Correlated states in charge-transfer heterostructures based on rhombohedral multilayer graphene

TL;DR

The paper develops a comprehensive framework for charge-transfer heterostructures based on rhombohedral multilayer graphene (RMG) on insulating substrates with gate-tunable band alignment. It constructs a self-consistent electrostatic screening theory that includes a Fock correction, explaining the experimentally observed bent and broadened charge neutrality region. Depending on the substrate's carrier mass, the system hosts either Wigner-crystal–induced topological flat bands yielding Chern insulators at integer fillings, or an interlayer excitonic insulator stabilized by interlayer Coulomb coupling at charge neutrality. Together, these results establish charge-transfer heterostructures as a versatile platform for exploring correlated topological and excitonic states in van der Waals systems, with implications for tunable interlayer many-body phases.

Abstract

Charge transfer is a common phenomenon in van der Waals heterostructures with proper work function mismatch, which enables electrostatic gating to control band alignment and interlayer charge distributions. This provides a tunable platform for studying coupled bilayer correlated electronic systems. Here, we theoretically investigate heterostructures of rhombohedral multilayer graphene (RMG) and an insulating substrate with gate-tunable band alignment. We first develop a self-consistent electrostatic theory for layer charge densities incorporating charge transfer, which reproduces the experimentally observed broadened and bent charge neutrality region. When the substrate's band edge has a much larger effective mass than RMG, its carriers can form a Wigner crystal at low densities. This creates a quantum superlattice that induces topological flat bands in the RMG layer, which may lead to Chern insulators driven by intralayer Coulomb interactions. Conversely, with comparable effective masses, we find an interlayer excitonic insulator state at charge neutrality stabilized by interlayer Coulomb coupling. Our work establishes these charge-transfer heterostructures as a rich platform for topological and excitonic correlated states, opening an avenue for ``charge-transferonics''.

Figures (6)

• Figure 1: (a) Upper panel: schematic image of device and the interface electron crystal formed at the surface of substrate. Lower panel: schematic image of an interlayer exciton. (b) Non-interacting energy band of BLG modulated by interlayer superlattice potential. (c,d) Carrier densities of the RMG $n_{\text{g}}$ in a RMG-CrOCl heterostructures given in (c) for BLG-CrOCl and in (d) for TriLG-CrOCl. The black solid lines mark iso-doping levels in RMG.
• Figure 1: (a) Schematic illustration of the self-consistent screening model of vertical electric field applied to trilayer graphene-based charge transfer heterostructure. $\epsilon_r$ is the dielectric constant. $d_0$ denotes the interlayer distance between the surface of substrate and the bottom graphene layer of RMG while $d_g$ denotes the intrinsic interlayer distance of the RMG. (b) Calculated phase boundaries for BLG-CrOCl under three levels of theoretical treatment: with initial band alignment denoted by "Bare" (dotted lines), with dielectric screening included denoted by "Screening" (dashed lines), and with both screening and Fock energy correction incorporated denoted by "Screening+Fock" (solid lines). The green, blue, and red curves denote, respectively, the phase boundaries separating (i) non-charge-transfer and charge-transferred regions, (ii) the hole-doped and CNP regions, and (iii) the CNP and electron-doped regions.
• Figure 2: HF single particle spectra for HF ground state of BLG: (a) at $E_\text{ext}=-0.2375$$\text{V}/\text{nm}$ and $n_\text{tot}= 1.48\times10^{12}$ cm$^{-2}$ with filling factor $\nu=1$; and (b) at $E_\text{ext}=-0.25$$\text{V}/\text{nm}$ and $n_\text{tot}= 1.48\times10^{12}$ cm$^{-2}$ with filling factor $\nu=2$. The HF ground states along iso-filling lines $\nu=1$ and $\nu=2$ are shown in (c) for BLG-CrOCl, and in (d) for TriLG-CrOCl, where color coding represents carrier density $n_\text{g}$ of RMG, "CI" denotes Chern insulator state.
• Figure 2: Phase diagrams of the Chern number for the LCB of BLG-CrOCl (a) and TriLG-CrOCl (b), computed using the effective continuum model of RMG with parameters renormalized via the RG approach. The green solid line represent the phase boundary between no charge transfer region and charge transfer region. The non-zero Chern number $|C|=1$ region is marked by light orange. The shaded regions correspond to parameters where the lowest conduction band (LCB) has a direct gap separating it with high-energy bands $\lessapprox 1$ meV, precluding a well-defined Chern number in numerical evaluation due to finite mesh. Along iso-filing lines with filling factors $\nu=1$ and $\nu=2$, however, the LCB is well isolated, enabling unambiguous evaluation of its topological invariant.
• Figure 3: (a) HF ground state phase diagram of BLG-substrate heterostructure. Insets at lower left corner and upper right corner schematically show the band structures of metallic state and band insulator state, respectively. Green lines and black lines denote substrate's and BLG's bands, respectively. (b) HF ground state phase diagram of TriLG-substrate heterostructure. (c) HF single particle spectrum of IEI state with $E_{\text{CBM}} = -70$ meV and effective mass $m^*=0.05m_0$. (d) Substrate's carrier density $n_\mathrm{sub}$ as a function of $m^*/m_0$ with $E_\mathrm{CBM}^0=-100$ meV.