Charge-polarized interfacial superlattices in marginally twisted hexagonal boron nitride

TL;DR

Moiré superlattices generated by twisted insulating crystals of hexagonal boron nitride are shown to have a ferroelectric-like character, attributed to strain-induced polarized dipoles formed by pairs of interfacial bor on and nitrogen atoms that create bilayer-thick ferro electric domains.

Abstract

When two-dimensional crystals are brought into close proximity, their interaction results in strong reconstruction of electronic spectrum and local crystal structure. Such reconstruction strongly depends on the twist angle between the two crystals and has received growing attention due to new interesting electronic and optical properties that arise in graphene and transitional metal dichalcogenides. Similarly, novel and potentially useful properties are expected to appear in insulating crystals. Here we study two insulating crystals of hexagonal boron nitride (hBN) stacked at a small twist angle. Using electrostatic force microscopy, we observe ferroelectric-like domains arranged in triangular superlattices with a large surface potential that is independent on the size and orientation of the domains as well as the thickness of the twisted hBN crystals. The observation is attributed to interfacial elastic deformations that result in domains with a large density of out-of-plane polarized dipoles formed by pairs of boron and nitrogen atoms belonging to the opposite interfacial surfaces. This effectively creates a bilayer-thick ferroelectric with oppositely polarized (BN and NB) dipoles in neighbouring domains, in agreement with our modelling. The demonstrated electrostatic domains and their superlattices offer many new possibilities in designing novel van der Waals heterostructures.

Figures (13)

• Figure 1: | Electrostatic imaging of charge polarization in marginally twisted hBN. (a) Illustration of six high-symmetry stacking configurations for the hBN-hBN interface. Nitrogen atoms are shown in red; boron atoms in blue. (b) Schematic of adjacent hBN atomic layers (red and grey) misaligned by a small angle,$\theta$. Dark and light triangles represent predominantly AB and BA regions. (c) Schematic of our experimental setup. Red and grey hexagonal lattices are in the top and bottom hBN, respectively. A voltage bias is applied between the AFM probe and the silicon substrate. Inset: representative dc-EFM curves as a function of the applied dc bias in two adjacent triangular domains. The horizontal shift of the maximum of the curves yields the variation in surface potential, $\Delta V_{s}$, between the domains. (d) Representative dc-EFM image of twisted hBN showing large areas with triangular potential modulation. Changes in domains' shape and periodicity are due to small changes in $\theta$ caused by irregular strain and the wrinkles seen in the corresponding AFM topography image in (e). The top hBN crystal has 4-, 8 - and 12-layer thick regions. (f) Zoom-in of a region in (d) with regular domains. Scale bars: (d,e) $2 \mu \mathrm{~m}$; (f) 200 nm . Colour bars: (d,f) $10^{\circ}$; (e) 12 nm .
• Figure 2: | Effect of mono- and bi- layer terraces on occurrence of charged-polarized domains. (a) Illustration of hBN alignment over a monolayer terrace in the bottom hBN. The terrace forces an alignment change from parallel (left) to antiparallel (right) at the interface between top hBN (light red) and bottom hBN (light grey; AA' stacking). Dark-grey areas indicate BA and AB'NN stacking. (b) AFM topography image of a representative sample, showing an hBN bilayer crystal covering a monolayer terrace in the bottom hBN. Inset: height profile across the step. (c) Corresponding dc-EFM image. The triangular potential modulation is visible only on one side of the step, marked by the yellow dashed lines in (b) and (c). (d) Schematic as in (a) but for a bilayer terrace. The terrace in the bottom hBN (AA' stacking) does not influence the parallel alignment of the top hBN. The dark-grey shaded areas indicate BA stacking. (e) AFM topography image of an hBN crystal covering a bilayer step in the bottom crystal (inset: the step profile). (f) Corresponding dc-EFM image. The triangular modulation is visible on both sides of the step marked in yellow. Scale bars: (b,c) 250 nm ; (e,f) 500 nm . Colour bars: (b,e) 12 nm ; (c,f)$10^{\circ}$.
• Figure 3: | Calculated charge-density distribution in marginally twisted hBN. (a,b) Dominant stacking order for twisted-bilayer hBN, calculated as in Refs.${ }^{34,35}$, for $\theta=0.33^{\circ}$ in the case of parallel (a) and antiparallel (b) alignment. AB staking is shown in dark green, BA dark blue, AA - red, $\mathrm{A} \mathrm{A}^{\prime}$ - dark cyan, $\mathrm{BA} \mathrm{A}^{\prime \mathrm{BB}}$ - dark yellow, and $\mathrm{AB} \mathrm{B}^{\prime} \mathrm{NN}$ - magenta. The AA and $\mathrm{B} \mathrm{A}^{\prime} \mathrm{BB}$ alignments occur at the intersections of the $A B$ and $B A$ regions, and $A A^{\prime}$ and $B A^{\prime N N}$ regions, respectively. The colour intensity indicates the degree of alignment of boron and nitrogen atoms located in the two hBN monolayers. The atoms are perfectly aligned in the domains' centres. Scale bar: 40 nm . ( $\mathbf{c , d , e}$ ) Charge density distribution within individual hBN monolayers, which is induced by interlayer interaction for the case of parallel alignment for $\theta=0.52^{\circ}$. Scale bar: 20 nm . (c) Relatively weak interlayer hopping without lattice relaxation. (d) Same hoping but accounting for the lattice relaxation. (e) Stronger hopping with lattice relaxation. Twisted bilayer hBN remains charge-neutral, and the charge polarity is reversed between the two layers (red and blue reverse), which also reflects the inversion symmetry of AB/BA stacking. (f) Electrostatic potential variation in the centre of AB and BA , as illustrated in the inset. The experimental values (symbols) as a function of domain size. Within our accuracy, the potential is size-independent. The yellow-shaded region denotes the calculated surface potential values delimited by the two hopping amplitudes used in (d,e).
• Figure 4: Figure S1 | Schematic of the procedure used to fabricate marginally twisted hBN heterostructures. (a) Bottom (light grey) and top (light red) hBN crystals are identified on a $\mathrm{SiO}_{2} / \mathrm{Si}$ substrate. The bottom hBN is confirmed to have a monolayer or bilayer terrace in its surface (yellow step). (b) A PDMS (faint green) and PMMA (green) membrane is brought into contact with the top hBN. (c) The membrane and top hBN are lifted from the substrate. (d) The membrane is translated above the bottom hBN with no rotation and brought into contact. (e) The membrane is removed leaving both crystals in place.
• Figure 5: Figure S2 | Optical and AFM images of marginally twisted hBN on terraces. (a,b) Representative optical images of one of our twisted samples, shown in Fig. 1d-f and Fig. 2e,f in the main text. The top hBN crystal (red line) was transferred on the bottom hBN crystal in a region with a bilayer step, marked by the yellow dashed line, which is visible in the dark-field image in (b). (c,d) Corresponding AFM topography and EFM image of the top hBN in the region near the bilayer step (yellow dashed line). The top hBN crystal has 4-layer, 8-layer and 12-layer-thick regions. The triangular potential modulation is detected in all the regions, regardless of their thickness, and on both sides of the bilayer step. Scalebar: (c,d) $2 \mu \mathrm{~m}$. Colour bar: (c) 12 nm ; (d) $10^{\circ}$.