Anisotropic moiré optical transitions in twisted monolayer/bilayer phosphorene heterostructures

Moiré superlattices of van der Waals heterostructures provide a powerful way to engineer electronic structures of two-dimensional materials. Many novel quantum phenomena have emerged in graphene and transition metal dichalcogenide moiré systems. Twisted phosphorene offers another attractive system to explore moiré physics because phosphorene features an anisotropic rectangular lattice, different from isotropic hexagonal lattices previously reported. Here we report emerging anisotropic moiré optical transitions in twisted monolayer/bilayer phosphorenes. The optical resonances in phosphorene moiré superlattice depend sensitively on twist angle and are completely different from those in the constitute monolayer and bilayer phosphorene even for a twist angle as large as 19°. Our calculations reveal that the Γ-point direct bandgap and the rectangular lattice of phosphorene give rise to the remarkably strong moiré physics in large-twist-angle phosphorene heterostructures. This work highlights fresh opportunities to explore moiré physics in phosphorene and other van der Waals heterostructures with different lattice configurations.

3 Stacked van der Waals heterostructures with a finite twist angle can generate a moiré superlattice, which is characterized by a periodic variation of the interlayer stacking order.
In this letter, we reported the first experimental study of rectangular moiré superlattices of twisted monolayer/bilayer phosphorene heterostructures. Phosphorene features a puckered honeycomb structure that forms an anisotropic rectangular unit cell 13,23,24 , and it has a direct bandgap lying at the Γ point in the first Brillouin zone [11][12][13][14] . In addition, few-layer phosphorene is known to exhibit unusually strong interlayer interactions, which leads to a dramatic change of the direct bandgap from 1.73 eV in monolayer phosphorene to 0.62 eV in tetralayer phosphorene 13,25 . Here we demonstrate the moiré potential completely changes the electronic band structure and gives rise to a new 4 set of optical transitions in twisted monolayer/bilayer phosphorene heterostructure even for twist angles larger than 19°. This behavior is in striking contrast to other moiré systems, where prominent moiré effects exist only for twist angles smaller than a few degrees. The emerging optical resonances in the phosphorene moiré heterostructure are linearly polarized, and the polarization axis is closer to but different from the armchair direction of the bilayer phosphorene. Our ab initio density functional theory (DFT) calculations show that the remarkably large moiré superlattice potential at large twist angle originates from the Γ-point direct bandgap as well as the strong and stacking-dependent interlayer electron hybridization in twisted phosphorene heterostructures. The theory also reveals the extremely important role of the underlying electron Bloch wavefunction in the interlayer coupling, which results in a strongly hybridized conduction band but a negligibly coupled valence band in twisted phosphorene heterostructure. The calculated optical responses of the monolayer-bilayer moiré superlattice agree well with our experimental observations. Figure 1a illustrates the configuration of a twisted monolayer/bilayer phosphorene heterostructure encapsulated between thin hBN layers. Few-layer phosphorene samples were first mechanically exfoliated onto the surface of polydimethylsiloxane (PDMS) thin films, and then transferred to 285-nm thick silicon dioxide/silicon (SiO2/Si) substrates (see methods) 25,26 . The layer number of phosphorene was determined from the optical image contrast and verified by photoluminescence (PL) measurements. Thin hBN layers were also mechanically exfoliated from their bulk crystals. We then sequentially assembled the top hBN, monolayer phosphorene, bilayer phosphorene, and the bottom hBN using a drytransfer method 27,28 (see Methods). The whole structure was then transferred onto a 90-nm thick SiO2/Si substrate for further optical measurements. To minimize sample degeneration, 5 the whole fabrication process was done inside a nitrogen-gas-filled glovebox with both moisture and oxygen levels lower than 0.1 ppm. Figure 1b illustrates the moiré superlattice of the phosphorene heterostructure with a large twist angle of 19°. The gray dashed rectangle indicates the supercell of the moiré superlattice with four high symmetry points at A, B, C, and D (see Fig. S1 and S2 in Supplementary Information for the atom configurations of these high symmetry points).  Figure 1d shows the polarization-dependent PL of the monolayer and bilayer phosphorene, from which we can determine a rotation of the principal axis of 19° ± 1° between the monolayer and bilayer. Two different devices (D2 and D3) with the monolayer-bilayer twist angle of 6° and 2° are shown in Fig. S4 (Supplementary Information). Fig. 1e display the PL spectra of the monolayer (red), bilayer (black), and heterostructure regions (blue) in the device D1, respectively. Surprisingly, we observe an emerging moiré optical transition at 0.83 eV in the twisted monolayer/bilayer phosphorene heterostructure, which is distinctly different from the monolayer resonance at 1.73 eV and the bilayer resonance at 1.10 eV. It shows that moiré superlattice has a dramatic effect on the optical properties of the phosphorene heterostructure even for twist angles as large as 19°.

6
Next we investigate optical resonances of the phosphorene heterostructures with different monolayer-bilayer twist angles using photoluminescence excitation (PLE) spectroscopy. Fig. 2a, 2b, 2c, and 2d show the 2D color plot of the PLE results for the twisted phosphorene heterostructure with the twist angle at 19°, 6°, 2°, and 0° (i.e. exfoliated trilayer), respectively. The color scale bar corresponds to the PL intensities. In addition, the right panels in the figure show the integrated PL intensity between 0.8 eV -0.9 eV as a function of the excitation energy. The PLE spectra show that optical properties of the twisted monolayer/bilayer phosphorene depend strongly on the twist angles, and they exhibit optical transitions distinctly different from the monolayer and bilayer phosphorene. We further investigated the polarization dependence of the PL emission in the 19° twisted phosphorene heterostructure (blue dots, Fig. 3a). The PL intensity shows a welldefined cos 2 θ pattern (blue line, Fig. 3a), which indicates a linearly polarized emission from the twisted phosphorene heterostructure. Interestingly, the polarization principal axis does not align with that of either the monolayer (red line) or the bilayer (black line). Instead  It has a VBM energy that is almost identical to that of the bilayer phosphorene, but a CBM energy much lower than those of both bilayer and trilayer phosphorene. The unusual electronic bands of the twisted phosphorene heterostructure are further illustrated in the partial charge density distribution of the CBM and VBM, as shown in Fig. 4c and 4d, respectively. Apparently, the conduction band is strongly hybridized between the monolayer and bilayer. Electrons at the CBM are mostly localized at the monolayer-bilayer interface, and the charge density exhibit strong periodic modulation commensurate with 9 the moiré superlattice (Fig. 4c). The largest electron density is observed at the near-ABC-  Fig. 4e. It leads to the highest CBM electron density in these regions in the moiré superlattice, as observed in Fig. 4c. In contrast, the electron wavefunctions at the VBM exhibit oscillating signs at the monolayerbilayer interface (Fig. 4f). As a result, the electron coupling at different atom sites interferes destructively with each other, giving rise to an extremely weak interlayer coupling. 10 Consequently, the VBM electrons are mostly localized in the bilayer phosphorene with negligible hybridization with the monolayer (Fig. 4d).
In summary, our experimental observations reveal that moiré superlattices can strongly modulate the electronic band structures and optical transitions of the twisted phosphorene. The moiré superlattice effect remains strong even for a very large twist angle, highlighting new moiré physics that can emerge in van der Waals heterostructures with rectangular lattices.

Fabrication of twisted phosphorene structures.
Bulk black phosphorus crystals were synthesized from red phosphorus with Sn and SnI4 as transport agents using a chemical vapor transport method, and details can be found in

Optical measurements
Samples were kept at the liquid nitrogen temperature for all optical measurements. PL measurements were conducted using a lab-build micro-PL setup in reflection geometry with a long working distance near-infrared objective (50x, N.A. 0.42) and the spectrometer equipped with both silicon and InGaAs detectors. PLE measurements were performed using a super-continuum laser (SC-Pro, YSL) as the excitation source. Tunable excitation light with the linewidth less than 0.5 nm was spectrally picked up by a grating and filtered out by suitable filters. The spot size of the focused light was ~2 μm. The result spectra were normalized to both integration time and incident power. For polarization-dependent PL measurements, linearly polarized light was set with a Glan-Thompson polarizer and rotated by a half-wave plate.

First-principles calculations
The supercell of twisted phosphorenes was constructed based on the coincidence site lattice theory 33 . The commensurate 20.04° twisted phosphorene heterostructure was used to model the electronic band structure and optical properties of the experimental 19° one.
We performed DFT calculations using the projector augmented wave method 34 and the plane-wave basis as implemented in the VASP 29 . The cutoff energy of the plane-wave basis was set to be 450 eV. The vacuum thickness was set to be 15 Å to avoid the interaction between adjacent layers. In addition, the supercells were fully optimized until the residual force per atom was less than 0.01 eVÅ -1 . For monolayer, bilayer, and trilayer phosphorene, Monkhorst-Pack 10 × 8 × 1, 20 × 16 × 1, and 50 × 40 × 1 k-meshes were adopted to sample the first Brillouin zones, calculate electronic band structures, and obtain absorption spectra, respectively. For large-angle twisted phosphorene, the k-meshes were 5 × 3 × 1. The non-

Competing interests
The authors declare no competing interests.

Data and materials availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.

Corresponding author
Correspondence and Requests for materials should be addressed to:       The intrinsic stacking order of few-layer phosphorene is ABA stacking, as illustrated in Fig. S1a.

Supplementary Information for
The relative translation between the top monolayer and bottom bilayer phosphorene gives rise to different stacking orders, see Fig. S1 (bf). In large-angle twisted phosphorene heterostructure, the stacking orders of the high-symmetric point A, B, C, and D in Fig. 1b (main text) are close to ABA (Fig. S1d), ABB (Fig. S1e), ABC (Fig.S1c), and ABD stacking (Fig.S1f), respectively.
Therefore, the stacking orders of point A, B, C, and D in the 19° twisted heterostructure are referred as near-ABA (Fig. S2a), near-ABB (Fig. S2b), near-ABC (Fig. S2c), and near-ABD stacking (Fig.   S2d), respectively.  S3. Angle determination for twisted phosphorene heterostructures Two more devices (D2 and D3) were fabricated using the same method described in the main text. We fit the experimental angle-dependent PL emission spectra with the function: where I represents the PL emission intensity, I0 and C are constants to be fitted, θ and φ indicate the incident angle of polarized light and the phase angle, respectively. Based on this method, the relative angle difference between monolayer and bilayer in device D1, D2 and D3 are 19° ± 1.1°, 5.9° ± 0.8°, and 2.2° ± 0.9°, respectively, see Fig. 1f in the main text, Fig. S4c and S4d. with an angle of φ gave rise to the angle difference (with value of -φ) between the primary optical axis and the x-direction of the twisted phosphorene heterostructure, where matrix M and R were constructed by equation (2) and (3). where Λ indicated a diagonal matrix. The calculation then gave φ ≈ -3.1°, which indicates that the primary optical axis of the twisted phosphorene heterostructure locates close to that of its constituent bilayer phosphorene with a ~7° angle difference. Pz orbitals contribute mainly to the wavefunctions at the CBM and VBM of the 19° twisted phosphorene structure, as shown in Table 1.