Stability of the Mott phase in excitonic double layers

Abstract

We study the stability of excitonic Mott phases in the presence of a periodic potential and a non-local exciton-exciton interaction. The non-local interaction is treated in a mean-field approximation, while the local repulsion of the excitons is treated in a hopping expansion. The convergence of the latter is the criterion for the stability of the Mott phase with respect to quantum and thermal fluctuations. This hybrid approach enables us to establish a phase diagram for a bosonic Mott to superfluid transition. Our results could be useful to interpret recent experiments on electron-hole crystals in van der Waals heterostructures.

Figures (3)

• Figure 1: Schematic of the formation of an electron-hole gas in two parallel layers separated by distance $D$, where the electrons reside in one, the holes in the other layer. Due to the electron-hole Coulomb attraction, indicated by the green lines, the electrons and holes form indirect excitons. The stability of the system requires an energy minimum. However, quantum fluctuations tend to destroy a spatial ordering.
• Figure 2: The density $n_{\bf r}$ of the excitonic Mott insulator in the presence of a periodic potential with honeycomb structure $V_{\bf r}=\cos y+\cos(\sqrt{3}x/2+y/2)+\cos(\sqrt{3}x/2-y/2)$ (top panel): a) for $\beta\mu=-10$ and b) for $\beta\mu=10$. $n_{\bf r}$ is calculated with Eq. (\ref{['hc_mf2']}) for $U_{{\bf r}-{\bf r}'}=0$.
• Figure 3: Phase diagram from the hopping expansion of the HCB gas. The Mott insulator exists above the phase boundaries for the honeycomb lattice, the square lattice and the triangular lattice, respectively, which obeys the inequality (\ref{['condition2']}). The dimensionless chemical potential $\beta{\hat{\mu}}$ on the vertical axis is obtained as ${\hat{\mu}}=\min_{\bf r}(\mu_{\bf r})$. The straight dashed red line is the phase boundary when the kinetic energy versus interaction energy obey the condition $\beta J<\beta{\hat{\mu}}$ for the Mott phase.