Doping Asymmetry and Layer-Selective Metal-Insulator Transition in Trilayer ${\mathrm{K}}_{3+x}{\mathrm{C}}_{60}$

Thin films provide a versatile platform to tune electron correlations and explore new physics in strongly correlated materials. Epitaxially grown thin films of the alkali-doped fulleride ${\mathrm{K}}_{3+x}{\mathrm{C}}_{60}$, for example, exhibit intriguing phenomena, including Mott transitions and superconductivity, depending on dimensionality and doping. Surprisingly, in the trilayer case, a strong electron-hole doping asymmetry has been observed in the superconducting phase, which is absent in the three-dimensional bulk limit. Using density-functional theory plus dynamical mean-field theory, we show that this doping asymmetry results from a substantial charge reshuffling from the top layer to the middle layer. While the nominal filling per fullerene is close to $n=3$, the top layer rapidly switches to an $n=2$ insulating state upon hole doping, which implies a doping asymmetry of the superconducting gap. The interlayer charge transfer and layer-selective metal-insulator transition result from the interplay between crystal field splittings, strong Coulomb interactions, and an effectively negative Hund coupling. This peculiar charge reshuffling is absent in the monolayer system, which is an $n=3$ Mott insulator, as expected from the nominal filling.

Figure 1

Schematic phase diagram of three-orbital systems. (a) Generic phase diagram of an orbitally degenerate three-orbital Hubbard model with $J>0$. The black lines indicate the Mott insulating solutions with filling $n=2$, 3, and 4 and the white region a metallic solution. (b) Generic phase diagram of an orbitally degenerate three-orbital Hubbard model with $J<0$. The yellow area shows the stability region of the $s$-wave superconducting phase at low temperatures. (c) Modification of the phase diagram by a crystal field splitting $\mathrm{\Delta }E$ of the type two-up, one down, which favors the $n=2$ insulating state. (d) Surface layer of the trilayer system. The red arrows indicate that there is no solution in the corresponding filling region, because of interlayer charge transfer which results in $n=2$. The red star indicates the filling in the nominally undoped trilayer system. (e) STM measures the properties of the top layer.

Figure 2

Crystal structure and electronic structure of monolayer and trilayer ${\mathrm{K}}_3{\mathrm{C}}_{60}$ with graphene substrate. (a) Conventional unit cell of bulk ${\mathrm{K}}_3{\mathrm{C}}_{60}$. (b)–(c) [(d)–(e)] Top and side view of monolayer [trilayer] ${\mathrm{K}}_3{\mathrm{C}}_{60}$ with graphene substrate (honeycomb lattice). For better visualization, the bottom ($A$), middle ($B$) and top layer ($C$) of ${\mathrm{C}}_{60}$ in (b)–(e) are colored red, dark green, and blue, respectively. The primitive unit cell is marked by the rhombus in (b) and (d). The DFT (black) bands and their Wannier interpolations (violet) are shown in panels (f) for the monolayer and in panel (i) for the trilayer, respectively. The corresponding orbital-resolved DOS per spin for each layer are shown in panels (g) and (j)–(l), where the solid line with dark color shows the projected DOS for the lowest-energy orbital and the dot-dashed line with lighter color that for the degenerate higher-energy orbitals. Panels (h) and (m) plot the total DOS for the substrate in (c) and (d), respectively.

Figure 3

$\mathrm{DFT}+\mathrm{DMFT}$ results for the trilayer ${\mathrm{K}}_{3+x}{\mathrm{C}}_{60}+\mathrm{substrate}$ system at $T=50\mathrm{K}$, $U=0.7\mathrm{eV}$, $J=-0.03\mathrm{eV}$. (a) Fillings in the different layers and in the substrate ($S$) as a function of doping $x$. (b)–(d) Orbital-resolved fillings per spin $\sigma$ in the different layers as a function of $x$. (e)–(g) Orbital-resolved spectral weight per spin at $\omega =0$ in the different layers as a function of $x$.

Figure 4

$\mathrm{DFT}+\mathrm{DMFT}$ spectra for the trilayer ${\mathrm{K}}_{3+x}{\mathrm{C}}_{60}+\mathrm{substrate}$ system at $T=50\mathrm{K}$, $U=0.7\mathrm{eV}$, and $J=-0.03\mathrm{eV}$. (a)–(c) Momentum-resolved spectra $\log A(\mathbf{k},\omega )$ for doping $x=-0.1$, 0, and 0.1. $A$, $B$, and $C$ label the different layers and $S$ the substrate. (d) Corresponding orbital-resolved local spectra per spin $A_{\alpha \sigma }(\omega )$. The thick lines correspond to orbital 1 and the dashed lines to orbitals 2, 3.