Emergence of Topological Electronic Crystals in Bilayer Graphene--Mott Insulator Heterostructures

Abstract

We predict a new class of topological electronic crystals in bilayer graphene-Mott insulator heterostructures. Interlayer charge transfer creates a charge neutral electron hole bilayer, in which itinerant carriers in graphene interact attractively with localized carriers from a flat Hubbard band. In the heavy fermion limit and dilute limit, this interplay leads to symmetry breaking crystalline phases stabilized not only by pure repulsion, but also by interlayer Coulomb attraction shaped by band topology. Using comprehensive Hartree Fock calculations, we uncover triangular, honeycomb, and kagome charge orders hosting different quantized anomalous Hall effects at moderate interlayer attraction.

Figures (5)

• Figure 1: (a) Schematic of the BLG–Mott insulator heterostructure, encapsulated by boron nitride (BN) layers. (b) Schematic density of states (DOS) of bilayer graphene (BLG) and the Mott insulator (MI), showing energy alignment and charge transfer: the BLG valence band is aligned with the MI upper Hubbard band. Filled regimes indicate occupied states. The band gap opened on BLG is due to displacement field. (c) Real-space depiction of itinerant electrons in BLG (blue curves) and localized electrons in the Mott layer (red dots), illustrating the coexistence of mobile and localized carriers forming a electron hole bilayer.
• Figure 2: (a) Single particle band structure of bilayer graphene (BLG) under the superlattice Coulomb potential induced by a triangular arrangement of electrons on the surface of the Mott insulator (MI). Flat bands near the Fermi level are observed. Solid (dashed) lines indicate bands from the $K$ ($K'$) valley. The displacement field $Dd$ on BLG is set to be 20 meV. (b) Self consistent Hartree Fock quasiparticle band structure at one-hole filling per superlattice unit cell, based on the bands in (a). The system forms a spin valley polarized state with a single isolated flat band. Blue (red) lines denote spin up (spin down) bands. (c) Valley Chern numbers $C_c$ and $C_v$ of the first conduction and valence minibands, respectively, for different $f$-electron superlattice configurations: triangular (T), honeycomb (H), and kagome (K). The variable $n$ denotes the electron–hole pair density; its sign indicates the direction of charge transfer ($n < 0$: electrons transfer from BLG to MI; $n > 0$: reverse). (d) Wilson loop spectrum of the isolated flat band shown in (b), confirming a quantum anomalous Hall insulator with nontrivial topology.
• Figure 3: Real-space carrier density profiles $\rho(\mathbf{r})\Omega_0$ obtained from self-consistent Hartree Fock calculations at fixed total electron–hole density $n=1.5 \times 10^{11}$ cm$^{-2}$. $\Omega_0$ is the unit cell size. White (grey) circles indicate localized electrons (holes) in the Mott insulator (MI). The first row (a–c) corresponds to electrons transferred from BLG to MI ($n<0$); the second row (d–f) corresponds to electrons transferred from MI to BLG ($n>0$). (a–c) Electrons on the MI form triangular, honeycomb, and kagome superlattices, leaving one, two, and three holes per unit cell in BLG, respectively. The displacement field on BLG is set to be 20 meV. The resulting states are: (a) a quantum anomalous Hall (QAH) insulator, (b) a band insulator (BI), and (c) another BI. (d–f) Reversed charge transfer, with BLG now hosting the electron crystal.The displacement field on BLG is set to be 12 meV. The resulting topological phases are: (d) BI, (e) quantum spin Hall (QSH) insulator, and (f) QAH insulator.
• Figure 4: Phase diagrams of electronic crystals as functions of the electron–hole pair concentration $n$ and displacement field strength $Dd$, for opposite charge transfer directions. Panels (a,b) correspond to charge transfer from the Mott insulator to BLG, while (c,d) correspond to the reverse direction. The compared energies are (a,c) the Hartree only energy $E_H$, and (b,d) the total energy including kinetic and Fock contributions, $E_T = E_H + E_{\mathrm{kin}} + E_F$. Colors denote the lowest energy phases, labeled by their lattice geometry and band topology: QAH: quantum anomalous Hall insulator ($C=1$); QSH: quantum spin Hall insulator ($C_s=1$); BI: band (correlated) insulator; AHM: anomalous Hall metal. The grey blocks in (c,d) labels metallic honeycomb crystal.
• Figure 5: Finite size scaling of the Hartree energy and total energy per electron hole pair for the case shown in Fig. \ref{['fig3']}, computed at different $k$-meshes. Panels (a,b) correspond to charge transfer from BLG to the MI ($n<0$), and (c,d) to the reverse direction ($n>0$). Energies are plotted as functions of $1/N_k$, where $N_k$ is the total number of $k$ points. Solid lines indicate linear extrapolations to the thermodynamic limit, with extrapolated values labeled in the legend.