Real-Space Switching of Local Moments Driven by Quantum Geometry in Correlated Graphene Heterostructures

TL;DR

The paper proposes a decorated graphene platform in which Dirac bands hybridize with localized orbitals to produce a correlated flat band with strong quantum geometry. A hybridization-controlled topological transition occurs between two symmetry-distinct site-selective Mott states, separated by a geometrically stabilized metallic phase, as reflected by Green's function zeros (the Luttinger surface) rather than conventional poles. The authors validate the mechanism in a minimal 1×1 model and in a 2×2 real-space cell, and corroborate it with DFT and DFT+DMFT calculations for graphene/X/SiC(0001) structures using group-IV intercalants, showing robust moment switching between Wyckoff sites as $V$ is tuned. The work highlights that quantum geometry—encoded in the quantum metric and Luttinger surface—controls Mottness at high energy scales, offering a pathway to higher-temperature correlated states in chemically functionalized graphene and connections to topological heavy-fermion physics in moiré systems.

Abstract

Graphene-based multilayer systems serve as versatile platforms for exploring the interplay between electron correlation and topology, thanks to distinctive low-energy bands marked by significant quantum metric and Berry curvature from graphene's Dirac bands. Here, we investigate Mott physics and local spin moments in Dirac bands hybridized with a flat band of localized orbitals in functionalized graphene. Via hybridization control, a topological transition is realized between two symmetry-distinct site-selective Mott states featuring local moments in different Wyckoff positions, with a geometrically enforced metallic state emerging in between. We find that this geometrically controlled real-space switching of local moments and associated metal-insulator physics may be realized through proximity coupling of epitaxial graphene on SiC(0001) with group IV intercalants, where the Mott state faces geometrical obstruction in the large-hybridization limit. Our work shows that chemically functionalized graphene provides a correlated electron platform, very similar to the topological heavy fermions in graphene moiré systems but at significantly enhanced characteristic energy scales.

Figures (15)

• Figure 1: Flat band hybridized to graphene. (a) Lattice structure of decorated graphene honeycomb lattice with impurity X hybridized to sublattice site A created with VESTA VESTA_Momma2011. Only hopping $t$ between sublattices A and B as well as $V$ between X and A exist. (b) Wyckoff positions and their respective local point symmetry groups for the wallpaper group $p3m1$ (No. 156) representing the geometry in panel a. (c) Orbital weight $w_m = \sum_{\bm{k}} |w_{\bm{k}m}|^2/N_{\bm{k}}$ ($m\in\lbrace\mathrm{A,B,X}\rbrace$) with weight $|w_{\bm{k}m}|^2$ of the flat band crossing the Fermi level at $\bm{k}$, and minimal quadratic Wannier function spread $\Omega_{\mathrm{I}}$ as obtained from the quantum metric (c.f. Eq. (\ref{['eq:wf_spread_qgt']}) and panel e). (d) Band structure for different values of $V/t$. The orbital character of the X and graphene atoms (A+B) are colored in red and blue, respectively. (e) Quantum metric $\mathop{\mathrm{\mathrm{Tr}}}\nolimits g(\bm{k}) = g_{xx}(\bm{k}) + g_{yy}(\bm{k})$ of the band crossing the Fermi level for $V/t=0.5$ (left) and $V/t=3.0$ (right). Note the different magnitude of scales. The middle panels show corresponding Wannier functions which change the maxima from the X sites ($V/t=0.5$) to the B sites ($V/t=3.0$) by increasing $V$.
• Figure 2: Interacting decorated honeycomb model. (a) Momentum-resolved spectral functions from DMFT at $T/t=0.025$ and $U/t=1.6$. From left to right for hybridization $V/t=0.5$, $V/t=1.4$, and $V/t=4$. (b) The imaginary part of the local self-energy at the lowest Matsubara frequency of X (red), A (gray), and B (blue) as function of $V$.
• Figure 3: Hybridization control via proximity coupling of epitaxial graphene and group-IV triangular adatom lattices. From left to right, the DFT band structure for different group IV elements X$\in\!\!\lbrace$C, Si, Ge, Sn, Pb$\rbrace$ is shown with the weight of the X-$p_z$ and graphene-$p_z$ orbitals as fatband plots. For X = Ge, two close-in-energy configurations exist (c.f. Fig. \ref{['fig:DFT_structure']} in the End Matter) for which the band structure of the local minimum is additionally drawn with dashed lines and no orbital weight.
• Figure 4: Decorated graphene with smaller impurity density. (a) Unit cell of decorated graphene with 1/8 impurity X coverage. The index of sublattice sites A$_i$, B$_i$ refers to distance from the impurity X. (b) Imaginary part of the local self-energy at the lowest Matsubara frequency of X (red), cumulative A sites (gray), and cumulative B sites (blue) as function of $V$. Arrows indicate hybridization values estimated for different group IV atoms from fitting the DFT band structures (Fig. \ref{['fig3']}). Arrows for X = Ge at larger and smaller $V$ refer to the local and global energy minimum's configuration, respectively. (c) Momentum-resolved spectral functions from DMFT at $T/t=0.025$ and $U/t=1.6$. From left to right for hybridization $V/t=0.5$, $V/t=1.5$, and $V/t=4$.
• Figure 5: Structure of epitaxial graphene proximitized to group-IV triangular adatom lattices. (a, b) Top and side view of the graphene/X/SiC(0001) heterostructure with distance $\Delta z$ between the graphene layer and the intercalated X atom layer of group IV elements. The X atoms are in a $\sqrt{3}\times\sqrt{3}$ triangular lattice reconstruction on SiC(0001) and graphene is stretched in a $2\times2$ cell. (c) Energy as a function of layer distance $\Delta z$ for different group IV atoms. The minimum energy $E_{\mathrm{min}}$ is taken as zero and the minimum position is marked with an arrow. In case of X = Ge, two minima close in energy exist.