Mott-Enhanced Exciton Condensation in a Hubbard bilayer

TL;DR

The paper investigates exciton condensation in a half-filled two-layer Hubbard bilayer with intra-layer repulsion $U$ and inter-layer repulsion $V$, using Dynamical Mean-Field Theory to map the phase diagram and uncover how Mott localization influences EC. By solving the DMFT impurity problem with exact diagonalization and incorporating an excitonic bath, the authors identify a sizeable EC region that emerges near the Mott transition, with large $U$ extending EC into the $V<U$ regime due to enhanced inter-layer spin correlations. They further characterize the EC via a mapping to an attractive inter-layer model, extracting the superfluid stiffness $D_S$ and coherence length $\xi$ to reveal a BCS–BEC crossover as pairing strengthens. These results highlight a mechanism where strong correlations and magnetism stabilize EC in bilayers and offer a framework applicable to more complex multi-orbital systems.

Abstract

We study the conditions to realize an excitonic condensed phase in an electron-hole bilayer system with local Hubbard-like interactions at half-filling, where we can address the interplay with Mott localization. Using Dynamical Mean-Field Theory, we find that an excitonic state is stable in a sizeable region of a phase diagram spanned by the intra-layer (U) and inter-layer (V) interactions. The latter term is expected to favour the excitonic phase which is indeed found in a slice of the phase diagram with V > U . Remarkably, we find that when U is large enough, the excitonic region extends also for U > V in contrast with naive expectations. The extended stability of the excitonic phase can be linked to in-layer Mott localization and inter-layer spin correlations. Using a mapping to a model with attractive inter-layer coupling, we fully characterize the condensate phase in terms of its superconducting counterpart, thereby addressing its coherence and correlation length.

Figures (4)

• Figure 1: Quasiparticle weight (top), intra-orbital density-density correlation (center) and inter-orbital density-density correlation (bottom), as a function of $V/D$ for $U/D=0.0$ (black), $2.0$ (green), $3.0$ (red) and $4.0$ (blue). Dotted lines are data in the normal state, solid lines mark the same quantities in the excitonic phase
• Figure 2: $V$ vs $U$ Ground State Phase Diagram. In yellow the region of EC phase, in orange the metallic phase, in blue the U-Mott insulator and in green the V-Mott one. The dashed lines with crosses symbols indicate the two Mott-transition boundaries in the normal state, while the gray dashed line highlight the $U=V$ line.
• Figure 3: Excitonic order parameter $\Delta_0$ (top), stiffness $D_s$(center) and coherence length $\xi$ for (from left to right) $U/D=0.0$, $2.0$, $3.0$, $4.0$ with the same color codes of Fig. 1. The vertical dashed line indicate the first order Metal-EC phase transition.
• Figure 4: Local magnetic moments (intra-orbital spin correlations) (top) and inter-orbital magnetic correlation (bottom). Dotted and solid lines indicate, respectively, the normal and the excitonic phase solution. Data are for $U/D=0.0$ (black), $2.0$ (green), $3.0$ (red) and $4.0$ (blue).