Spatially Indirect Exciton Condensation in Two-Dimensional Strongly Correlated Semimetals

Abstract

Identifying materials hosting an excitonic insulator ground state has been one of the major pursuits in condensed matter physics in recent years. Promising candidates in transition metal chalcogenide compounds (TMC), including $1T-\mathrm{TiSe_2}$, $\mathrm{Ta_2Pd_3Te_5}$, and $\mathrm{Ta_2NiSe_5}$, share a crucial common characteristic: their low-energy physics is governed by electrons in $d-$ orbitals subject to strong on-site Coulomb interactions. In this work, we investigate spatially indirect exciton condensation in two-dimensional semimetals on triangular lattice. Using a combination of dynamical mean-field theory and the determinant quantum Monte Carlo method, we study two- and three-orbital Hubbard models incorporating strong on-site ($U$) and inter-orbital interactions ($V$). Our results demonstrate that on-site Hubbard $U$ can strongly suppress the condensation temperature $T_c$, an effect that is particularly pronounced at higher electron-hole pair densities. This behavior contrasts sharply with the case without on-site $U$, where $T_c$ grows with pair density at fixed $V$. Moreover, we uncover competition among multiple electron-hole pairing channels in the three-orbital model, which also acts to suppress $T_c$ of exciton condensation. An orbital-selective electron-hole pairing state is identified. These findings may help explain the large discrepancy between strong binding-energy and relative low transition temperature for indirect excitons in TMCs materials, offering important insights for understanding and engineering exciton condensation in materials with strongly correlated $d-$ shell electrons.

Figures (6)

• Figure 1: (a) Schematic illustration of the two-orbital (two-layer) Hubbard model on 2D triangular lattice. $U$ represents the on-site intra-orbital(intra-layer) Coulomb interaction, while $V$ denotes the inter-orbital (inter-layer) Coulomb interaction in a unit cell. The orbital/layer $a$ (upper) is designated as electron-active, while orbital/layer $b$ (lower) acts as hole-active. Dotted line indicates a possible electron--hole pairing. (b) Schematic illustration of the non-interacting band structure we use which is a semimetal at $U=0, V=0$. Red (black) curves indicate the conduction (valence) bands. The pairing of holes at the CB bottom (red hollow circles) and electrons at the VB top (black filled circles) leads to the formation of indirect excitons. Dashed line indicates Fermi level.
• Figure 2: The inverse susceptibility $1/\chi$ as a function of temperature $T$. When $1/\chi$ approaches zero, the system enters the excitonic condensate phase, and the corresponding temperature is defined as the critical transition temperature $T_c$. Here, $U_a=U_b=1,V=4$, density, $\langle n_a \rangle= 0.2, \langle n_b \rangle = 0.8$ (thus $n_e = n_h = 0.2$). An excitonic condensation $T_c$ is found about $T_c \sim 0.07$. The DQMC calculations were performed on a $4 \times 4 \times 2$ lattice, while DMFT calculations were performed on $1 \times 2$- and $12 \times 2$-site clusters.
• Figure 3: Transition temperature $T_c$ as a function of the inter-orbital interaction $V$ for different values of the on-site interaction $U_a=U_b\equiv U$. Here, electron-hole density is fixed at $n_e = n_h=0.06$, the data points represent results for $U=0$ (red circles) and $U=4$ (blue circles). The dashed lines depict fits to the BCS scaling trend, $T_c = A e^{-B/V}$, while shaded ribbons indicate the corresponding confidence intervals. The extracted fitting parameters are $A \approx 5.73$, $B \approx 19.28$ for the non-interacting case ($U=0$) and $A \approx 7.59$, $B \approx 25.90$ for the interacting case ($U=4$).
• Figure 4: Transition temperature $T_c$ as a function of the on-site Coulomb interaction $U$ at different values of inter-orbital interaction $V$. Orange symbols correspond to $V=5$, while blue symbols correspond to $V=4$. Here $n_e = n_h = n = 0.06$. $1 \times 2-$ site CDMFT is used here.
• Figure 5: Transition temperature $T_c$ as a function of the electron--hole density at different values of the on-site interaction $U$. The inter-orbital interaction is fixed at $V=5$, while the intra-orbital interaction is set to $U=0$ (green line) and $U=8$ (orange line). $1 \times 2-$ site CDMFT is used here.