, and interlayer couplings, the authors map Chern-number transitions as functions of the interlayer bias $\Delta$, proximity strength $\alpha$, and NNN hopping $t_2'$, revealing Chern numbers up to $|C|=3$. The study shows that the resulting Fermi surfaces are highly tunable, transitioning among single, annular, and pocket-like shapes depending on $\Delta$ and carrier density, with valley dominance controlled by the field direction. In multilayer RTG, valley imbalance persists across 2L–4L, accompanied by layer-dependent orbital magnetization that scales with energy and layer count, underscoring robust valley-specific physics with potential links to superconductivity via unconventional pairing channels. These findings highlight gate-tunable valley control and topological phases in proximitized graphene platforms, offering a pathway to engineer novel quantum states.

Abstract

We investigated the electronic structure, Fermi surface topology and the emergence of valley imbalance in rhombohedral trilayer graphene (RTG) 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| =$3 can 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 either $e^-$ or $h^+$ 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 rhombohedral trilayer graphene may have potential applications toward the realization of superconductivity.

Figures (10)

• Figure 1: A schematic diagram of rhombohedral trilayer graphene (RTG) aligned on a Haldane layer ($\rm RTG/\tilde{\rm G}$). The gray-filled circles labeled (A1, B1), (A2, B2), and (A3, B3) represent the two sublattices of each graphene layer in RTG. The integer index of each sublattice denotes the layer index. Intra-layer hopping within RTG is represented by $t_0$, while inter-layer coupling is represented by $t_i$ ($i = 1, 2, 3, 4$). The black-filled circles H1 and H2 represent the two distinct sublattices of the Haldane layer. Intra-layer hopping within the Haldane layer is represented by $t^{\prime}_0$, and inter-layer hopping between the Haldane layer and the proximity layer of RTG is represented by $t^{\prime}_1$ and $t^{\prime}_4$. The next-nearest-neighbor (NNN) complex hopping process in the Haldane layer is represented by $t_2^{\prime}e^{i\phi}$.
• Figure 2: Low energy band structures of RTG/$\tilde{\rm G}$ (a) for different values of $\alpha$ with $\Delta=$ 0 and $t_2^{\prime}=$ 0.1 eV. (b) for different values of $\alpha$ and $t_2^{\prime}$ with $\Delta=$ 50 meV and (c) for different values of $\Delta~(meV)$ with $t_2^{\prime}=$ 0.1 eV and $\alpha=$ 1.
• Figure 3: Chern phase diagram of the $\rm{VB1}$ as a function of (a) $\Delta$ and $\alpha$ with $t_2^{\prime}=0.1$ eV, (b) $\alpha$ and $t_2^{\prime}$ with $\Delta =$ 50 meV and (c) $\Delta$ and $t_2^{\prime}$ with $\alpha =$ 1.
• Figure 4: The low energy bands and the Fermi surfaces of RTG/$\tilde{G}$ for applied $\Delta$ and carriers doping. Different possible Fermi surface topology with $e^-$ (red region) and $h^+$ (blue region) carrier fillings for different $E_F$'s along with bands. (a-b) for $\Delta>0$ and (c-d) for $\Delta<0$.
• Figure 5: (a) DOS as a function of density ($n$) and interlayer potential difference ($\Delta$) with $t_2^{\prime} =$ 0.1 eV. (b) The Fermi surfaces of the competing states are representing at [$n~(10^{12}~cm^{-2}),\Delta$ (meV)], i.e., (1) [0.16,0], (2) [-5.5,25], (3) [-4.5,60], (4) [-3.1,60], (5) [-2.7,60], (6) [-2.5,25], (7) [-1.6,25], (8) [-1.7,60], (9) [1.65,-20], (10) [2.4,-75], (11) [3.22,-75], (12) [5,-75]