Moiré Mott correlated mosaics in twisted bilayer 1T-TaS$_2$

Abstract

The tunability and twist engineering of van der Waals materials enable the emergence of electronic states not present in individual monolayers. Among them, monolayer 1T-TaS$_2$ is a well-known Mott insulating system, whose star-of-David charge density wave reconstruction realizes an emergent triangular lattice of local magnetic moments. Interestingly, in its bulk form, the insulating gap is not correlation-driven, but stems from interlayer coupling. Here, we exploit the stacking-dependent nature of the insulating gap to show that in twisted 1T-TaS$_2$ bilayers, the spatially dependent competition between many-body and single-particle gaps creates Mott-trivial mosaic superlattices, featuring regions with local magnetic moments and non-magnetic insulating regions. We further demonstrate the tunability of the mosaic correlated state with an interlayer bias, giving rise to controllable charge transfer and quenching of correlations. Our results establish twisted 1T-TaS$_2$ as a flexible platform to engineer mixed spatially modulated correlated insulating phases, arising from the moiré profile.

Figures (5)

• Figure 1: (a) CCDW atomic structure of monolayer 1T-TaS$_{2}$ (top view), depicting the closest bonds between Ta atoms. CCDW supercell delineated in yellow. (b) Hopping $t_\perp$ considered in the bilayer model between two SoD sites in different layers as a function of the distance between them $r$ for $\tau = 0.2$ eV PhysRevLett.129.016402. (c--f) Stacking orders found in bulk 1T-TaS$_2$. (c,e) Ta atoms of the 2 SoD structures that make up the unit cells of A-stacking (c) and L-stacking (e). (d,f) Top view of the SoD sites of the A-stacked (d) and L-stacked (f) bilayers. Star symbols represent the center of each SoD structure, where the electrons are localized. (g) Moiré structure of twisted bilayer 1T-TaS$_{2}$ with twist angle $\theta = 7.34^\circ$ (top view).
• Figure 2: (a) Average absolute magnetization of each SoD site for the A-stacked and L-stacked 1T-TaS$_2$ bilayers. Dashed lines highlight the values of $\tau$ of the twisted calculations shown in (c--f). (b) Average absolute magnetization of each SoD site for 1T-TaS$_2$ bilayers twisted at different angles $\theta$ and considering different interlayer hopping strengths $\tau$. Dashed lines highlight the angles $\theta$ shown in (c--f). (c--f) Top view of the magnetization on each SoD site in 1T-TaS$_2$ bilayers with twist angles $\theta=9.43^\circ$ (c,e) and $\theta=3.15^\circ$ (d,f) in the low interlayer coupling regime, $\tau = 0.3 \,U$ (c--d), and the high coupling regime $\tau = 0.7 \,U$ (e--f). (c,e) Magnetization vectors on each SoD site of a moiré supercell. (d,f) Norm of the magnetization of each site for multiple moiré supercells.
• Figure 3: (a) Band gap of the non-twisted A-stacked and L-stacked 1T-TaS$_2$ bilayers for different interlayer hopping strengths $\tau$. The dashed line indicates the value of $\tau$ used in plots (c--d). (b) Band gap of twisted bilayers with different twist angles $\theta$ and interlayer hopping strengths $\tau$. The value of $\tau$ and the twist angles used in plots (c--d) are highlighted. (c--d) Density of states of the 1T-TaS$_2$ bilayer with interlayer hopping strength $\tau = 0.7 \,U$ and twist angles $\theta = 9.43^\circ$ (c) and $\theta = 4.41^\circ$ (d). Bottom: Total DOS divided by the number of SoD sites in the moiré supercell alongside LDOS of sites A and L. Top: LDOS of every SoD site plotted as a top view in real space, at peaks of the LDOS spectrum of the A site (left) and L site (right). Sites labeled "A" and "L" are circled.
• Figure 4: (a) Schematic of a bias voltage $2V$ applied between two twisted 1T-TaS$_2$ layers. (b) Occupation of the top and bottom sites of A-stacking in contrast with those of L-stacking with increasing $V$, for interlayer hopping strength $\tau = 0.7 \, U$. (c) Magnetization of the top sites of A- and L-stacking with increasing interlayer bias $V$, for $\tau = 0.7 \, U$. (d--e, h--i) Occupation of the A and L sites (d--e) and of each site of the moiré supercell (h--i) of bilayer structures with twist angles $\theta = 9.43^\circ$ (d,h) and $\theta = 4.41^\circ$ (e,i), with increasing $V$, for $\tau = 0.7 \, U$. (f--g, j--k) Magnetization of the top A and L sites (f--g) and of each site of the moiré supercell (j--k) of bilayer structures with twist angles $\theta = 9.43^\circ$ (f,j) and $\theta = 4.41^\circ$ (g,k), with increasing $V$, for $\tau = 0.7 \, U$. The corresponding L sites are circled (h--k). Note that the magnetization in the bottom sites, not shown in (c,f--g) is equal in magnitude with opposite direction.
• Figure 5: (a--b) DOS of the A-stacked (a) and L-stacked (b) 1T-TaS$_2$ bilayers with interlayer hopping strength $\tau = 0.7 \, U$ and LDOS of their top and bottom sites for increasing interlayer bias $2V$. (c--d) Top view of bilayer lattice structures with twist angles $\theta = 9.43^\circ$ (c) and $\theta = 4.41^\circ$ (d), with A sites marked by a green circle and L sites marked by magenta circles. (e--f) For the 1T-TaS$_2$ bilayers with $\tau = 0.7 \, U$ and twist angle $\theta = 9.43^\circ$ (e) and $\theta = 4.41^\circ$ (f): total DOS, LDOS at the A sites in the top and bottom layers, and LDOS at the L sites in the top and bottom layers.