Discovery of a Single-Band Mott Insulator in a van der Waals Flat-Band Compound

Open Access

Discovery of a Single-Band Mott Insulator in a van der Waals Flat-Band Compound

Shunye Gao et al.

Phys. Rev. X 13, 041049 – Published 13 December 2023

Abstract

The Mott insulator provides an excellent foundation for exploring a wide range of strongly correlated physical phenomena, such as high-temperature superconductivity, quantum spin liquid, and colossal magnetoresistance. A Mott insulator with the simplest degree of freedom is an ideal and highly desirable system for studying the fundamental physics of Mottness. In this study, we have unambiguously identified such an anticipated Mott insulator in a van der Waals layered compound ${Nb}_{3} {Cl}_{8}$ . In the high-temperature phase, where interlayer coupling is negligible, density functional theory calculations for the monolayer of ${Nb}_{3} {Cl}_{8}$ suggest a half-filled flat band at the Fermi level, whereas angle-resolved photoemission spectroscopy experiments observe a large gap. This observation is perfectly reproduced by dynamical mean-field theory calculations considering strong electron correlations, indicating a correlation-driven Mott insulator state. Since this half-filled band derived from a single $2 a_{1}$ orbital is isolated from all other bands, the monolayer of ${Nb}_{3} {Cl}_{8}$ is an ideal realization of the celebrated single-band Hubbard model. Upon decreasing the temperature, the bulk system undergoes a phase transition, where structural changes significantly enhance the interlayer coupling. This results in a bonding-antibonding splitting in the Hubbard bands, while the Mott gap remains dominant. Our discovery provides a simple and seminal model system for investigating Mott physics and other emerging correlated states.

Received 2 March 2023
Revised 19 October 2023
Accepted 31 October 2023

DOI:https://doi.org/10.1103/PhysRevX.13.041049

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Many-body localization

Mott insulators Strongly correlated systems Van der Waals systems

Angle-resolved photoemission spectroscopy Dynamical mean field theory

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Click to Expand

Popular Summary

Mott insulators, a distinctive class of materials where the insulating state arises from strong electron-electron interactions, serve as a solid foundation for exploring a diverse array of strongly correlated physical phenomena, such as high-temperature superconductivity, quantum spin liquids, and colossal magnetoresistance. The most fundamental model for understanding Mott physics is the celebrated single-band Hubbard model, which considers electrons in a single band consisting of a single orbital. However, low-energy excitations in real Mott insulators tend to be intricate, leading to challenges and controversies in both experimental validation and theoretical analysis. Here, we report a textbook example of the single-band Mott insulator within the van der Waals compound ${Nb}_{3} {Cl}_{8}$ .

In the high-temperature phase, where interlayer coupling is negligible, the perfect agreement between our experiments and calculations unequivocally identifies that the insulating behavior of the monolayer of ${Nb}_{3} {Cl}_{8}$ arises from strong electron-electron interactions. A half-filled flat band, previously pinned at the Fermi level, splits into the upper and lower Hubbard bands, with the Fermi level sandwiched between them. Since this half-filled band, derived from a single orbital, is isolated from all other bands, the monolayer of ${Nb}_{3} {Cl}_{8}$ is an ideal realization of the single-band Hubbard model. Upon decreasing the temperature, the interlayer coupling is significantly enhanced due to a structural phase transition. This results in band splitting within the Hubbard bands of the bulk system, while the insulating behavior is still dominated by Mott physics.

This discovery provides a simple yet powerful model system for investigating Mott physics and other emerging correlated states. It is helpful to enhance our understanding of correlated physical phenomena and has potential for future technological applications.

Key Image

Article Text

Click to Expand

Supplemental Material

Click to Expand

References

Click to Expand

Issue

Vol. 13, Iss. 4 — October - December 2023

Subject Areas

Condensed Matter Physics

Reuse & Permissions

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Half-filled flat band in the monolayer of $α − {Nb}_{3} {Cl}_{8}$ . (a) Schematic illustrations of a metal for $U ≪ W$ (left) and a Mott insulator for $U ≫ W$ (right). (b) Crystal structure of $α − {Nb}_{3} {Cl}_{8}$ . (c) Top view of the monolayer of ${Nb}_{3} {Cl}_{8}$ showing the ${Nb}_{3}$ trimers. Blue lines indicate the Nb–Nb metal bonds within each ${Nb}_{3}$ trimer. Dark- and light-green spheres represent the Cl atoms below and above the Nb layer, respectively. (d) Schematic illustration of the molecular orbitals in an isolated ${Nb}_{3} {Cl}_{13}$ cluster, occupied by seven Nb $4 d$ valence electrons for a ${[{Nb}_{3}]}^{8 +}$ trimer. Inset: top view of a ${Nb}_{3} {Cl}_{13}$ cluster composed of three edge-sharing ${NbCl}_{6}$ octahedra. (e) Calculated band structure of the monolayer of ${Nb}_{3} {Cl}_{8}$ using the HSE06 functional.
Reuse & Permissions
Figure 2
Band gap at $E_{F}$ revealed by ARPES and PL spectra. (a) Calculated valence band structure of the monolayer of ${Nb}_{3} {Cl}_{8}$ using the HSE06 functional. Red and blue curves represent the bands originating from the Nb $4 d$ and Cl $3 p$ orbitals, respectively. (b) Intensity plot of the ARPES data along $M - K - Γ - M$ . (c) $h ν$ dependence of the spectral intensities at three constant energies indicated by the dashed lines in the inset. Inset: intensity plot of the ARPES data at the $M$ point with varying $h ν$ . The spectral intensities are normalized by photon flux. (d) PL spectrum excited by 1.1-eV photons (red curve). Stray signals caused by the incident light have been subtracted (see Fig. S3 in Supplemental Material [36]). The peak at 1.0 eV is fitted to a Gaussian function (blue curve). (e) Same as in (d) but excited by 0.75-eV photons. (f) Temperature-dependent magnetic susceptibility measured upon cooling (blue) and warming (red). The green dashed curve represents a fitting of the cooling data from 100 to 400 K to the Curie-Weiss function.
Reuse & Permissions
Figure 3
Single-band Mott insulator state in $α − {Nb}_{3} {Cl}_{8}$ . (a) Comparison between the calculated and experimental bands. Red dashed curves represent the calculated bands based on the HSE06 functional. The experimental bands are extracted by tracking the peak positions of energy distribution curves in the ARPES data. Raw ARPES data are shown in Figs. S5(a) and S5(b) in the Supplemental Material [36]. (b) Density of states (DOS) of the single-band Hubbard model with increasing $U$ from 0 to 1.2 eV. (c) Spectral function of the LHB and UHB along the high-symmetry path with $U = 1.2 eV$ . (d) Intensity plot of the ARPES data along $M - K - Γ - M$ . (e) Combined band structure from the HSE06 (red) and DMFT (blue) calculations, which nearly perfectly reproduces the ARPES data in (d). (f) Schematic illustration of the electronic structure of $α − {Nb}_{3} {Cl}_{8}$ , showing a single-band Mott insulator state.
Reuse & Permissions
Figure 4
Electronic structure changes between the $α$ and $β$ phases in ${Nb}_{3} {Cl}_{2} {Br}_{6}$ . (a) Temperature-dependent magnetic susceptibility measured upon cooling (blue) and warming (red). (b) Energy distribution curves at the Γ point measured at different temperatures upon warming. Red dashed curves are guides to the eye for the peak positions, showing a splitting of the LHB below $T^{*}$ . (c) Spectral function of the bilayer of $β − {Nb}_{3} {Cl}_{8}$ calculated by DMFT with $U = 1.2 eV$ and $t_{⊥} = 0.1 eV$ , showing the splitting of both LHB and UHB. (d,e) Intensity plots of the ARPES data along $Γ - M - K - Γ$ collected at 340 and 200 K, respectively. (f,g) Top view of the ${Nb}_{3}$ trimers of one bilayer in the $α$ and $β$ phases, respectively. Red and blue circles indicate the Nb ions in the top and bottom monolayers, respectively. (h,i) Schematic illustrations of the electronic structures in the $α$ and $β$ phases, respectively. The insets show the $d_{z^{2}}$ orbitals of the ${Nb}_{3}$ trimers in the bilayer, which are staggered in the $α$ phase (h), but directly on top in the $β$ phase to form an interlayer spin singlet (i).
Reuse & Permissions

Physical Review X