Multiferroic Dark Excitonic Mott Insulator in the Breathing-Kagome Lattice Material Nb$_3$Cl$_8$

TL;DR

This work demonstrates that single-layer Nb$_3$Cl$_8$ hosts a dark spin-triplet Frenkel exciton as its ground state, located below the GW band gap by $-0.14$ eV and held together by a large binding energy of $2.64$ eV, signaling an excitonic Mott insulator in two dimensions. Bright excitons at $0.93$ eV and $1.21$ eV possess substantial binding energies ($2.05$ and $1.77$ eV) due to flat-band physics and reduced screening. Mapping the low-energy dynamics to a spin-1 Bose-Hubbard model on a triangular lattice reveals a 120$^ ext{o}$ spin-ordered ground state and strong electric dipole ordering with an out-of-plane orientation, driven by excitonic rather than electronic charge transfer mechanisms. The results indicate a pathway to 2D multiferroicity and strongly correlated exciton physics, with potential for enhanced nonlinear optical responses and tunable quantum phases via thickness control and external fields. Experimentally, ESR/EPR and thickness-dependent studies could validate the spin-1 exciton picture and the predicted dipolar ferroelectric order, while the approach provides a framework for exploring correlated excitonic states in breathing Kagome lattices.

Abstract

Flat electronic bands strongly enhance Coulomb interactions and can stabilize unconventional insulating states. Motivated by the recent discovery of flat bands in breathing Kagome lattices, we use first-principles GW--Bethe--Salpeter theory to investigate the excitonic spectrum of single-layer Nb$_3$Cl$_8$. We find a dark spin-triplet Frenkel exciton whose spectral peak lies at negative energy ($-0.14$~eV) relative to the quasiparticle gap, directly signaling a preformed bound state and an excitonic Mott insulating phase potentially stable at room temperature. Bright excitons appear at $0.94$~eV and $1.21$~eV, with ultra-large binding energies of $2.05$~eV and $1.77$~eV. By mapping the low-energy dynamics onto a spin-1 Hubbard model on a triangular lattice, we show that frustrated antiferromagnetic and ferroelectric tendencies naturally emerge. These results identify Nb$_3$Cl$_8$ as a candidate multiferroic dark excitonic insulator, opening a pathway to correlated quantum phases in two dimensions.

Figures (8)

• Figure 1: a) Top and side view of Nb$_3$Cl$_8$, shaded grey (orange) region (rhombus) is the unit cell (Brillouin zone) of Nb$_3$Cl$_8$ consisting of 3 Nb (dark green balls) and 8 Cl (light green balls) atoms. Breathing Kagome lattice is formed by Nb atoms creating irregular hexagons (black lines) with two sets of sides of different lengths, resulting in two sets of outer equilateral triangles with different areas (shaded red and blue). SL Nb$_3$Cl$_8$ has C$_{3v}$ symmetry. b) GW band structure of SL Nb$_3$Cl$_8$, showing substantial increase in the electronic band gap E$_g^{\textrm{GW}}=$2.27 eV as compared with the PBE band gap of E$_g^{\textrm{PBE}}=$0.27 eV, which is shown in the Supplementary Information (SI). Colored lines show flat bands. the blue (red) represents the up (down) spin component, with no preferential direction, as the flat bands are spin-polarized. Black solid lines correspond to the continuum of states with dispersion. Irreducible representations correspondinng to the energy levels at $\Gamma$ point are also shown as a$_1$ and e.
• Figure 2: a) The absorption spectra of SL Nb$_3$Cl$_8$, shown without (dashed black curve) and with (solid blue curve) electron-hole interactions, exhibit a prominent peak at 1.2 eV. This peak aligns remarkably well with experimental optical absorption measurements, highlighting the precision of the GW calculations. b) The oscillator strength f$_{ij}$ as a function of energy reveals key insights into the system's excitonic properties. The Bethe-Salpeter Equation (BSE) solution at E$_{\rm EMI}=-0.14$ eV, which corresponds to the IPA state at 2.5 eV, giving a binding energy of 2.64 eV, E$_{ev}<0$ exhibits clear signatures of an exciton insulator. In contrast, the first two bright exciton peaks can be seen at 0.93 eV and 1.2 eV with binding energies 2.05 eV and 1.77 eV, respectively.
• Figure 3: Molecular orbital configuration constructed in the Nb$_3$ trimer in Nb$_3$Cl$_8$. Blue (red) line show spin-up (spin-down) states with no preferential direction. Optical transition between VB and CB is forbidden because of the spin selection rules, which makes the ground state spin-triplet exciton dark. Black arrows show two of the optically allowed transitions between 2a$_1$ (VB) and 2e (CB+1), corresponding to the bright exciton at 0.93 eV, and between 1e (VB-1) and 2a$_1$ (CB), corresponding to the bright exciton at 1.2 eV (see Fig. \ref{['fig:BSE_fatbands']}).
• Figure 4: a) Fat bands obtained for the BSE ground state, corresponding to the eigenenergy of -0.14 eV (dark Frenkel exciton), are mapped onto the electronic band structure, helping to identify which electron-hole Bloch states contribute most significantly to the BSE eigenstate. Radius of the red (blue) circles show the amplitude in the exciton wavefunction. b) The exciton wavefunction distribution in real space for the dark Frenkel exciton ground state. c) Fat bands are mapped onto the electronic band structure for the bright exciton with eigenenergy 0.93 eV. d) The exciton wavefunction for the bright exciton at 0.93 eV. e) Fat bands are mapped onto the electronic band structure for the bright exciton with eigenenergy 1.2 eV. f) The exciton wavefunction for the bright exciton at 1.2 eV.
• Figure 5: There is one Frenkel exciton on each trimer of Nb atoms (dark green balls). Each Frenkel exciton carries an electric dipole (red arrows). The electric dipoles are oriented perpendicular to the plane of SL Nb$_3$Cl$_8$.