Charge density wave phase, Mottness, and ferromagnetism in monolayer 1T−NbSe2

Abstract

The recently investigated 1T -polymorph of monolayer NbSe2 revealed an insulating behaviour suggesting a star-of-David phase with √ 13 × √ 13 periodicity associated with a Mott insulator, reminiscent of 1T -TaS2. In this work, we examine this novel two-dimensional material from first principles. We find an instability towards the formation of an incommensurate charge-density-wave (CDW) and establish the star-of-David phase as the most stable commensurate CDW. The mottness in the star-of-David phase is confirmed and studied at various levels of theory: the spin-polarized generalized gradient approximation (GGA) and its extension involving the on-site Coulomb repulsion (GGA+U ), as well as the dynamical mean-field theory (DMFT). Finally, we estimate Heisenberg exchange couplings in this material and find a weak nearest-neighbour ferromagnetic coupling, at odds with most Mott insulators. We point out the close resemblance between this star-of-David phase and flat-band ferromagnetism models.

Direct identification of Mott Hubbard band pattern beyond charge density wave superlattice in monolayer 1T-NbSe2

“…The spatial distribution of the Mott UHB at +0.2 eV is yet to be elucidated. In the literature of density functional theory (DFT) calculations about NbSe 2 38 – 40 , the UHB is believed to arise from the central Nb atom in the SOD with an isolated dz 2 orbital, which is inconsistent with our observations that the electronic states at the top sites are relatively lower than the hollow sites (Figs. 2d and 3d ).…”

“…The CDW order with a superstructure of √13 × √13 R13.9° to the topmost layer can be well distinguished. This type of CDW pattern is often known as the SOD pattern, reminiscent of those in 1T-TaS 2 37 , 38 and 1T-TaSe 2 8 , 32 .

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“…To provide visual guidance, we denoted four important orbitals (pronounced states at −0.28, −0.75, and +1.0 eV, and a faint state at +0.2 eV) by arrows, and named them as V1, V2, CB, and UHB. ML-1T NbSe 2 is generally believed to be a Mott insulator 36 , 38 , 39 , thus the states right above and below the Fermi level probably are the upper and lower Hubbard band (UHB and LHB), respectively. Our GGA + U calculation confirmed the Mott insulator nature and show the LHB is highly mixed with valence band (VB).…”

Yang-Mills structure for electron–phonon interactions in vanadium dioxide

“…Mechanisms of metal-insulator transitions in metal oxides 1 , 2 and high temperature superconductivity in the cuprates and pnictides are two examples 3 , 4 . In addition, the cooperative interplay of magnetism and lattice distortions has also been emphasized in layered transition-metal dichalcogenides 5 – 7 , but a complete and convenient mathematical description is yet to be published.…”

Controlling magnetic frustration in 1T-TaS$_2$ via Coulomb engineered long-range interactions

“…Yet for long-range V ij up to 3 rd neighbor, such an approach involves heavy computation that would go beyond the scope of this work. Third, although we used the 1T-TaS 2 band structure as an example here, the same methodology can be applied to other van der Waals materials such as 1T-NbSe 2 [59,[72][73][74], 1T-NbS 2 [75], 1T-TaSe 2 [76], as well as other 1T-dichalcogenide alloys, and potentially twisted graphene multilayers [77,78], driving them to exotic magnetic phases. As an outlook, Coulomb engineering can also be performed with spatially structured [37,38,41,46,47] or anisotropic [79,80] screening environments giving rise to spatially dependent exchange interactions, that potentially leads to coexisting ground states of different character within the same, homogeneous layered material.…”