Charge-polarized interfacial superlattices in marginally twisted hexagonal boron nitride

Abstract

When two-dimensional crystals are brought into close proximity, their interaction results in reconstruction of electronic spectrum and crystal structure. Such reconstruction strongly depends on the twist angle between the crystals, which has received growing attention due to interesting electronic and optical properties that arise in graphene and transitional metal dichalcogenides. Here we study two insulating crystals of hexagonal boron nitride stacked at small twist angle. Using electrostatic force microscopy, we observe ferroelectric-like domains arranged in triangular superlattices with a large surface potential. The observation is attributed to interfacial elastic deformations that result in out-of-plane dipoles formed by pairs of boron and nitrogen atoms belonging to opposite interfacial surfaces. This creates a bilayer-thick ferroelectric with oppositely polarized (BN and NB) dipoles in neighbouring domains, in agreement with our modeling. These findings open up possibilities for designing van der Waals heterostructures and offer an alternative probe to study moiré-superlattice electrostatic potentials.

Fig. 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, θ. Dark and light triangles represent predominantly AB and BA regions, respectively. 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, ∆V_s, between the domains. d Representative dc-EFM image (phase) of twisted hBN showing large areas with triangular potential modulation. Changes in domains’ shape and periodicity are due to small changes in θ 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.

Fig. 2. Effect of mono- and bi-layer terraces on occurrence of charge-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; AAʹ stacking). Dark-grey areas indicate BA and ABʹ^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 (AAʹ 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.

Fig. 3. Calculated charge-density distribution in marginally twisted hBN.

a, b Dominant stacking order for twisted-bilayer hBN, calculated as in refs. ^,, for θ = 0.33° in the case of parallel (a) and antiparallel (b) alignment. AB staking is shown in dark green, BA—dark blue, AA—red, AAʹ—dark cyan, BAʹ^BB—dark yellow and ABʹ^NN—magenta. The AA and ABʹ^NN alignments occur at the intersections of the AB and BA regions, and AAʹ and BAʹ^BB 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. c, d, e Charge-density distribution within individual hBN monolayers, which is induced by interlayer interaction for the case of parallel alignment for θ = 0.52°. Scale bar: 20 nm. c Relatively weak interlayer hopping without lattice relaxation. d Same hopping 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, measured at scan height h_s = 8–12 nm from the domains plane. The x-axis and y-axis error bars show the uncertainty of the technique in lateral size and surface potential. 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.