Mott phase in a van der Waals transition-metal halide at single layer limit

Two-dimensional materials offer opportunities for unravelling unprecedented ordered states at single layer limit. Among such ordered states, Mott phase is rarely explored. Here, we report the Mott phase in van der Waals chromium (II) iodide (CrI2) films. High quality CrI2 films with atomically flat surface and macro size are grown on graphitized 6H-SiC(0001) substrate by molecular beam epitaxy. By in situ low temperature scanning tunneling microscopy and spectroscopy (STM/STS), we reveal that the film has a band gap as large as ~3.2 eV, which is nearly thickness independent. Density functional plus dynamic mean field theory calculations suggest that CrI2 films may be a strong Mott insulator with a ferromagnetically ordered ground state. The Mott phase is corroborated by the spectral band splitting, that is consistent with the extended Hubbard model, and gap reduction at charge dopants. Our study provides a platform for studying correlated electron states at single layer limit.


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In low-dimensional electronic systems, correlations among electrons are enhanced due to the quantum confinement effect, which favors the formation of long-range collective ordered states 1,2 that are unprecedented according to the Mermin-Wagner theorem 3 . Recent advances in the studies of single-layers of two-dimensional (2D) materials have shown success in the discovery of magnetic order 4,5 , charge density waves 6,7 , as well as superconductivity 8,9 . The long-range order in single layer limit has delivered surprising quantum behaviors that are distinct from their bulk counterpart, such as magnetic field enhanced magnetism 5 , enhanced charge density wave order 7 , and Ising superconductivity 8 .
Moreover, the ordered states in 2D materials are readily accessible for manipulations with external means [10][11][12] such as electric field, optical stimuli, etc., which opens a new paradigm for their study and applications.
In Mott insulators, strong electron-electron Coulomb repulsion overwhelms the kinetic hopping energy, which induces gap opening in an otherwise metallic band 13,14 . The Mott physics not only constitutes an intriguing metal-insulator transition mechanism beyond the conventional band theory, but also is relevant to exotic physics of high temperature superconductivity and colossal magnetoresistance. Particularly, the 2D Mott-Hubbard model is widely studied as the basis for generating high Tc superconductivity upon charge doping 15 .
While the parent state of cuprate superconductors is a Mott insulator that is considered as 2D identity, there still exists interlayer coupling that prohibits an unambiguous attribution of the property from single layers 15 . Moreover, in Mott systems with John-Teller distortion, the Hubbard bands can split under the cooperative effect of John-Teller distortion and Coulomb repulsion 16 . The resulting Hubbard bands are endowed with distinct orbital characters. This 3 constrains orbital selections for optical excitation, creating dark excitons that aid the development of excitonic insulator phase 17 . In the monolayer limit, the carrier doping of Mott insulators, a crucial parameter for tuning the Coulomb energy, can be controlled with external electrical gating, that is devoid of structural or chemical disorder. To these ends, the exploration of a monolayer Mott insulator with John-Teller effect is highly desirable for indepth controlled study of rich exotic correlated states, and for building functional devices.
Existing experimental single layer Mott systems involve the flat band in magic angle bilayer graphene 18 , the surface reconstruction of Sn on Si(111) or Ge(111) 19,20 , and single layer 1T-NbSe2. [21][22][23] However, the Mott mechanism of magic angle graphene is challenged with alternative explanations 24 , and the Mott phase in Sn-reconstructed Si(111) or Ge(111) surface is essentially quasi-2D which is stabilized by the substrate. Furthermore, none of the above system exhibits d-orbital degeneracy lifting.
CrI2, as a layered van der Waals crystal, has its Cr ion centered around a John-Teller distorted idiom octahedron. The strong Coulomb energy in d orbitals of Cr makes it a promising system for the realization of a single layer Mott insulator with degeneracy lifted Hubbard bands. While this crystal has been synthesized in bulk form, its thin film layers have never been achieved so far. Here, we report the growth of CrI2 films with varying film thickness down to the monolayer limit and identify its Mott insulator phase with STS and theoretical calculations, which features a thickness independent large band gap, characteristic band splitting and gap reduction at dopants. 4 The CrI2 films were grown on a graphene covered 6H-SiC(0001) substrate with molecular beam epitaxy, whose details are in SI-Note 1. The STM measurements 25 were performed at 4.2 K if not specified exclusively. The STS were performed with a lock-in bias modulation of 14.14 mV (rms) at 829 Hz.
CrI2 is a polymorph of the celebrated ferromagnetic insulator CrI3 4 . It is a layered van der Waals crystal with monoclinic structure belonging to the space group of C2/m 26  negligible. This is distinct from many layered 2D semiconductors, where the band gap size increases with decreasing film thicknesses due to quantum confinement effect 27 . The gap was also measured at 77 K for the films with all different thicknesses, and no difference in spectral shape was detected. The negligible interlayer coupling in conjunction with the narrow peak width and the associated high peak intensity imply electrons in the bands may subject to correlation effect.
To understand the electronic structure of the films, we perform first-principles calculations for the free-standing single-layer CrI2 based on density functional theory (DFT) However, such U is abnormally large for Cr-compounds 30,31 . One possible reason is that the effective U added to the correlated electrons in the DFT+U method could be severely screened by the other electrons 32,33 .
To more reasonably describe effective U, we performed DFT+DMFT calculations on the single-layer CrI2. We mainly focus on its FM state, which has shown to be the ground