Metastable square Bismuth allotrope oriented by six-fold symmetric mica

Abstract

Layered bismuth (Bi) has been focused on two Peierls distortion derivatives, i.e., bulk stable β-phase (A7 phase), black phosphorus-like α-phase (A17 phase), and their mutated structures. Metastable structures beyond Peierls distortion system are yet rarely accessible. Here, Bi in square symmetry (${C}_{4v}$), called s-Bi, was grown via physical vapor deposition. The co-existence of three 120°-associated s-Bi crystal grains was analyzed using transmission electron microscopy. 120°-oriented one-dimensional (1D) nuclei indicate s-Bi heteroepitaxy on six-fold symmetric (${C}_{6v}$) mica (001). A subsequent nanorod-like nuclei coalescing could promote a morphology evolution, resulting in triangular or hexagonal nanosheets with the unique triple s-Bi structure suitable for later β-Bi growth. Lattice misfit and strain calculations suggest a supercell match between $4\times 7$ s-Bi and $3\times 3$ mica (001). This work demonstrates the metastable s-Bi structure via anisotropic heteroepitaxy of ${C}_{4v}$ s-Bi on ${C}_{6v}$ mica.

Introduction

Single- or few-layered bismuth (Bi) allotropes with distinct physical and chemical properties are attractive for future nanoelectronics^1,2, semimetal contacts for two-dimensional (2D) semiconductors³, superconductivity⁴, etc. Exploring growth mechanisms of layered Bi allotropes is a preliminary step towards innovative material solutions to engineering challenges. Nanoislands of Bi were grown either in bulk-stable β-phase (the rhombohedral A7 phase) or black phosphorus-like α-phase (the orthorhombic A17 phase). These two phases are Peierls distortion derivatives from the same simple cubic lattice^5,6, rendering six-atom-ring-linked biatomic monolayers with contrasting 2D buckling extents. As suggested by theoretical calculations, the formation energy of high-buckled (puckered) α-bismuthene is lower than low-buckled β-bismuthene⁷. Past experiments indicated that epitaxial α-phase Bi would be more readily available under weak interactions with the substrates^8,9, and epitaxial β-phase Bi is selective to specific rotational orientations of substrate surfaces^9,10. Structural mutations from α-bismuthene and β-bismuthene were also observed using substrates with specific atomic arrangements. For example, growth of high-buckled and symmetric α-bismuthene (being more unstable than asymmetrical α-bismuthene⁷) was demonstrated^11,12,13, and nontrivial topological states¹² and Dirac fermions¹³ were found in the flat bilayer. On the other side, the biatomic monolayer of low-buckled β-bismuthene could be stretched into a graphene-like monoatomic monolayer via heteroepitaxy, and a useful bandgap from the zero-buckling mutation of β-bismuthene was discovered². Yet, these experimentally-reported Bi allotropes¹⁴ are either from or associated with the Peierls distortion system in a way that each Bi atom covalently bonds with three neighboring atoms. It remains challenging to acquire a Bi allotrope beyond the Peierls distortion realm from experiments.

Past theories investigated layered allotropes of group V elements^15,16, and a few peculiar allotropes of layered Bi were further proposed^17,18. Unfortunately, growth of as-predicted Bi allotropes is scarce owing to unfavorable formation energies and/or lacks of kinetics strategies^19,20. Notably, the Bi monolayer with an unique rectangular symmetry, called M-Bi, was found locally between α-Bi nanoislands using scanning tunneling microscope (STM)²¹. Different from Peierls distortion system, each Bi atom in M-Bi covalently bonds with four neighboring atoms. The growth of M-Bi was triggered by α-Bi edge kink defects, and multiple Dirac cones in M-Bi Brillouin zone were theoretically predicted²¹. Yet, due to an inconvenient formation energy of M-Bi¹⁹, there is a lack of further growth to help to elucidate the growth phenomenon. Herein, a metastable Bi in square symmetry was grown on mica (001) via physical vapor deposition (PVD). The unusual Bi allotrope is named s-Bi to highlight the 4-fold symmetric (i.e., ${C}_{4v}$) 2D lattice. The square lattice was analyzed using transmission electron microscopy (TEM), and the co-existence of three 120°-associated s-Bi crystal grains (called s-Bi triplets) was observed in early-stage nanosheets. For large-and-thick β-Bi dominant nanosheets, a layer of s-Bi triplets could be identified underneath β-Bi. In such a stacking structure, rotational relationships of 2D lattices between ${C}_{6v}$ mica (001), ${C}_{4v}$ s-Bi triplets, and ${C}_{3v}$ β-Bi were determined based on selected area electron diffraction (SAED) analyses. Combining with atomic force microscopic (AFM) analyses of one-dimensional (1D) s-Bi nucleus morphologies, the triple s-Bi structure could be ascribed to random coalescence process of 120°-associated nanorod-like or nanowire-like s-Bi nuclei growing along six equivalent directions of mica’s [100]. Lattice misfits and strains of s-Bi on mica (001) were calculated, which suggests $4\times 7$ s-Bi supercell as the nucleation basis for the 1D hetero-epitaxy of ${C}_{4v}$ s-Bi on ${C}_{6v}$ mica (001). The anisotropic s-Bi formation as well as the subsequent β-Bi growth on s-Bi triplets are delineated and discussed.

Results and discussion

Triple s-Bi structure

Triangular and hexagonal Bi nanosheets were grown at 200 ~ 230 °C on Muscovite mica using the furnace PVD system²². Considering a high formation energy of metastable Bi in unusual square symmetry, such as M-Bi¹⁹, pre-heating mica substrate was found necessary to allow reliable s-Bi nucleation for forming the triple s-Bi structure. The pre-heated substrate temperature would also reduce $\alpha$-Bi nucleation, because the calculated formation energy of $\alpha$-Bi monolayer is relatively small^7,19 and $\alpha$-Bi could nucleate at a lower temperature here (to be discussed elsewhere). The substrate temperature is quite different from previous room temperature PVD systems for $\alpha$-Bi or β-Bi (110) growth^8,9,10. All experiments are noted in Methods section, and supplementary figures are available in the Supplementary Information (SI). As sketched in Fig. 1a, there are two types of Bi nanosheets: (1) Early-stage nanosheets with the unique triple s-Bi structure, as further detailed in Fig. 1, and (2) large-and-thick nanosheets predominantly in β-phase and yet still with s-Bi triplets underneath β-Bi, to be later presented in Fig. 2. Figure 1b is the 4-fold symmetric crystal model of monolayer s-Bi (see Methods section and Supplementary Fig. 1 for model convergence test and optimization). Note that crystal structures of s-Bi, β-Bi, and mica were used for simulating SAED patterns. Figure 1c shows TEM image of an early-stage triangular nanosheet with triangle altitude, roughly as ~190 nm. Interestingly, the SAED pattern shown in Fig. 1d is with a quasi-12-fold symmetry, but the simulated SAED pattern of s-Bi monolayer model (see Supplementary Fig. 2a) is with a square symmetry. SAED analyses were performed to examine additional early-stage nanosheets (see Supplementary Fig. 2), and the same quasi-12-fold symmetric SAED pattern was consistently observed from early-stage nanosheets. With s-Bi being imaged along crystallographic axis in ${\left[001\right]}_{{s-Bi}}$, the observed quasi-12-fold symmetry should be understood as an overlay of three s-Bi SAED patterns with rotation angles, as -120°, 0°, and 120°. Thus, three sets of s-Bi SAED spots, as $(200)$ and (020), are labeled in Fig. 1d for s1-Bi, s2-Bi, and s3-Bi, respectively.

Fig. 1: Triple s-Bi structure in the early-stage triangular nanosheet.

a Schematics of early-stage (s-Bi) and large (s-Bi/β-Bi) triangular nanosheets. b Ball-and-stick model of s-Bi from top view and side view. c TEM image of the early-stage nanosheet. Inset: Schematics of s-Bi nanosheet. d SAED pattern of the early-stage nanosheet. Each set of diffraction spots is labeled by dashed square, as s1-Bi in light green, s2-Bi in light yellow, and s3-Bi in magenta, respectively. Three s-Bi [100] crystallographic axes for s-Bi triplets are labeled. e HRTEM image of the nanosheet from box area in (c). f FFT pattern of the HRTEM image. Color dashed squares label three sets of s-Bi spots. g Overlay image of inverse FFT of three s-Bi domains. h–k Zoom-in HRTEM images from color box areas in (e). l–o Zoom-in inverse FFT overlay images from color box areas in (g). h, l Domain of s1-Bi. i, m Domain of s2-Bi. j, n Domain of s3-Bi. k, o Domain of s1-Bi+s2-Bi+s3-Bi. Square grids in (h–j) are for ease of viewing the s-Bi lattice. Scale bars in (h–o) are all 1 nm.

Fig. 2: Lattice orientations of s-Bi triplets, β-Bi, and mica.

a Optical image of as-grown large-and-thick triangular nanosheets on mica (001). Two orientations of triangular nanosheets are upward-facing (blue) and downward-facing (yellow). Inset: XRD spectrum of transferred nanosheets and β-Bi PDF card. b, c Mica and β-Bi ball-and-stick crystal models in top view. Hexagonal unit cells are colored, and surface atoms are drawn. d, e TEM image and SAED pattern of the β-dominant nanosheet. Insets in (d): Sample schematic and HRTEM image. f Overlay of simulated SAED dots of s1-Bi (light green), s2-Bi (light yellow), s3-Bi (magenta), and β-Bi (turquoise). g, h TEM image and SAED pattern of the β-dominant nanosheet with mica substrate flake. Insets in (g): Sample schematic and HRTEM image. i Overlay of simulated SAED dots of s-Bi triplets, β-Bi, and mica (red). SAED spots of s-Bi triplets are colored in (e, h). Secondary diffraction spots in (f) and (i) are labeled as white dots due to s-Bi and β-Bi, and as black dots due to β-Bi and mica. Note that three 120° crystallographic axes of β-Bi in (f), mica in (i), and s-Bi triplets in Fig. 1d are aligned.

In Fig. 1e, HRTEM image of the nanosheet shows an intricate pattern, as three 120°-associated domains of square lattice, randomly adjoining each other. To map out the spatial distributions of three s-Bi domains, inverse fast Fourier transform (inverse FFT) analyses were performed. First, Fig. 1f is the FFT pattern of the HRTEM image, which shows the quasi-12-fold symmetric pattern owing to s-Bi triplets. Each set with eight dots for s-Bi single domain in the FFT pattern could be individually selected for an inverse FFT treatment. As a result, approximate spatial distributions for s1-Bi, s2-Bi, and s3-Bi were acquired (see Supplementary Fig. 3). Figure 1g is an overlay of three inverse FFT patterns used to further analyze the HRTEM pattern. In specific, zoom-in overlay images of inverse FFT fringes in Fig. 1l–n are in good agreement with zoom-in HRTEM images in Fig. 1h–j. Thus, the square crystal lattice with ${d}_{(100)}^{s-{Bi}}$ ~ 0.39 nm (labeled zoom-in HRTEM images) could be identified, and single-domain areas are labeled as s1-Bi, s2-Bi, and s3-Bi, respectively. Furthermore, a zoom-in overlay in Fig. 1o shows three inverse FFT images of s1-Bi, s2-Bi, and s3-Bi, suggesting that the HRTEM image in Fig. 1k is likely a Moiré pattern owing to a stacking structure of three 120°-associated s-Bi lattices.

2D lattice orientations

Figure 2a is optical image showing large-and-thick, β-dominant triangular nanosheets that are aligned as upward- or downward-facing triangles on mica (001). The X-ray diffraction (XRD) spectrum of transferred nanosheets on SiO₂, in Fig. 2a inset, contains only two peaks related to β-Bi (003). The appearance of aligned triangular β-Bi nanosheets on mica with two opposite triangular nanosheet orientations was previously reported²³, which was ascribed to a minimized lattice misfit following the lattice unit vector alignment, as ${{\bf{a}}}_{{\boldsymbol{\beta }}{\boldsymbol{-}}{\boldsymbol{Bi}}}\parallel \,{{\bf{b}}}_{{\boldsymbol{mica}}}$. Differently, the alignment of triangular β-Bi nanosheets here is owing to anisotropic heteroepitaxy of s-Bi on mica. Our system would render an unexpected lattice unit vector alignment, as ${{\bf{a}}}_{{\boldsymbol{\beta }}{\boldsymbol{-}}{\boldsymbol{Bi}}}\parallel \,{{\bf{a}}}_{{\boldsymbol{mica}}}$, to be further discussed later. To verify 2D lattice orientations showing in our system, β-dominant nanosheets, both without and with substrate as attached mica flake, were analyzed using TEM. Top view structural configurations of mica and β-Bi are provided in Fig. 2b, c for an ease of viewing TEM data. It is worthy to note that the monoclinic lattice vectors of mica (001), i.e., ${{\bf{a}}}_{{\boldsymbol{mica}}}$ and ${{\bf{b}}}_{{\boldsymbol{mica}}}$ labeled in Fig. 2b, are orthogonal, and each offers 6 equivalent directions on ${C}_{6v}$ mica (001). Figure 2d shows TEM image of the β-dominant nanosheet, and HRTEM image as inset shows the lattice fringe in a hexagonal arrangement, consistent with β-Bi. Interestingly, SAED pattern of the nanosheet, in Fig. 2e, shows not only a bright β-Bi diffraction pattern, but also a weak quasi-12-fold symmetric pattern for the triple s-Bi structure. To further resolve the SAED pattern, Fig. 2f presents an overlay of simulated SAED patterns of s-Bi triplets and β-Bi with specific lattice orientations to be identified. Note that secondary diffraction spots in Fig. 2e (also drawn in Fig. 2f) were resolved based on further analyses, as summarized in Supplementary Fig. 4. Importantly, three symmetric crystallographic axes of ${C}_{3v}$ β-Bi, ${\left[100\right]}_{\beta -{Bi}}$, ${\left[010\right]}_{\beta -{Bi}}$, and ${\left[\bar{1}\bar{1}0\right]}_{\beta -{Bi}}$, could be labeled in Fig. 2f, and according to orientations of s-Bi triplets shown in Fig. 1d, three β-Bi crystallographic axes are parallel to ${\left[100\right]}_{s1-{Bi}}$, ${\left[100\right]}_{s2-{Bi}}$, and ${\left[100\right]}_{s3-{Bi}}$, respectively. Thus, the lattice unit vector alignment between s-Bi triplets and β-Bi was affirmed, briefly as ${{\bf{a}}}_{{\boldsymbol{s}}{\boldsymbol{1}}{\boldsymbol{-}}{\boldsymbol{Bi}}}\parallel \,{{\bf{a}}}_{{\boldsymbol{\beta }}{\boldsymbol{-}}{\boldsymbol{Bi}}}$. We carried out SAED analyses for additional large-and-thick nanosheets without mica flake (see Supplementary Fig. 5), and their results re-affirmed the lattice orientation relationship.

TEM image and SAED pattern of the β-dominant nanosheet attached to mica flake, in Fig. 2g, h, were analyzed to further identify mica’s orientation. The SAED pattern of s-Bi triplets could still be identified in Fig. 2h, together with SAED patterns of mica and β-Bi. In the same manner, Fig. 2i presents an overlay of simulated SAED patterns of mica, s-Bi triplets, and β-Bi with the same lattice orientations as Fig. 2h. Note that more complicated secondary diffraction spots in Fig. 2h were shown, and they are drawn in Fig. 2i as well. According to secondary diffraction analyses summarized in Supplementary Fig. 6, white secondary diffraction dots are due to stacking effect of triple s-Bi layer and β-Bi layer, and black secondary diffraction dots are due to stacking effect of mica layer and β-Bi layer. Therefore, three crystallographic axes of mica, ${\left[100\right]}_{{mica}}$, ${\left[\bar{1}10\right]}_{{mica}}$, and ${\left[\bar{1}\bar{1}0\right]}_{{mica}}$, could be labeled in Fig. 2i, and they are parallel to ${\left[100\right]}_{s1-{Bi}}$, ${\left[100\right]}_{s2-{Bi}}$, and ${\left[100\right]}_{s3-{Bi}}$, respectively. We also carried out SAED analyses for additional large-and-thick nanosheets with mica flake (see Supplementary Fig. 7), and their results also recommends such a lattice orientation relationship. In short, lattice unit vector alignments of s-Bi triplets, β-Bi, and mica (001) were affirmed, briefly as ${{\bf{a}}}_{{\boldsymbol{s}}{\boldsymbol{1}}{\boldsymbol{-}}{\boldsymbol{Bi}}}\parallel \,{{\bf{a}}}_{{\boldsymbol{mica}}}$ and ${{\bf{a}}}_{{\boldsymbol{\beta }}{\boldsymbol{-}}{\boldsymbol{Bi}}}\parallel \,{{\bf{a}}}_{{\boldsymbol{mica}}}$, respectively. These lattice orientation analyses also indicate that one edge (or two edges) of a triangular (hexagonal) nanosheet is (are) parallel to lattices vectors of ${{\bf{a}}}_{{\boldsymbol{mica}}}$, ${{\bf{a}}}_{{\boldsymbol{s}}{\boldsymbol{1}}{\boldsymbol{-}}{\boldsymbol{Bi}}}$, and ${{\bf{a}}}_{{\boldsymbol{\beta }}{\boldsymbol{-}}{\boldsymbol{Bi}}}$, as labeled in Fig. 2g. Hence, edge orientations of large-and-thick nanosheets could be used as an indicator to point out crystal orientations for the s-Bi/mica hetero-epitaxy system as well as for the β-Bi/s-Bi triplets growth system.

Cross-sectional TEM

Figure 3 presents cross-sectional analyses of s-Bi triplets in the large-and-thick nanosheet. The cross-sectional sample was prepared by focused ion beam (FIB) equipment. Large-and-thick nanosheets were first transferred to the highly-doped Si (100) substrate. To capsulate nanosheets, ~40 nm-thick amorphous aluminum oxide (a-Al₂O₃) was deposited at 100 °C using atomic layer deposition, followed by FIB-induced carbon deposition. Figure 3a is low magnification image of the cross-sectioned Bi nanosheet (see top inset for the nanosheet before FIB). As shown in bottom inset, there is a clear interface between bottom s-Bi triplets and top β-Bi. Clearly, the bottom layer is composed of laterally-adjoining grains, which is consistent with random s-Bi domains as-observed in the early-stage nanosheet (see Fig. 1). Figure 3b is HRTEM image of the s-Bi grain showing lattice planes with interplane distance, roughly 0.33 nm. At the nanosheet edge, it is without triple s-Bi bottom layer. Figure 3c is HRTEM image of the nanosheet edge showing lattice planes of β-Bi (003). In specific, ${d}_{(003)}^{\beta -{Bi}}$ ~ 0.39 nm could be identified. SAED pattern, in Fig. 3d, was captured from the nanosheet edge, and major dots of β-Bi could be identified. Energy-dispersive X-ray spectroscopy (EDS) was further carried out for the cross-sectional nanosheet. The stacking structure of β-Bi on s-Bi triplets as well as two capping layers could be clearly identified in annular dark field (ADF)-scanning TEM (STEM) image, shown in Fig. 3e. Cross-sectional EDS elemental maps of Bi, Al, O, C, and Si, are displayed in Fig. 3f–j, respectively. Corresponding EDS intensity profiles of these elements are plotted in Fig. 3k, which helps to illustrate elements of individual layers. The EDS results indicate that the nanosheet bottom layer is with trace amount of oxygen, in contrast to the strong oxygen signal of a-Al₂O₃ layer. Thus, the bottom layer of laterally-adjoining grains is not Bi oxide. Despite that the cross-sectional crystal lattice could not be further analyzed due to a lack of three-dimensional s-Bi structure model, the HRTEM and EDS results affirmed the appearance of s-Bi triplets as bottom layer in large-and-thick β-dominant nanosheet.

Fig. 3: Cross-sectional analyses of the large-and-thick nanosheet.

a TEM image of the cross-sectional nanosheet. Insets: top is SEM image of the nanosheet before FIB milling, and bottom is zoom-in image from area 1. b Cross-sectional HRTEM image of the s-Bi grain, as indicated by green arrow in (a) bottom inset. Inset: Ball-and-stick model of s-Bi monolayer from side view. c Cross-sectional HRTEM image of edge β-Bi, from area 2 in (a). Inset: Ball-and-stick model of β-Bi monolayers from side view. d SAED pattern of the edge β-Bi domain. e Cross-sectional ADF-STEM image from area 3 in (a). All layers are as labeled. f–j EDS elemental maps of Bi, Al, O, C and Si, respectively. k Plot of EDS counts vs. depth, using data from elemental maps in (f–j).

Oriented 1D nuclei

Evidences of 1D growth of s-Bi were indicated by nucleus morphologies. Figure 4a shows AFM image of newly-formed irregular nanosheets that are next to hexagonal nanosheets. At edges of newly-formed irregular nanosheets, nanorod-like morphologies could be seen. AFM image in Fig. 4b shows morphologies of 120°-oriented nanowires and nanorods coalescing. Three 120°-oriented, equivalent crystallographic axes of ${\left[100\right]}_{{mica}}$ could be labeled in Fig. 4b, according to three sets of parallel edges of the hexagonal nanosheet. Schematic drawing of two zoom-in topographic images, in Fig. 4c, d, further depict clusters of nanorods and nanowires with random cluster morphologies. These results indicate that s-Bi nuclei would grow along six equivalent directions of ${\left[100\right]}_{{mica}}$, rendering three preferred orientations for 1D nuclei. Three topographic line profiles, in Fig. 4e, show that height of the newly-formed irregular nanosheet (from nanorods coalescing) is as 2 ~ 3 nm, and heights of three nanowires are also similar. Note that two AFM images were captured from the same mica substrate, but in quite different areas. Using monolayer thickness of built model plus an assumed van der Waals gap thickness, heights of individual nanowires and nanorod clusters might be approximated as 6 ~ 9 layers of s-Bi. Figure 4f presents a schematic drawing of morphology evolution from individual nanorods with three rotations, to nanorods coalescing, to newly-formed irregular nanosheet, and eventually to a nearly triangular morphology that is similar to the one shown in Fig. 1. In Addition, after nanorods coalescing and due to excessive growth of s-Bi triplets, each s-Bi domain may grow on top of the other s-Bi domain, as depicted in Fig. 4g. Once two islands of different s-Bi domains are connected, thick islands would inhibit the edge growth of thin islands, and thus a stacking growth might occur to generate a stacking structure as the Moiré pattern shown in Fig. 1k.

Fig. 4: Oriented growth of s-Bi 1D structures.

a AFM image of early-stage irregular nanosheets, as box 1. b AFM image of 120°-oriented nanorods and nanowires coalescing, as box 2 and box 3. c, d Schematic drawings of nanorods and nanowires coalescing for box 2 and box 3, respectively. e Topographic line profiles of three scanning lines in (a, b), showing s-Bi layer number estimations for an early-stage irregular nanosheet (green, in line 1) and three nanowires (orange, in line 2 and 3). f Schematic drawing of morphology evolution based on 120°-oriented nanorod growth and nanorods coalescing. g Schematic drawing of s-Bi stacking structure formation.

The observed three nanowire orientations of s-Bi nuclei on mica could be addressed by the crystal symmetry interplay effect between 2D growth and substrate, as ${N}_{1}=\frac{\left|{G}_{{sub}}\right|}{\left|{G}_{2{D@sub}}\right|}$^24,25,26. In specific, the symmetry group for s-Bi, as$\,{G}_{2D}$, is ${C}_{4v}$, and the symmetry group for mica, as ${G}_{{sub}}$, is ${C}_{6v}$. ${G}_{2{D@sub}}$ for the epitaxy system, as the largest common subgroup of ${G}_{2D}$ and ${G}_{{sub}}$, is then ${C}_{2v}$. The absolute symbol presents a summed order of rotational operations and mirror operations, and hence $\left|{G}_{{sub}}\right|=12$ and $\left|{G}_{2{D@sub}}\right|=4$ generate ${N}_{1}=3$. Here, ${N}_{1}=3$ could be understood as 6-fold symmetric mica (001) being divided by 2, i.e., two equivalent rotational operations, 180° and 360°, for both mica (001) and s-Bi. On the other hand, only one out of two anisotropic lattice constants of mica (001) (i.e., ${{\bf{a}}}_{{\boldsymbol{mica}}}$ or ${{\bf{b}}}_{{\boldsymbol{mica}}}$) would offer the minimized $2{D@sub}$ lattice constant misfit, mainly owing to three observed nanowire orientations of s-Bi nuclei. It was found that s-Bi would grow into 1D nanorods on mica (001) along three orientations, i.e., ${\left[100\right]}_{{mica}}$, ${\left[\bar{1}10\right]}_{{mica}}$, and ${\left[\bar{1}\bar{1}0\right]}_{{mica}}$, respectively. Accordingly, the co-existence of three 120°-associated s-Bi crystal grains could be ascribed to a coalescence phenomenon of 120°-associated s-Bi 1D nucleation. It should be pointed out that the controlling factor for length differences between nanorods and nanowires, shown in Fig. 4b, is unclear at this moment. Franceschi et al. recently showed local potassium atom (K) reordering arrangements, forming 1D atomic trenches on cleaved mica²⁷. Likelihood 1D atomic trenches along six ${\left[100\right]}_{{mica}}$-equivalent directions may promote the s-Bi nucleation into long nanowires. In most of our growth experiments, ultrathin, newly-formed, and irregular nanosheets, as Fig. 4a, were observed by AFM, which were evolved from nanorods coalescing. Once β-Bi growth occurs and the morphology evolves into large-and-thick triangular or hexagonal nanosheets, thin and irregular nanosheets were hardly observed likely owing to that sites for β-Bi growth would take over. Here, a reliable 1D growth of metastable s-Bi allotrope has been demonstrated based on an anisotropic 2D material and substrate interplay. This is an opposite contrary to the 2D growth and substrate interplay for scaling up epitaxy of transition metal dichalcogenides and perovskite materials²⁸.

Lattice misfits and strains

Two TEM-affirmed lattice orientation alignments, ${{\bf{a}}}_{{\boldsymbol{s}}{\boldsymbol{1}}{\boldsymbol{-}}{\boldsymbol{Bi}}}\parallel \,{{\bf{a}}}_{{\boldsymbol{mica}}}$ and ${{\bf{a}}}_{{\boldsymbol{\beta }}{\boldsymbol{-}}{\boldsymbol{Bi}}}\,\parallel \,{{\bf{a}}}_{{\boldsymbol{s}}{\boldsymbol{1}}{\boldsymbol{-}}{\boldsymbol{Bi}}}$, represent s-Bi/mica (001) hetero-epitaxy and β-Bi/s-Bi triplets growth, respectively. Figure 5a briefly delineates both cases using aligned unit cells. In specific, the initial s-Bi formation guided by mica based on ${{\bf{a}}}_{{\boldsymbol{s}}{\boldsymbol{1}}{\boldsymbol{-}}{\boldsymbol{Bi}}}\parallel \,{{\bf{a}}}_{{\boldsymbol{mica}}}$ lattice alignment and the subsequent β-Bi growth on s-Bi triplets based on ${{\bf{a}}}_{{\boldsymbol{\beta }}{\boldsymbol{-}}{\boldsymbol{Bi}}}\,\parallel \,{{\bf{a}}}_{{\boldsymbol{s}}{\boldsymbol{1}}{\boldsymbol{-}}{\boldsymbol{Bi}}}$ lattice alignment are drawn along three equivalent directions, and in each direction, three aligned crystallographic axes of ${C}_{6v}$ mica (001), ${C}_{4v}$ s-Bi triplets, and ${C}_{3v}$ β-Bi are labeled. Lattice misfit calculations²⁴ were carried out to first address the non-existent ${C}_{3v}$ β-Bi epitaxy on ${C}_{6v}$ mica. Considering mica’s two anisotropic lattice unit vectors, two orientations to place a triangular β-Bi atomic sheet on mica (001) are depicted in Fig. 5b, as ${{\bf{a}}}_{{\boldsymbol{\beta }}{\boldsymbol{-}}{\boldsymbol{Bi}}}\,\parallel \,{{\bf{b}}}_{{\boldsymbol{mica}}}$ and ${{\bf{a}}}_{{\boldsymbol{\beta }}{\boldsymbol{-}}{\boldsymbol{Bi}}}\,\parallel \,{{\bf{a}}}_{{\boldsymbol{mica}}}$. A minimized lattice misfit shall determine a favored direction. Also, the crystal symmetry interplay for ${C}_{3v}$ β-Bi epitaxy on ${C}_{6v}$ mica renders ${N}_{1}=2$. With ${{\bf{a}}}_{{\boldsymbol{\beta }}{\boldsymbol{-}}{\boldsymbol{Bi}}}\,\parallel \,{{\bf{b}}}_{{\boldsymbol{mica}}}$, ${N}_{1}=2$ offers left- (not drawn) or right-facing triangular β-Bi atomic sheet. With ${{\bf{a}}}_{{\boldsymbol{\beta }}{\boldsymbol{-}}{\boldsymbol{Bi}}}\,\parallel \,{{\bf{a}}}_{{\boldsymbol{mica}}}$ as our experiments (see Fig. 2(a)), ${N}_{1}=2$ would yet generate upward- or downward-facing (not drawn) triangular β-Bi atomic sheet. Strain calculations²⁹ were further carried out for two orientations offered by mica (001), and as-illustrated in Fig. 5b, a supercell of 2${{\bf{a}}}_{{\boldsymbol{\beta }}{\boldsymbol{-}}{\boldsymbol{Bi}}}\times$2${{\bf{b}}}_{{\boldsymbol{\beta }}{\boldsymbol{-}}{\boldsymbol{Bi}}}$ is used to match with a rhombus area on mica (001). Outcomes of misfit and strain calculations are summarized in Fig. 5c. The experimentally-observed orientation, as ${{\bf{a}}}_{{\boldsymbol{\beta }}{\boldsymbol{-}}{\boldsymbol{Bi}}}\,\parallel \,{{\bf{a}}}_{{\boldsymbol{mica}}}$, was unexpected owing to a large lattice misfit (14.1%) and strain (9.5%). As a consequence, a layer of s-Bi triplets serving as an intermediate layer between mica (001) and β-Bi is indispensable. Owing to a very good lattice match between ${d}_{\left(010\right)}^{\beta -{Bi}}=$ 0.394 nm (see Fig. 2c) and ${d}_{\left(010\right)}^{s-{Bi}}=$ 0.390 nm (see Fig. 1b), upward- and downward-facing, β-Bi growth could be oriented by the triple s-Bi structure to form β-Bi dominant large-and-thick nanosheets. As a piece of supporting data, dark field TEM analyses of the nanosheet partially covered by β-Bi are provided in Supplementary Fig. 8, and phase domains of s1-Bi, s2-Bi, s3-Bi, and β-Bi could be roughly resolved. The β-Bi domain shows unique blank areas with contour angles in 60° and 120°, implying oriented β-Bi formation on the surface of s-Bi triplets. It should be noted that the β-Bi formation on s-Bi triplets, as depicted in Fig. 5a, may also refer to s-Bi triplets to β-Bi phase transformation. Because of an increase of nanosheet thickness by a long deposition time, bulk-stable β-Bi would take over via phase transformation, similar to thickness-induced α-Bi to β-Bi conversion^8,9,11.

Fig. 5: Formation pathway of 1D s-Bi on mica (001).

a Orientated unit cells of mica (001), s-Bi triplets, and β-Bi on three shared crystallographic axes, as growth orientations observed from experiments. b Schematics of orientating a triangular atomic sheet of β-Bi on mica (001) in two directions of lattice alignments, ${{\bf{a}}}_{{\boldsymbol{\beta }}{\boldsymbol{-}}{\boldsymbol{Bi}}}\,\parallel \,{{\bf{b}}}_{{\boldsymbol{mica}}}$ and ${{\bf{a}}}_{{\boldsymbol{\beta }}{\boldsymbol{-}}{\boldsymbol{Bi}}}\,\parallel \,{{\bf{a}}}_{{\boldsymbol{mica}}}$. Yellow triangles label β-Bi lattice orientations of triangular atomic sheets, i.e., right-facing (not drawn) and upward-facing (not drawn). The 2${{\bf{a}}}_{{\boldsymbol{\beta }}{\boldsymbol{-}}{\boldsymbol{Bi}}}\times$2${{\bf{b}}}_{{\boldsymbol{\beta }}{\boldsymbol{-}}{\boldsymbol{Bi}}}$ supercell (light blue rhombus area) is in match with two different red rhombus areas on mica in strain calculations. c Two orientations of β-Bi on mica with different lattice misfits. For ${{\bf{a}}}_{{\boldsymbol{\beta }}{\boldsymbol{-}}{\boldsymbol{Bi}}}\,\parallel \,{{\bf{a}}}_{{\boldsymbol{mica}}}$ alignment as observed, ${N}_{1}=2$ results in upward- and downward-facing triangular atomic sheets, and yet such a β-Bi epitaxy directly on mica is with an inconvenient strain. d Absolute lattice misfits for s-Bi 1D growth along ${{\bf{a}}}_{{\boldsymbol{mica}}}$ and ${{\bf{b}}}_{{\boldsymbol{mica}}}$. Minimized misfits are at (4${{\bf{a}}}_{{\boldsymbol{s}}{\boldsymbol{-}}{\boldsymbol{Bi}}}$, 3${{\bf{a}}}_{{\boldsymbol{mica}}}$) and (7${{\bf{a}}}_{{\boldsymbol{s}}{\boldsymbol{-}}{\boldsymbol{Bi}}}$, 3${{\bf{b}}}_{{\boldsymbol{mica}}}$). e Schematics of $4\times$7 s-Bi supercell in match with $3\times 3$ mica supercell. Empty and solid yellow stars in (b, e) denote origin points for matching supercells. f Depiction of s-Bi nanowire epitaxy on mica with three orientations (i.e., ${N}_{1}=$ 3), as repeating $4\times$7 s-Bi supercells along six equivalents of ${\left[100\right]}_{{mica}}$.

Lattice misfit and strain minimums were further investigated to address the s-Bi epitaxy on mica (001) that is guided by ${N}_{1}=3$ crystal symmetry interplay. Figure 5d presents two absolute lattice misfits as a function of number of s-Bi lattice constant, i.e., considering 1D growth of s-Bi along ${{\bf{a}}}_{{\boldsymbol{mica}}}$ or ${{\bf{b}}}_{{\boldsymbol{mica}}}$. Minimized lattice misfits are found at 4${{\bf{a}}}_{{\boldsymbol{s}}{\boldsymbol{-}}{\boldsymbol{Bi}}}$ in match with 3${{\bf{a}}}_{{\boldsymbol{mica}}}$ as 0.2%, and at 7${{\bf{b}}}_{{\boldsymbol{s}}{\boldsymbol{-}}{\boldsymbol{Bi}}}$ in match with 3${{\bf{b}}}_{{\boldsymbol{mica}}}$ as 1.1%, respectively. Thus, s-Bi 1D growth orientation favors the orientation along ${{\bf{a}}}_{{\boldsymbol{mica}}}$ over ${{\bf{b}}}_{{\boldsymbol{mica}}}$. More detailed 2D lattice strain calculations were performed based on Jelver and Stradi et al. method^29,30, as noted in Methods section. Results were summarized in Supplementary Fig. 9. Briefly, a rectangular supercell composed of $4\times 7$ s-Bi unit cells could match with $3\times 3$ mica supercell, as illustrated in Fig. 5e. Remarkably, the strain is minimized down to merely ~0.5%. In fact, such a strain is even less than the strain of ~0.8% for β-Bi supercell on mica, if β-Bi epitaxy via ${{\bf{a}}}_{{\boldsymbol{\beta }}{\boldsymbol{-}}{\boldsymbol{Bi}}}\,\parallel \,{{\bf{b}}}_{{\boldsymbol{mica}}}$ alignment is applicable. Figure 5f depicts 1D growth of metastable s-Bi on mica. It could be alternatively understood as repeating $4\times 7$ s-Bi supercells along six equivalent directions of ${\left[100\right]}_{{mica}}$, resulting in three orientations of s-Bi nanorod nuclei. Note that the quasi-12-fold symmetric SAED pattern was also shown in two recent reports; in addition to the ${C}_{6v}$ mica (001)²², ${C}_{3v}$ hexagonal boron nitride (001)³¹ also offers ${N}_{1}=3$ crystal symmetry interplay for a potential formation of triple s-Bi structure. Our experimental findings are useful to understand the atomic surface effect on anisotropic epitaxy of group V metastable structure beyond the Peierls distortion realm.

In summary, the anisotropic growth of ${C}_{4v}$ s-Bi on ${C}_{6v}$ mica (001) at 200 ~ 230 °C has been demonstrated using a furnace-based PVD method. Owing to a high formation energy of s-Bi, a kinetic strategy to acquire high temperature nucleation is useful to promote the nucleation of the ${C}_{4v}$ metastable allotrope. TEM observations of the square lattice provided direct evidences of 2D metastable Bi allotrope. SAED analyses of the triple s-Bi structure in early-stage nanosheets as well as the s-Bi triplets/β-Bi stacking structure in large-and-thick nanosheets helped to understand specific 2D crystal orientations of mica (001), s-Bi triplets, and β-Bi, respectively. 120°-oriented nanorod-like and nanowire-like s-Bi nuclei were observed by AFM, and their 1D nucleus orientations are consistent with three s-Bi orientations of the triple s-Bi structure in triangular or hexagonal nanosheets. Morphology evolution from 1D nuclei to triangular nanosheet was depicted, in which phenomena of 1D s-Bi nuclei coalescing was considered. Cross-sectional TEM of s-Bi grains underneath top β-Bi layer is presented mainly for EDS elemental analysis, and extensive works will still be necessary to better resolve the 3D lattice. Our experimental findings here have provided critical information to understand the unique ${N}_{1}=3$ and ${N}_{1}=2$ crystal symmetry interplay effects. Calculations of lattice misfits and strains revealed some insights into epitaxial anisotropies of the ${C}_{4v}$ symmetric s-Bi on ${C}_{6v}$ symmetric mica (001) and ${C}_{3v}$ symmetric β-Bi on the triple s-Bi surfaces. It is noteworthy that β-Bi epitaxy directly on mica via the most favorable ${{\bf{a}}}_{{\boldsymbol{\beta }}{\boldsymbol{-}}{\boldsymbol{Bi}}}\,\parallel \,{{\bf{b}}}_{{\boldsymbol{mica}}}$ alignment would not occur in our system, but only s-Bi epitaxy on mica is available via substrate pre-heating. Previous calculated formation energy of β-Bi monolayer was found to be higher than that of α-Bi monolayer^7,19. Based on a high nucleation temperature for the reliable s-Bi epitaxy on mica (001), our experimental data suggest otherwise that the formation energy of s-Bi monolayer may be lower than that of β-Bi monolayer, but still higher that of α-Bi monolayer¹⁹. In future works, using substrates with ${C}_{4v}$ symmetry, such as metallic substrates of Ag (001), Ni (100), or ionic substrate of NaCl (001), will likely be useful to scale up epitaxial growth of s-Bi using the common isotropic lattice matching strategy. This work provides a way for experimental explorations of 2D pnictogen metastable allotropes with unusual ${C}_{4v}$ symmetry.

Methods

Bi nanosheet growth

Bismuth nuclei and nanosheets were grown using a 1-inch tube furnace with two temperature zones. 50 mg Bi powders (Alpha Aesar, 99.999%) were placed in the upstream 650 °C zone for source evaporation, and a freshly-cleaved mica (V5 Muscovite, SPI) was placed in the downstream 200 ~ 230 °C zone as the substrate. Undesired low temperature nucleation could be mitigated by shortening temperature ramping time, or simply by reversing the flow directions³². The background vacuum was ~1 mtorr. Bi vapor was carried downstream by 100 sccm mixed gas of 10% NH₃ in Ar, and the growth pressure was controlled at ~4 torr. The growth duration is varied between 10 ~ 60 min, and the sample was cooled down naturally.

Bi sample transfers

As-grown bismuth nanosheets could be transferred onto different substrates using a polymer sacrificial layer for further characterizations³³. Assisted by wafer dicing blue tape, as-grown bismuth nanosheets attached with a mica (substrate) flake could be mechanically exfoliated for TEM characterizations. Basic steps are as following: A mica substrate with as-grown Bi nanosheets was spin-coated by PMMA (polymethyl methacrylate, M.W. = 950 k, 9 wt.% in anisole, from Micro Chem) at 3500 rpm for 1 min, and then baked at 150 °C for 5 mins. Two pieces of blue tapes were applied to the upper and lower surfaces of the sample. The PMMA-coated mica could be protected during mechanical exfoliations without changing the tape. The flake was thinned down by repeating tape peeling (without PMMA side) to meet the requirement of TEM analysis. A thinned sample with tape was brought in contact with the SiO₂/Si substrate, and then baked at 100 °C for 5 min for removing the tape from the sample. Finally, the sample was transferred using PMMA onto a copper grid and the sacrificial layer was removed by acetone.

Crystal models

Square Bi

The s-Bi crystal structure was modeled by density functional theory (DFT) method. The initial structure of s-Bi was derived from the crystal parameters of M-Bi reported in literature²¹. The initial lattice parameters were 3.90 Å × 3.90 Å × 31.45 Å, and two bismuth atoms were placed in the unit cell with fractional positions as (0, 0, 0) and (0.500, 0.500, 0.036), respectively. A vacuum space in 30 Å-thickness separated the slab from its periodic image. The DFT calculations were performed with the Atomistix ToolKit (ATK) simulation tool³⁴. The linear combination of atomic orbitals (LCAO) was chosen for the basis sets. The Perdew-Burke-Ernzerhof (PBE) of Generalized gradient approximation (GGA) method was chosen as the exchange-correlation functional. The PseudoDojo pseudopotential was used for bismuth atoms³⁵. The Gaussian smearing occupation of 1000 K was chosen as the electronic occupation method. To ensure the accuracy of crystal structure optimization, convergence tests, including k-point and cut off energy, were conducted. The calculation-suggested density mesh cut-off energy and k-point shown in Supplementary Fig. 1a, b are 75 Hartree and $10\times 10\times 1$, respectively. Using the Limited-memory Broyden Fletcher Goldfarb Shanno (LBFGS) optimizer, the s-Bi crystal structure was optimized zwith convergence criteria of the stress error less than 0.1 GPa and the maximum force on each atom less than 0.005 eV/Å. The max force and stress error in the optimization are displayed in Supplementary Fig. 1c, d. The optimized lattice constants were 3.90 Å × 3.90 Å × 31.61 Å, and the bismuth atom fractional positions were (0, 0, 0) and (0.500, 0.500, 0.051), respectively. The optimized lattice constants are comparable with that in literature²¹, and yet the monolayer thickness (the distance between two bismuth atoms in the c-direction) is 10% larger, likely due to variances in calculation methods and accuracy.

β-phase Bi

The β-Bi crystal model is available in the ATK database³⁴.

Muscovite mica

The mica model is built using crystal parameters from the Springer Materials database³⁶.

TEM characterizations

The SAED patterns, HRTEM images and EDS elemental maps were performed by JEOL JEM-F200 with Gatan Rio camera. All simulated SAED patterns were calculated by MacTempasX software. HRTEM images were processed with DigitalMicrograph^® software for acquiring FFT patterns and inverse FFT images. The EDS experiments were performed with a JEOL SDD system (100 mm² × 1) controlled by software, Analysis Station. The cross-sectional specimen was prepared by a FIB equipment (JEOL JIB-4700F). The a-Al₂O₃ capping layer for the cross-sectional nanosheet was deposited by Veeco Savannah S200.

XRD characterizations

Nanosheets sample were transferred onto the SiO₂/Si substrate for the X-ray diffraction (XRD) analyses (D8 Advance, from Bruker). The wavelength of X-ray was Cu Kα = 1.540562 Å.

AFM characterizations

Atomic force microscope (AFM, Dimension ICON, from Bruker) was used to characterize the Bi nanosheet topologies. The tapping scan mode were used with the AFM tips (AC160TS-R3), and the Collected AFM images were processed with Nanoscope Analysis software.

Lattice misfit and strain calculations

Individual lattice misfits were calculated based on formulas: $|mistfit\,of\,{\bf{a}}|=|\frac{|{{\bf{a}}}_{{\boldsymbol{mica}}}|}{|{{\bf{a}}}_{{\boldsymbol{s}}-{\boldsymbol{Bi}}}|}-1|$ and $|mistfit\,of\,{\bf{b}}|=|\frac{|{{\bf{b}}}_{{\boldsymbol{mica}}}|}{|{{\bf{b}}}_{{\boldsymbol{s}}-{\boldsymbol{Bi}}}|}-1|$. The lattice strains were calculated by the Interface Builder feature using ATK simulation tools³⁴. Flowchart of lattice matching calculations between mica (001) and s-Bi (001) supercell is shown in Supplementary Fig. 9a, which is drawn based on Jelver et al.’s report³⁰. In essence, a lattice average strain of a supercell could be calculated using the formula, $\bar{\epsilon }=\sqrt{\frac{{\epsilon }_{{xx}}^{2}+{\epsilon }_{{yy}}^{2}+{\epsilon }_{{xx}}{\epsilon }_{{yy}}+{\epsilon }_{{xy}}^{2}}{4}}$^29,30, where ${\epsilon }_{{xx}}$,${\epsilon }_{{yy}}$, and ${\epsilon }_{{xy}}$ are components of 2D strain tensors. All data for determining of the optimal s-Bi supercell on mica (001) are summarized in Supplementary Fig. 9.