Fabrication and the Interlayer Coupling Effect of Twisted Stacked

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Fabrication and the Interlayer Coupling Effect of Twisted Stacked Black Phosphorus for Optical Applications Tao Fang, Teren Liu, Zenan Jiang, Rui Yang, Peyman Servati, and Guangrui Xia ACS Appl. Nano Mater., Just Accepted Manuscript • DOI: 10.1021/acsanm.9b00462 • Publication Date (Web): 26 Apr 2019 Downloaded from http://pubs.acs.org on April 28, 2019

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Fabrication and the Interlayer Coupling Effect of Twisted Stacked Black Phosphorus for Optical Applications Tao Fang1, 4, Teren Liu2, Zenan Jiang3, Rui Yang2, Peyman Servati3 and Guangrui (Maggie) Xia2,* 1Department

of Physics and Astronomy, University of British Columbia, Vancouver, BC,

Canada, V6T1Z4 2Department

of Materials Engineering, University of British Columbia, Vancouver, BC,

Canada, V6T1Z4 Tel: +1-604-8220478, Fax: +1-604-8223916, E-mail: [email protected]* 3Department

of Electrical and Computer Engineering, University of British Columbia,

Vancouver, BC, Canada, V6T1Z4 4Stewart

Blusson Quantum Matter Institute, University of British Columbia, Vancouver,

British Columbia V6T1Z4, Canada

Abstract With a new polycarbonate-film-based dry transfer method, we successfully fabricated twisted stacked black phosphorus. Optical characterization showed the overlapping area had special optical response, and high frequency Raman spectroscopy showed unexpected blue shifts in Ag1 and Ag2 modes. Density functional theory (DFT) calculations confirmed these blue shifts in twisted bilayer black phosphorus, and revealed significant interlayer coupling effects. Charge distribution calculations indicated other interactions beyond van der Waals force may exist in twisted bilayer black phosphorus. This finding may cast some insight on phonon modulation effect and give some potential applications such as optical filters and infrared photodetectors.

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Keywords: Black phosphorus, Raman spectroscopy, density functional theory, two-dimensional heterostructure, phonon modulation. Introductions Two dimensional (2D) materials have attracted much attention in recent years, due to their unique properties and wide applications [1-3]. 2D black phosphorus, first isolated in 2013, is a good candidate for flexible electronic and photonic devices [4-6]. Like other 2D materials, black phosphorus is composed of 2D atomic layers and the interlayer interactions are weak van der Waals type. Strong in-plane anisotropy is a significant feature of BP [7, 8]. When two identical 2D structures are superposed with a twist angle θ, this new structure may generate interference, which is caused Moiré pattern. They can also change electron properties and activate new phonon modes. These changes can be examined by optical observation and Raman spectra. New peaks or shifts of Raman peaks are expected [9, 10]. Stacked 2D structures were first studied in graphite and graphene [11], and later in transition metal dichalcogenides including molybdenum disulfide (MoS2) and molybdenum diselenide (MoSe2). Previous studies have shown that for twisted bilayer graphene, new Raman peaks appear depending on the twist angle and the excitation laser [9]. Also, optical reflection changes by changing the twist angle, which leads to ‘microscopic rainbows’ in twisted bilayer graphene [12, 13]. For MoSe2, a shift in interlayer breathing modes and shearing modes were observed [10]. As a result, previous study indicated that interlayer interactions in 2D materials strongly depend on the twist angle [14, 15]. For 2D black phosphorus, previous theoretical studies predicted that twisted bilayer black phosphorus has different band structure and optical response, compared to untwisted bilayer black phosphorus because of interlayer interactions. For example, its absorption spectra have one additional peak, which makes it useful as a filter material [16]. Also, theoretical calculations predicted that its electronic structure and optical transitions are tunable by external gating [14]. Other band structure simulations predicted that the twist angle adds a new degree of freedom in this superlattice and the bandgap of BP will decrease after stacking, which is important for the applications in infrared photodetectors [17]. However, these effects have not been observed experimentally, because 2D black phosphorus is delicate [18], difficult to transfer and not stable in air. Moreover, black phosphorus made from chemical vapor deposition (CVD) is not sufficiently crystalline [19]. Wet and dry transfer methods are commonly used to fabrication 2D heterostructures [20, 21]. However, these methods are not suitable for making twisted black phosphorus without careful considerations or modifications. Water is essential in wet transfer, which may oxidize black phosphorus. Polydimethylsiloxane (PDMS), 2



which is used commonly in a dry transfer process, is so adhesive that BP flakes on a PDMS film tend to stick on it, rather than stacking to another BP flake. In this work, we figured out a modified dry transfer method, and were able to fabricate twisted stacked black phosphorus successfully.

Experiments After mechanical exfoliation, we used a modified dry transfer method to fabricate twisted stacked black phosphorus. A 6% polycarbonate (PC) in chloroform solution was dropped on a glass slide to make a PC film. After that, BP flakes were transferred to this film by dry transfer. Optical microscopy was used to select proper BP flakes of sufficient sizes and uniformity on the PC film to be further transferred. Then, we positioned the PC film with BP flakes on a BP-flake-bearing silicon substrate by a micro-feeding unit. In this step, the BP/PC film/glass slide was in contact with the BP/Si substrate face-to-face. The Si substrate was mounted on a heating stage. It was then heated to 190 °C for five minutes to make the PC film crack and the top BP/PC film was then peeled off from the PC/glass slide. Finally, the PC film was removed by putting the sample in the chloroform solution for one minute. This transfer method may be called as a “PC-film-based transfer”. This method provides a convenient way to transfer BP on other materials for structure or device fabrication. BP/graphene heterostructures and BP on copper grids have been successfully made by this method. Figure 1 below gives an illustration of this new method.

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Figure 1 Schematic of the PC-film-based transfer method for BP So far, theoretical calculations and simulations have mainly focused on twisted bilayer black phosphorus, which is composed of two single layer BP flakes. However, it is difficult to fabricate two stacked monolayer BP experimentally. BP is well known to oxidize easily in air [22]. It is hard to obtain monolayer BP by pure mechanical exfoliation [5, 23], and BP flakes made from liquid phase exfoliation have a comparatively small sizes (less than 5μm) even with a size selection method [24, 25]. Currently, thinning methods for black phosphorus, such as thermal sublimation, plasma thinning and local anodic oxidation with water rinsing, are still not sufficient to ensure a stable outcome [26-28]. Therefore, in our experiment, we could only fabricate twisted black phosphorus of 5 to 30 nm thick. They are different from twisted bilayer graphene and molybdenum diselenide, which are composed of two 4



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single atomic layers. The thickness influence will be discussed in the following section.

Density functional theory (DFT) calculations DFT calculations of twisted and untwisted bilayer black phosphorus were conducted to provide some theoretical insights on the impact of the interlayer coupling and the Raman responses. The construction of twisted bilayer black phosphorus superlattice followed the work by D. Pan et. al [29]. According to the coincidence-site lattice (CSL) theory, the new lattice basis vectors were constructed by 2D rotation and a rigid translation. For pure twisted stacking without slipping, the relative translation term cancels, and the rotation operator could be written in a matrix form as the following:

(𝑏𝑏 ) = ( ―𝑝𝑠𝑖𝑛φ 𝑞𝑠𝑖𝑛φ 1

𝑎

2

2

)( )

𝑞𝑐𝑜𝑠φ 𝑖 𝑝𝑐𝑜𝑠φ 𝑗

.

(1)

Here, i, j are basis vectors for untwisted black phosphorus. φ is the angle between i and j, which is 35.27 °. b1, b2 are the new basis vectors for twisted bilayer black phosphorus superlattice. p, q are two integers starting from 1. a is the norm of two basis vectors a1+a2 in regular BP. For pure twisted stacking without slipping, the Moiré twist angle is given by [30, 31] (𝑞2 + 𝑝2)𝑐𝑜𝑠2φ + 𝑞2 ― 𝑝2

cos𝜃 = 𝑞2 + 𝑝2 + (𝑞2 ― 𝑝2)𝑐𝑜𝑠2φ 𝑝,𝑞 ∈ 𝑁 +

(2)

Simple unit cells and thus superlattices only exist with discrete p and q values. The simplest unit cell exists when p = q = 1. In this case, the twist angle is 70.53° between two layers. On each atomic layer, the area occupied by a unit cell of a twist bilayer black phosphorus is three times that of an untwisted bilayer black phosphorus. Since there are two atomic layers, altogether there are 4×3×2=24 phosphorus atoms in one unit cell (Fig. 2b). Therefore, there are 24×3=72 phonon modes in this superlattice.

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Figure 2 (a) Crystal structure of 70.53°twisted bilayer black phosphorus. (b) Unit cell of 70.53° twisted bilayer black phosphorus. The projection direction is along b-axis (perpendicular to 2D BP plane). This is the simplest case in twisted bilayer black phosphorus superlattice.

The DFT calculations were based on the simplest superlattice discussed above. Even for this simplest case, the calculations of phonon modes were quite time consuming (see Methods for details). For comparison, we calculated Raman spectra and phonon modes for untwisted bilayer black phosphorus. Due to the time and computing resource constraints, we did not calculate the phonon modes of more complicated superlattices with more phosphorus atoms in one unit cell.

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Results and Discussions

Figure 3 (a) Optical image of twisted

black phosphorus. (b) Color-thickness relation of

untwisted black phosphorus. The thicknesses were measured by AFM. When thickness is less than 5 nm, BP sample is almost transparent and the color may differ for different substrates. Therefore, these colors are not included. (c) Twist angle characterization by angle-resolved polarized Raman spectroscopy (ARPRS). Crystal orientations of top flake and bottom flake were measured simultaneously. The twist angle for this sample is 90±3 degrees. (d) AFM data of twisted BP. The thicknesses of top and bottom flake are 20 nm (~20 layers) and 8 nm (~8 layers) respectively. The total thickness is 28 nm. The thickness fluctuation (noise) is 2 nm in the AFM tapping mode.

Five twisted stacked BP structures were fabricated with different twist angles, which are 7, 50, 75, 80 and 90 degrees respectively. The optical image of a twisted BP sample is shown in Fig. 3. The top and bottom flakes are 20 and 8 nm thick respectively, and the twist angle is 90±3 degrees measured by angle resolved polarized Raman spectroscopy (ARPRS). In the ARPRS measurement, the crystal 7


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orientations of top and bottom flakes were measured at the same time. The polarized diagrams of intensity ratio Ag1 and Ag2 were overlapped, and the angle between the two zigzag directions was the twist angle. The color of the overlapping area is obviously different from the two non-overlapping areas. According to the color-thickness correlation for untwisted BP, the color should be light green for 28 nm thick untwisted BP, but the actual color of the overlapping area with a twist angle of 90° is dark green. The color-thickness correlation for untwisted BP was based on the classical interference effect, but it could not fit the color observed in the experiment. The color difference was observed in three more twisted BP samples with twist angles of 50°, 75° and 80°. This color change indicates that the optical response is different for twisted BP, which could not be explained by classical interference effect and reflects the change in electron properties and band structure. [32] This presumption agrees with previous simulations in band structure [29]. The color difference between a sample with a 7° twist angle and its untwisted counterpart is insignificant, which is likely due to the very small twist angle. Experimentally, high frequency Raman spectra of BP have three significant Raman peaks, which are Ag1, B2g and Ag2 modes. The corresponding vibrations are illustrated in Fig. 4 (a). We define the two blue shifts between the Raman peaks of the overlapped areas and the non-overlapped areas as ∆𝜔𝑡 ≡ 𝜔𝑜𝑣 ― 𝜔𝑡𝑜𝑝,𝑛𝑜𝑣 and ∆𝜔𝑏 ≡ 𝜔𝑜𝑣 ― 𝜔𝑏𝑜𝑡𝑡𝑜𝑚,𝑛𝑜𝑣. From the Raman spectra in Fig. 3 (b), we can see that ∆ 𝜔𝑡,Ag1 = 0.40 𝑐𝑚 ―1, ∆𝜔𝑏,Ag1 = 0.14 𝑐𝑚 ―1, ∆𝜔𝑡,Ag2 = 0.14 𝑐𝑚 ―1 and ∆𝜔𝑏,Ag2 = 0.14 𝑐𝑚 ―1 for Ag1 and Ag2 Raman modes. B2g peak is blue-shifted in this sample, but it is

also red-shifted in other samples, depending on the twist angle. Previous studies have shown that Ag1, B2g and Ag2 modes should be red-shifted in untwisted BP on SiO2/Si substrates when thickness increases [23, 33, 34]. In our experiment, the overlapping area is thicker than the non-overlapping areas, but the Raman peaks observe a blue shift, rather than a red shift due to the thickness increase. Because of that, we call this phenomenon “unexpected blue shift”. Other influence factors, such as laser heating effect and equipment errors (+/-0.05 cm-1) were excluded by careful and repeated measurements. The detailed wavenumber and uncertainties are listed in the supporting information Table S3. This blue shift is noticeable because other similar effects, such as thermal and stain effects also result in Raman shifts around 0.5 cm-1 in the high frequency region for BP [35, 36]. For example, in Ref. [35], the Raman peak shift is 0.4 cm-1 in Ag1 mode when the laser power is increased by 10 times. The twist angle dependences of ∆𝜔𝑡 and ∆𝜔𝑏 for the three Raman peaks are shown in Fig. 4 (c) to (e). The Raman peaks of the sample with a 7° twist angle show red-shift with an increased thickness, which suggests that the phonon modes of a stacked BP with a small twist angle is close to an untwisted stacked BP. Excluding this sample, for the out-of-plane vibration mode Ag1, all Raman peaks blue-shift by 8



0.15 to 0.5 cm-1; for the in-plane vibration mode Ag2, a similar trend was observed with mostly blue shifts up to 0.2 cm-1; for in-plane vibration mode B2g, the peak shifts measured were more complicated showing one peak being red-shifted and others blue-shifted.

Figure 4 (a) Illustration of three high frequency Raman active phonon modes in BP. Ag1 mode has a vibration direction perpendicular to 2D BP plane, so interlayer coupling exerts more influence on it. (b) Raman spectra of top flake, bottom flake and stacked flakes in sample shown in fig. 2 (a). The wavenumber of stacked flakes is larger than both top flake and bottom flake, so the Raman 9


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spectra of overlapping area is not the superposition of that in top flake and bottom flake. We call this phenomenon ‘unexpected blue shift’. Figure 4 (c) - (e) plot ∆𝜔𝑡 and ∆𝜔𝑏 versus the twist angle for Ag1, B2g and Ag2 modes. ∆𝜔𝑡 and ∆𝜔𝑏 are plotted separately. Positive value means blue shift while negative value means red shift. The error bars are statistical deviations.

To investigate the thickness dependence, we used chemical thinning to etch one twisted stacked BP sample with a twist angle of 75° and compared ∆𝜔𝑡 and ∆𝜔𝑏 for different thicknesses. The results are compiled in Figure 5. The top and bottom flakes were around 50 nm before etching. After etching, top flake is 20 nm thick and bottom flake is 8 nm thick with some non-uniformity. For the etched sample, Raman measurements were made on regions of different thickness, and the difference was within the uncertainty range of the Raman system (0.05 cm-1).

(d)

(c)

Figure 5 Blue shift values before (with each flake thickness of 50 nm) and after chemical etching (with each flake thickness between 10 and 20 nm). (a) ∆𝜔𝑡 (b) ∆𝜔𝑏. Wavenumber versus sample

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thickness for (c) Ag1 mode (d) Ag2 mode. The wavenumbers of twisted BP (large twist angle) are significantly larger than the expected values for untwisted BP from the non-overlapping regions.

From Figure 5 (a), (b), we can see that the average value of ∆𝜔𝑡 and ∆𝜔𝑏 changed from ~0.2 cm-1 for preliminary flakes (50 nm thick) to ~0.5 cm-1 for etched flakes (10-20 nm thick). Generally speaking, the wavenumbers of Raman peaks decreases when thickness increases for untwisted BP on Si/SiO2 substrate. Above 10 nm, the changing rate is around 0.025 cm-1/nm for Ag1 and 0.004 cm-1/nm for Ag2 [34]. For twisted BP in our experiment, from 15 nm to 50 nm, the wavenumbers 𝜔𝑜𝑣,𝜔𝑡𝑜𝑝,𝑛𝑜𝑣, and 𝜔𝑏𝑜𝑡𝑡𝑜𝑚,𝑛𝑜𝑣 also decrease with the increased thickness, and this shows a similar trend as this for untwisted BP. According to our Raman measurements, ∆𝜔𝑡 and ∆ 𝜔𝑏 both increase. Also, in the thickness interval 25 nm to 35 nm, the shifts caused by thickness are subtle and less than the equipment error. Since our sample thicknesses in Fig 3 are all in this range, we can conclude that thickness does not have any significant effects on the blue shift, so the shift values are only dependent on the twist angle. Figure 5 (c), (d) related to wavenumber versus sample thickness give another prospective of the unexpected blue shifts.

DFT calculation results of the untwisted bilayer BP and the twisted bilayer BP Mode

Ag

Type of BP

Symmetry

Wavenumber

Raman Intensity

Untwisted bilayer

Ag1

351.86

18769

Twisted bilayer

A

356.56

26606

Untwisted bilayer

Ag2

455.57

28592

Twisted bilayer

A

456.88

1655.5

(cm-1)

1

Ag

2

Blue shift value (cm-1)

4.70

1.31

Table 1 DFT calculation results of the untwisted bilayer BP and the twisted bilayer BP. These two modes are selected from 24 phonon modes in the untwisted bilayer BP and 72 phonon modes in twisted bilayer BP with same kind of symmetry.

The result summary of the DFT calculations is shown in Table 1. The unit cell of the twisted bilayer black phosphorus is in space group P222 (point group D2), while the unit cell of the untwisted bilayer black phosphorus is in space group Pbcm (point group D2h). Due to the lower symmetry, or “symmetry breaking”, the 72 calculated phonon modes of the twisted bilayer BP with 70.53° angle (24 atoms per unit cell) do not have special parity, and the symmetry notations reduce to A and B instead of Ag1, B2g and Ag2. Out of the 72 modes calculated, to identify the corresponding Raman peaks of twisted bilayer BP, we select two high intensity Raman active modes with 11


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same symmetry notation A, whose wavenumbers are close to the wavenumbers we measured in the experiment. To make the discussion easier to understand, in the following, the measured and calculated Raman peaks of twisted stacked BP are still called Ag1, B2g and Ag2 peaks. For example, the measured Ag1 and Ag2 peaks were at 362.06 and 466.44 cm-1 for twisted BP as in Fig. 4(b) and the corresponding peaks selected from the DFT results of twisted bilayer BP are at 356.56 and 456.88 cm-1. The relative differences of the wavenumbers are less than 3%. The detailed list, for all the 24 phonon modes in untwisted bilayer black phosphorus and 72 phonon modes in twisted bilayer black phosphorus, is in the supplement information. Next, we compared the calculated results of an untwisted bilayer BP and a twisted bilayer BP with a 70.53° twist angle. DFT calculation results of Ag1 and Ag2 peaks of twisted bilayer BP are 4.70 cm-1 and 1.31 cm-1 higher than those of untwisted bilayer BP, which are consistent with the blue shifts observed in Raman spectra. Another interesting fact is that the shift values are larger in calculation than those in experiment. This may be explained by the BP layer thickness differences between the experiments (5-30 nm) and the calculations (bilayer). Thinner flakes may be more sensitive to the phonon modulation effect from the twisting and may generate bigger blue shifts. This is consistent with the blue shift values trend before and after chemical etching. If twisted bilayer BP could be fabricated by chemical vapor deposition, we could observe a larger blue shift value. In summary, the blue shift phenomenon is qualitatively explained by the DFT calculations.

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Figure 6 (a) 3D charge density map in a unit cell of the untwisted bilayer black phosphorus. (b) 3D charge density map in a unit cell of the 70.53° twisted bilayer black phosphorus. (c) 2D charge density map in the cutting plane of the untwisted bilayer black phosphorus. This cutting plane (020) is the middle-distance plane between the two 2D black phosphorus atomic planes. (d) 2D charge density map in the same cutting plane of the 70.53° twisted bilayer black phosphorus. (e) Another cutting plane (100) of the twisted bilayer black phosphorus, which is normal to the 2D atomic planes. The values on the left are the electron densities. The scale bars in figure (c) - (e) represent 0.1 nm.

To further explain the phenomenon, charge densities in twisted and untwisted bilayer black phosphorus were also calculated by DFT program. The results are compared in Fig. 6. The 3D charge distribution of the twisted bilayer BP in Fig. 6 (b) has more overlap between two layers, while that of the untwisted one in Fig. 65 (a) is more localized. The cutting planes (020) in Fig. 6(c) and (d) are the middle-distance planes between the two layers. Significant distribution differences exist between two BP unit cells. Other interaction beyond van der Waals force may exist, and this interaction has some similarities as covalent bond because electron cloud is more overlapped as indicated in the graph. Another cutting plane (100) of twisted bilayer BP in Fig. 6(e), which is normal to the 2D atomic planes, gives another perspective of the overlapping electron cloud between phosphorus atoms in different layers. Based on the experiment and calculation results, this unexpected blue shift can be explained by a strong interlayer coupling effect and thus a strong phonon mode change near Γ point in this 2D heterostructure. This is consistent with the significant interlayer interaction reported before [15]. A phosphorus atom has five valence 13


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electrons, three of which form covalent intralayer bonds and the rest two form electron lone pair. This electron lone pair may extend to the interlayer vacuum region and affect interlayer van der Waals interactions. When the twist angle is not equal to zero, there are different Coulomb interactions between layers because of electron distribution change. This change will lead a phonon modulation effect and cause unexpected blue shift in Raman spectra. Ag1 mode has a vibrating direction perpendicular to the 2D BP plane, so it has a larger shift compared to other modes. This phenomenon also indicates that BP interlayer interactions are not simply van der Waals interactions. Other interactions beyond van der Waals force, as indicated in Fig. 5, may exist between atoms in different layers of twisted bilayer black phosphorus. Other phenomenon reported before, such as surface reactivity, proves additional interactions may exist as well [37, 38]. A more sophisticated explanation could be made based on the Hamiltonian proposed by Pavlov and Felsov. The transitions due to the scattering of electrons by phonons can be written as [39, 40] 𝐻𝑝ℎ = 𝑉𝑝ℎ + 𝛾(𝜎 × ∇𝑉𝑝ℎ) × (𝑝 ― 𝑒/𝑐𝐴),

(3)

Vph is the phonon operator and γ is a parameter which presents the strength of the electron-phonon interaction. σ is the Pauli spin operator and A is the vector potential. The resulted Hph is also related to the bandgap, which is consistent with previous simulation predictions [16]. This Hamiltonian shows that phonon modulation effect will cause some changes in the electron behaviours. More insights may arise from this work. Previous simulation predicted that the Dirac cone and topological phase transition may be resulted from external electric field in black phosphorus [41]. Strong interlayer interactions are an indispensable part for this phenomenon [42]. Low frequency Raman measurements may be useful to find new peaks and more shifts in twisted stacked black phosphorus. This is a topic worthy more exploration.

Conclusion In conclusion, we experimentally fabricated twisted stacked black phosphorus structures and observed unique optical responses and unexpected blue shifts in their Raman spectra. The phonon behavior can be qualitatively explained by our density functional theory calculations. This work suggests that interlayer coupling has a significant effect in twisted stacked black phosphorus, where the interlayer interactions are not just van der Waals interactions. Additional interactions beyond van der Waals force may exist in this structure. This new fabrication method and structures are important for applications in optical filters and infrared photodetectors. 14



Methods Exfoliation: Bulk black phosphorus was purchased from Smart Elements. BP were mechanically exfoliated onto a Si substrate with a 300 nm SiO2 layer. Before exfoliation, the silicon substrate was cleaned by acetone and isopropanol subsequently. Optical observation was used to preliminarily determine the position and thickness of BP. The detailed examination of thickness was carried by Atom Force Microscopy (AFM) measurements. Optical characterization: Optical measurements were carried out by a Nikon TE2000 optical microscope, which was linked to an imaging spectrometer and a computer. A quartz-tungsten-halogen lamp was used to illuminate the black phosphorus sample. The magnification was 20 times. The color level in the computer image was set to be the same as vision and the light is unpolarized. Raman spectroscopy: Raman spectra were collected by a Horiba Scientific LabRam HR800 Raman system. The excitation laser was 441.6 nm in this experiment (2.81 eV, He-Cd laser). Between the detector and the filter, there was a polarization analyzer for angle-resolved polarized Raman spectroscopy (ARPRS). The spectral range measured was from 300 to 600 cm-1. Twist angle characterization: ARPRS was used to measure the twist angles. The intensities ratios between Ag1 and Ag2 are strongly dependent on the angles between the polarization direction of the incident laser and the crystal orientation of the sample [33, 43, 44]. In the ARPRS work, crystal orientations of non-overlapping and overlapping areas were measured simultaneously. BP samples were rotated by 15° each step with a total twenty four steps to cover 360°. Atom Force Microscopy (AFM): AFM measurements were performed in a nano IR system. The mode was tapping mode with a resonance frequency 285 kHz. The scanning rate was 1 Hz. DFT calculation: The construction of the Moiré pattern superlattice, as shown above, was based on the Coincidence Site Lattice (CSL) theory. Raman spectra of the twisted and untwisted bilayer black phosphorus were calculated within the framework of the DFT by Quantum Espresso software package [45]. Raman and infrared intensities were calculated by the phonon modes and second order derivatives of the electron density matrix in unit cell. PBE (John P. Perdew, Kieron Burke and Matthias Ernzerhof [46]) functional with norm conserving potentials was used, and the energy cutoff was set to 80 Ry. To increase the accuracy of the phonon calculations, the self-consistency thresholds were set to 10-14. The calculation was performed by 4 computing nodes with 32 cores and 128 GB memory on each node, and took about 20864 CPU hours. 15


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Author contribution Tao Fang and Guangrui Xia initiated the project. Tao Fang designed the experiments. Tao Fang and Rui Yang made BP samples. Tao Fang and Teren Liu carried Raman and AFM measurements. Teren Liu performed the chemical etching. Teren Liu and Tao Fang performed the DFT calculations and analysis. Tao Fang and Zenan Jiang (supervised by Peyman Servati) conducted wet transfer trials. Tao Fang, Teren Liu and Guangrui Xia led the writing and the revisions of the paper. The project was supervised by Guangrui Xia.

Acknowledgment We would like to acknowledge these people for their help in this project: Prof. Mona Berciu (Department of Physics and Astronomy, University of British Columbia) for helpful discussions, Prof. Joshua Folk (Department of Physics and Astronomy, University of British Columbia) for providing experimental apparatus, Qian Song (graduate student at Department of Physics, Massachusetts Institute of Technology), Jialun Liu (graduate student at Department of Electrical Engineering and Computer Science, University of Illinois at Urbana–Champaign), Prof. Ursula Wurstbauer (Walter Schottky Institute) and Poya Yasae (graduate student at Department of Mechanical and Industrial Engineering, University of Illinois at Chicago) for useful discussions. Also, we would like to acknowledge Westgrid and Compute Canada for the support of our DFT calculations.

Competing financial interests We would like to acknowledge Stewart Blusson Quantum Matter Institute (SBQMI) and the University of British Columbia to provide funding for this project.

Supporting Information 1. Demonstration of high frequency Raman modes in BP 2. 24 calculated phonon modes in untwisted bilayer BP and 72 calculated phonon modes in twisted bilayer BP 3. Supplement information for our Raman spectra 4. A list of sample thicknesses

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Fabrication and the Interlayer Coupling Effect of Twisted Stacked

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