Dimensionality-Dependent Exciton Dispersion in a Single-Band Mott Insulator

Abstract

Excitonic band structure is critical for investigating exciton dynamics. Theoretically, quantum effects from exchange scattering between electron-hole pairs significantly modulate exciton dispersion. Here, we report the direct observation of dimensionality-dependent exciton dispersion in a single-band Mott insulator Nb3Cl8 through high-resolution electron energy loss spectroscopy. In the high-temperature phase, the exciton in Nb3Cl8 hosts an exceptionally large binding energy, and exhibits clear quasi-two-dimensional massless linear dispersion. In contrast, in the low-temperature phase, the exciton splits into two bands, both displaying three-dimensional parabolic dispersion. These dramatic changes in the exciton dispersion stem from the dimensional mutation driven by a substantial enhancement of interlayer coupling across the phase transition. This Letter provides a clear and typical example of how exciton behavior evolves with dimensionality.

Figures (5)

• Figure 1: Illustration of the dimensional effects of excitonic band dispersions. Schematic diagrams of (a) the crystal structures and (b) the corresponding excitonic band structure near the BZ center for typical 3D semiconductors. (c) Crystal structures and (d) the corresponding excitonic band structure for typical 2D semiconductors.
• Figure 2: Structural and electronic properties of Nb3Cl8. (a) Side view of the crystal structure and exciton distribution, and (b) the corresponding electronic energy band in the high-temperature phase ($\alpha$ phase) of Nb3Cl8. (c) Crystal structure and exciton distribution, and (d) the corresponding electronic energy band in the low-temperature phase ($\beta$ phase). (e), (f) Magnetic susceptibility as a function of temperature for Nb3Cl8 and Nb3Cl2Br6. (g) LEED pattern on the (001) surface of Nb3Cl8, obtained at room temperature with incident beam energy of $100$ eV. Notice that the electronic band structure in (b) and (d) are reproduced from ref. RN522. Copyright 2025 by the American Physical Society.
• Figure 3: Exciton splitting from the HREELS measurements. (a), (b) Representative 2D momentum-energy mappings of HREELS along the $\overline{{\rm \Gamma}}\overline{{\rm K}}$ direction for Nb3Cl8 at 300 K ($\alpha$ phase) and Nb3Cl2Br6 at 106 K ($\beta$ phase). (c), (d) Stacks of momentum-dependent EDCs along $\overline{{\rm \Gamma}}\overline{{\rm K}}$ direction, with fitting results for the $\alpha$ phase and $\beta$ phase. The corresponding momentum values are indicated on the left. For clarity, the EDCs were multiplied by a scaling factor and shifted vertically. (e), (f) Schematic representation of the density of state and corresponding electron excitations for the $\alpha$ phase and $\beta$ phase. Inter-band transitions and excitons are denoted by IT and EX, respectively.
• Figure 4: Exciton dispersions from the HREELS measurements. (a), (b) Normalized HREELS mapping for Nb3Cl8 at 300 K ($\alpha$ phase) and Nb3Cl2Br6 at 106 K ($\beta$ phase). The white dashed lines represent the fitting results of the momentum-dependent EDCs. (c), (d) Extracted dispersions of the inter-band transitions for the $\alpha$ phase and $\beta$ phase, obtained by fitting the experimental data. (e), (f) The second derivative images of the inter-band transitions for the $\alpha$ phase and $\beta$ phase. (g), (h) Extracted dispersions of the excitons for the $\alpha$ phase and $\beta$ phase, with the gray curves represent the linear fit and parabolic fit to the correspond dispersions, respectively. (i), (j) The second derivative images of the exciton dispersions for the $\alpha$ phase and $\beta$ phase. Notice, to clearly display the dispersion shape near the BZ center, the data in (c-j) are symmetrized along the gamma point to show the negative momentum. The error bars are determined through the convolution of instrumental resolution ($\sim3.0\ {\rm meV}$) and the standard errors derived from the fitting process ($\sim0.3\ {\rm meV}$ for the $\alpha$ phase and $\sim5.0\ {\rm meV}$ for the $\beta$ phase).
• Figure 5: (a) Schematic of the scattering geometry. (b) Schematic of the experimental setup of the 2D HREELS.