Two-Dimensional Moiré Polaronic Electron Crystals

Two-dimensional moiré materials have emerged as the most versatile platform for realizing quantum phases of electrons. Here, we explore the stability origins of correlated states in ${\mathrm{WSe}}_2/{\mathrm{WS}}_2$ moiré superlattices. We find that ultrafast electronic excitation leads to partial melting of the Mott states on timescales 5 times longer than predictions from the charge hopping integrals and that the melting rates are thermally activated, with activation energies of $18\pm 3$ and $13\pm 2\mathrm{meV}$ for the one- and two-hole Mott states, respectively, suggesting significant electron-phonon coupling. A density functional theory calculation of the one-hole Mott state confirms polaron formation and yields a hole-polaron binding energy of 16 meV. These findings reveal a close interplay of electron-electron and electron-phonon interactions in stabilizing the polaronic Mott insulators at transition metal dichalcogenide moiré interfaces.

Figure 1

${\mathrm{WSe}}_2/{\mathrm{WSe}}_2$ device ($\theta =60°$, D1): structure and characterization. (a) Schematic of the device showing the top (${\mathrm{V}}_{\mathrm{t}}$) and bottom (${\mathrm{V}}_{\mathrm{b}}$) gates consisting of few-layer graphite (Gr) and hexagonal boron nitride (hBN) encapsulating the ${\mathrm{WSe}}_2/{\mathrm{WS}}_2$ heterobilayer. (b) Optical image of the sample where the top and bottom gates are labeled, along with outlines showing the Gr electrodes (blue and orange lines corresponding to the top and bottom electrodes, respectively) and the ${\mathrm{WSe}}_2/{\mathrm{WS}}_2$ overlap region (white line). (c) Steady-state reflectance contrast mapping with the white line highlighting the ${\mathrm{WSe}}_2/{\mathrm{WS}}_2$ overlap region. $\mathrm{\Delta }R=R-R_0$; $R$ is the reflectance from the sample in the bilayer region and $R_0$ is reflectance from the sample stack without the bilayer. (d) Gated (${\mathrm{V}}_{\mathrm{g}}={\mathrm{V}}_{\mathrm{t}}={\mathrm{V}}_{\mathrm{b}}$) steady-state photoluminescence spectrum (with intensity shown on a logarithmic scale). (e) Gated (${\mathrm{V}}_{\mathrm{g}}={\mathrm{V}}_{\mathrm{t}}={\mathrm{V}}_{\mathrm{b}}$) steady-state reflectance spectrum of the lowest energy moiré exciton of ${\mathrm{WSe}}_2$. All data collected at 11 K.

Figure 2

Pump and probe of a hole Mott state in hole-doped ${\mathrm{WSe}}_2/{\mathrm{WS}}_2$. (a) Excitation of a hole (green) from the lower Hubbard band (LHB) to a deep valence state, with subsequent cooling of the photoexcited hole (green sphere) to the upper Hubbard band (UHB). The hole energy scale is opposite to that of an electron scale. (b) Real space representation of the holon-doublon pair for the hole (green spheres) Mott state, with corresponding state representation on the top of each cartoon. (c) Partial melting (disordering) and gap closing from holon-doublon excitation. (d)–(f) Transient reflectance spectra plotted as a function of probe energy (covering the first moiré exciton of ${\mathrm{WSe}}_2$) versus gate voltage (${\mathrm{V}}_{\mathrm{g}}={\mathrm{V}}_{\mathrm{t}}={\mathrm{V}}_{\mathrm{b}}$) at $\mathrm{\Delta }\mathrm{t}=2$, 8, 50 ps in (d)–(f), respectively. Features specific to the $v=-1$, $-2$ states can be observed and seen to evolve as a function of $\mathrm{\Delta }\mathrm{t}$. Here, $\mathrm{\Delta }R/R$ is the transient reflectance signal calculated from pump-on and pump-off spectra. The pump fluence employed for the transient measurements was $57\mathrm{\mu }\mathrm{J}/{\mathrm{cm}}^2$. All spectra collected at 11 K.

Figure 3

Temperature-dependent temporal response of correlated states. (a)–(c) Transient reflectance traces of the $v=0$, $-1$, $-2$ states, respectively, averaged over a $\sim 0.01\mathrm{eV}$ probe energy range about the maximum of the lowest energy moiré band of ${\mathrm{WSe}}_2$. The coherent artifact resulting from pump-probe overlap can be seen at $\mathrm{\Delta }\mathrm{t}=0\mathrm{ps}$. The time traces have been offset for clarity. The colors corresponding to each temperature are labeled in panel (a) and are consistent throughout the figure. The employed pump fluence was $14\mathrm{\mu }\mathrm{J}/{\mathrm{cm}}^2$. All data shown are for sample D1.

Figure 4

Polaronic nature of correlated states. (a) Temperature-dependent melting time (${\tau }_{\mathrm{m}}$) of the $v=-1$, $-2$ states resulting from the pump pulse. (b),(c) Melting rates, $k_m$, corresponding to panel (a). The dashed lines are fits to the Arrhenius equation to extract thermal activation energies for $v=-1$, $-2$ of $E_a=18\pm 3\mathrm{meV}$ and $13\pm 2\mathrm{meV}$, respectively. Constant offsets account for nonzero melting rates at lower temperatures. (d) Temperature-dependent transient reflectance for the $v=0$, $-1$, $-2$ states (shown in gray, green, purple, respectively). For each data point, the corresponding transient reflectance spectra was averaged over a $\sim 0.01\mathrm{eV}$ probe energy range about the maximum of the lowest energy ${\mathrm{WSe}}_2$ moiré exciton peak and averaged over a pump-probe delay of $\mathrm{\Delta }\mathrm{t}=4–8\mathrm{ps}$. All error bars indicate 99% confidence intervals. All data shown are for sample D1.

Figure 5

Ab initio charge-induced lattice distortion. Structural reorganization averaged over the atomic positions on each lattice point upon injection of a positive charge in an aligned ${\mathrm{WS}}_2/{\mathrm{WSe}}_2$ bilayer. The color scale represents the degree of distortion at each lattice position, $⟨{\mathbf{r}}_{\mathrm{h}}-{\mathbf{r}}_0⟩$.