Infrared optoelectronics in twisted black phosphorus

Abstract

Electrons and holes, fundamental charge carriers in semiconductors, dominate optical transitions and detection processes. Twisted van der Waals (vdW) heterostructures offer an effective approach to manipulate radiation, separation, and collection processes of electron-hole pairs by creating an atomically sharp interface. Here, we demonstrate that twisted interfaces in vdW layered black phosphorus (BP), an infrared semiconductor with highly anisotropic crystalline structure and properties, can significantly alter both recombination and separation processes of electron-hole pairs. On the one hand, the twisted interface breaks the symmetry of optical transition states resulting in infrared light emission of originally symmetry-forbidden optical states along the zigzag direction. On the other hand, spontaneous electronic polarization/bulk photovoltaic effect is generated at the twisted interface enabling effective separation of electron-hole pairs without external voltage bias. This is supported by first-principles calculations and repeated experiments at various twisted angles from 0 to 90°. Importantly, these phenomena can be observed in twisted heterostructures with thickness beyond two-dimensional. Our results suggest that the engineering of vdW twisted interfaces is an effective strategy for manipulating the optoelectronic properties of materials and constructing functional devices.

Here, the authors report a study of the infrared optoelectronic properties of twisted 2D black phosphorus (BP), showing photoluminescence emission from optical transitions that are symmetry-forbidden in BP and spontaneous electronic polarization generating interfacial bulk photovoltaic effect.

Introduction

Manipulating radiation, separation, and collection processes of electron-hole pairs has enabled various photonic devices with new configurations and functions^1–5. In recent years, twisted van der Waals (vdW) heterostructure, with atomically sharp interface, tunable twisted angles, and strong moiré potential, provides an effective approach to realize unconventional physical phenomena^3–9, including unconventional superconductivity, moiré excitons, bulk photovoltaic effect (BPVE), and pseudo magnetic fields, and new-functional devices^5,9–12, including intelligent photon detectors and quantum emitters. A variety of twisted structures, including twisted bilayer graphene, twisted transition-metal dichalcogenides, and twisted black phosphorus (BP)-based structures, have been demonstrated^{3–11,13–15}. Among them, BP has a puckered lattice structure with lower crystalline symmetry than that in graphene, resulting in highly anisotropic physical properties^16,17. For example, light emission in BP shows perfect linear polarization along the armchair direction of the crystalline structure and is strictly forbidden along the zigzag direction due to symmetry requirements of optical transition states^18–25. It is worth noting that the bandgap of thin-film BP focused in this work is between 0.3 and 0.4 eV, which falls into the mid-infrared region where available materials are scarce. The ability to manipulate the recombination and separation processes of electron-hole pairs in BP, combining its high internal light-emitting efficiency and widely tunable bandgap, could show important implications for mid-infrared information processing^21–34. Here, through constructing twisted BP heterostructures, we not only brighten the symmetry-forbidden polarized mid-infrared light emission along the zigzag direction in thin-film BP but also generate interfacial BPVE to effectively separate and collect electron-hole pairs at zero external voltage bias (see Fig. 1). The first-principles calculations suggest that the broken symmetry of optical transition states and crystalline structure are responsible for the nonzero optical transition component along zigzag direction in the dipole operator and interfacial BPVE, respectively. In addition, the observed phenomena in twisted BP structures do not require atomically thin layers of BP and precisely aligned twisted angles. Instead, thin-film BP flakes with a thickness of several tens of nanometers and various twisted angles are able to generate a strong interfacial effect, which makes the device fabrication process more reliable and convenient.

Fig. 1. Schematics of applications of twisted black phosphorus (BP) heterostructures.

At large twisted angles, abnormal infrared light emission can be observed along the zigzag direction which is originally symmetry-forbidden. At small twisted angles, pronounced spontaneous polarization/bulk photovoltaic effect (BPVE) dominates electron-hole pair separation processes.

Results

Brightening symmetry-forbidden optical transition states

Figure 2a shows the optical image of a twisted BP sample (Sample LA) covered by hexagonal boron nitride (hBN) where the thicknesses of the top and bottom BP flakes are 19 and 41 layers, respectively (see Supplementary Fig. 1). Here, the top and bottom BP flakes are chosen with different thicknesses to distinguish their PL spectra since thicker BP has a smaller bandgap and longer PL wavelength^29,35–37. Insulating hBN serves as the protective layer. The twisted angle α is determined to be 90°, as demonstrated by their polarized PL spectra below.

Fig. 2. Mid-infrared light-emitting properties in pure and twisted BP at room temperature.

a Optical image of a twisted BP structure covered by hBN (Sample LA). The twisted angle α is 90°. θ represents the detection angle. The top and bottom BP and hBN layers are enclosed by the red, blue, and black dashed lines, respectively. The red arrow indicates the armchair direction of the top BP. The blue arrows indicate the armchair and zigzag directions of the bottom BP. The scale bar is 30 μm. b Normalized photoluminescence (PL) spectra of individual top and bottom BP in Sample LA along armchair and zigzag directions. The excitation source is a linearly polarized 532-nm laser. The polarization of the incident laser is fixed at the y-direction (armchair direction of bottom BP). PL along the zigzag direction is strictly forbidden due to symmetry requirements. c PL intensity of individual top (red scatters and fitting lines) and bottom BP (blue scatters and fitting lines) as a function of detection angle θ. The solid lines are fitting curves of PL intensities using the equation I = C cos²(θ + ϕ), where I is the PL intensity, C is the amplitude, and ϕ is the phase. The polarization of the incident laser is along the y-direction (armchair direction for bottom BP and zigzag direction for top BP). d PL spectra of twisted BP structure and individual top BP and bottom BP flakes at the same characterization condition in Sample LA. The detection angle is along the x-direction (zigzag direction of bottom BP). The inset is the schematic showing the PL detection along the x-direction. The polarization of the incident laser is fixed at the y-direction (armchair direction of bottom BP). e Estimated PL contribution from top and bottom layers in the twisted region. Red and green solid lines are the fitting curves of PL contribution from top and bottom BP, respectively. f Comparison of PL intensities between twisted BP structure I_twisted and added-up PL of top and bottom BP I_top+bot at different θ. Scatters and solid lines are experimental data and fitting curves (using the above equation I = C cos²(θ + ϕ)), respectively.

PL spectra of individual top and bottom BP are characterized before investigating the twisted region of Sample LA. The excitation source is a linearly polarized 532-nm laser. As shown in Fig. 2b, PL wavelengths are 3.38 and 3.60 μm for top and bottom BP, respectively. The shorter wavelength in top BP is due to its thinner thickness^29,35–37. We notice that PL peaks of individual BP cannot be well fitted using a single Gaussian shape (see Supplementary Fig. 2), since there exist contributions from multiple effects such as free, charged and bounded excitons^38–40. In addition, the PL spectra of both top and bottom BP exhibit perfect linear polarization, with the maximum value along the armchair direction and a vanishing value along the zigzag direction (see Fig. 2a, b). These results show excellent agreement with previous reports in thin-film BP^17,29,36,37. For Sample LA, the armchair directions of top and bottom BP are along the x- and y- directions, respectively, as demonstrated by their PL intensities at different polarization angles θ (see Fig. 2c). The forbidden light emission along the zigzag direction in BP can be understood through analyzing the symmetries of the wavefunctions of electron states in conduction and valence bands^18,20. As shown in Supplementary Fig. 3, our density functional theory (DFT) calculations reproduce the band structures and wavefunctions of electron states in BP. Without loss of generality, we adopt a 3-layer BP for the calculations. Here, the dipole moment M_ge for an electron-hole pair when the electron is excited from the ground state |g> to the excited state |e> can be defined as $M_{\mathrm{ge}}=<g\mid \widehat{d}\mid e>$, where $\widehat{d}$ is the dipole operator^18,20. Along the armchair direction, electron states in conduction and valence bands do not possess odd/even symmetry, resulting in a finite M_ge value. However, along the zigzag direction, electron states in conduction and valence bands possess even symmetry. This leads to a vanishing value for M_ge, and PL emission is forbidden along the zigzag direction^18,20.

PL spectra of twisted region in Sample LA with polarization along the x-direction (zigzag direction of bottom BP/armchair direction of top BP) are shown in Fig. 2d. A broader PL spectrum with multiple-peak feature is observed, covering the whole spectral region of PL from individual top and bottom BP flakes. The PL peak of ~3.4 μm can be attributed to the top BP flake since the detection polarization is along the armchair direction of top BP, which enables efficient light emission. Importantly, the PL spectra at longer wavelengths are symmetrically forbidden in individual bottom BP, while they appear in twisted structures. Because the broad PL in twisted BP might contain multiple peaks, it is difficult to obtain each PL component accurately through multi-peak Gaussian fittings. Hence, we estimated PL contributions from bottom BP in twisted region I_{twist_bot} = I_twist − AI_top by simply removing the contribution from individual top layers I_top from the total PL in twisted region I_twist, where A is a weight parameter. Figure 2e shows the estimated results when choosing A = 1.7. Although the estimated I_{twist_bot} will show some deviations from the true value, it can qualitatively explain the observation. Estimated I_{twist_bot} at other values of A is further shown in Supplementary Fig. 4, which shows a similar spectral shape. We also notice that I_{twist_bot} shows a redshift compared with that of individual BP. We further characterized PL spectra of twisted BP at various polarization angles (see Fig. 2f and Supplementary Fig. 5). The PL peaks all show very broad features covering spectra from 2.7 to 4.2 μm. We further compared I_twist (see purple scatters in Fig. 2f) with the added-up PL intensities of individual bottom and top BP flakes I_top+bot = I_top + I_bot different detection angles θ, where I_bot and I_top are PL intensities of individual bottom and top BP, respectively (see blue scatters in Fig. 2f). As shown in Fig. 2f, I_twisted is much larger than I_top+bot along the x-direction, indicating additional light emission along zigzag direction in bottom BP is enabled in the twisted region.

DFT calculations on a 3-layer/4-layer BP heterostructure with twisted angle of 90° provide a qualitative analysis to further support the experimental observations (see Fig. 3a–c). The direct bandgap transitions (from CB_D to valence bands VB_B and VB_T) still persist at Γ point. In addition, the conduction band minimum shifts to CB_ID, which is located at Γ–Y. This indicates that indirect bandgap transitions with lower photon energy from CB_ID to valence bands can also contribute to photon emissions in twisted BP. We further analyze the distribution and symmetry of electron states in different bands. Electron states in the highest two valence bands VB_B and VB_T are only confined in the bottom 4-layer and the top 3-layer BP, respectively (see Supplementary Fig. 6). Electron states in CB_ID are only confined in the bottom 4-layer BP. Hence, the indirect bandgap transition (CB_ID to VB_B) with lower photon energy only occurs in the bottom BP (the thicker side), which agrees with the experimental observation of the redshift of I_{twist_bot}. However, electron states in CB_D spread in the whole twisted heterostructures. Importantly, odd/even symmetries of electron states in CB_D are broken along both x- and y-directions, leading to a finite value of dipole moment M_ge for an electron–hole pair. We also notice that odd/even symmetries of zigzag-directional electron states in CB_ID, VB_B, and VB_T bands are broken very near the twisted interface (enlarged images are shown in Supplementary Fig. 7). Hence, light emission along the zigzag direction of BP from both direct and indirect band transitions is theoretically allowed in the twisted region.

Fig. 3. Symmetry-breaking-induced PL in twisted BP.

a Density Functional Theory (DFT) calculations of the energy band structure of a 3-layer/4-layer BP heterostructure with twisted angle of 90°. The conduction band minimum is denoted by CB_ID. The conduction band minimum at Γ point is denoted by CB_D. The highest two valence bands are denoted by VB_B and VB_T, respectively. b Distribution of electron states in CB_D and CB_ID along the x-direction. c Schematic processes of direct (from CB_D to VB_B) and indirect band transitions (from CB_ID to VB_B). The indirect band transitions only occur in the bottom BP. d Temperature-dependent PL spectra in individual top BP flake. Incident laser polarization and detection direction are both along the x-direction. e Temperature-dependent PL spectra in twisted BP. Laser polarization is fixed at the y-direction and detection is along the x-direction. f PL intensities of individual BP flakes (circles) and twisted BP region (blue stars) as a function of temperatures. Blue and gray solid lines serve as guidelines. g Schematic of origin of the abnormal temperature-dependent PL spectra in twisted BP.

The indirect bandgap transition (CB_ID to VB_B) in bottom BP can be further confirmed by analyzing the temperature dependence of PL spectra in twisted structures. As shown in Fig. 3d, e, PL spectra of both individual and twisted BP show obvious blueshift when temperature increases. This abnormal blueshift can be attributed to the temperature-induced stress due to the large thermal expansion coefficient of BP^29,34,41. However, PL intensities of twisted BP show distinct temperature-dependent behavior compared with those in individual BP. As shown in Fig. 3f, when temperature increases, PL intensities decrease monotonously in individual BP, while PL intensities first decrease and then increase in twisted BP. From DFT calculation, as shown in Fig. 3a, b, both direct and indirect optical transitions are allowed in twisted BP. The direct transition process will result in a decreasing PL intensity when temperature increases due to stronger electron-phonon scatterings (see Fig. 3g). However, for the indirect transition process, phonon scatterings are needed to compensate for the momentum mismatch between CB_ID band minimum and VB_B band maximum during the process^42–44 (see Fig. 3c and Supplementary Note 1). Hence, finite temperature is needed to generate sufficient phonons to assist the indirect transition process. Since higher temperature leads to a higher density of phonons, the PL intensity of the indirect transition process could increase when temperature increases. As a result, the total PL intensities and superposition of direct and indirect transition processes show the non-monotonic dependence on temperatures. In short, theoretical results show good agreement with experimental observations that light emission along the zigzag direction in bottom BP (thicker side) is enabled in the twisted region with a longer wavelength and indirect nature.

Broadband interfacial BPVE in twisted BP

DFT calculations are performed to investigate the charge distribution at the twisted BP interface. Here, the twisted angle α is chosen to be 36.78° with 480 phosphorus atoms in a unit cell (enclosed by the black square in Fig. 4a). The reason for choosing the twisted angle of 36.78° for calculation is shown in Supplementary Note 2 and Supplementary Table 1. Here, C_x direction denotes the angular bisector of twisted angle α and C_y direction is perpendicular to C_x direction. As shown in Fig. 4b–d, the calculated differential charge densities ρ show that the spontaneous polarization P reaches the maximum value along C_x direction and vanishes along C_y direction (see Supplementary Note 3 and Supplementary Figs. 8 and 9). The spontaneous polarization is a typical characteristic of BPVE, which can effectively separate photo-excited electron–hole pairs without any external voltage bias^{5,9,11,45–50}. On the contrary, for samples with large twisted angles of 90° (see Fig. 4e), ρ are mirror symmetric along both C_x and C_y directions, indicating vanishing polarization at the twisted interface (see Fig. 4f–h).

Fig. 4. Theoretical investigation of BPVE in twisted BP.

a Crystalline structure of twisted bilayer BP with twisted angle of 36.78°. The black-square-enclosed area shows the unit cell of twisted BP. C_x direction denotes the angular bisector of twisted angle α and C_y direction is perpendicular to C_x direction. b Calculated differential charge densities in a unit cell of twisted BP with the twisted angle of 36.78°. P_a and P_b are the polarization vectors along a- and b-directions, respectively. P is the total polarization vector. c, d Averaged differential charge densities in a unit cell along a (c) and b (d) direction. e Crystalline structure of twisted bilayer BP with twisted angle of 90°. The black-square-enclosed area shows the unit cell of twisted BP. C_x direction denotes the angular bisector of twisted angle α and C_y direction is perpendicular to C_x direction. f, Calculated differential charge densities in a unit cell of twisted BP with twisted angle of 90°. g, h Averaged differential charge densities in a unit cell along a (g) and b (h) direction.

Electron–hole pair separation processes in twisted BP were further investigated through photocurrent measurements. Figure 5a shows the optical image of a twisted BP photodetector (Sample PA). The armchair directions of the top and bottom flakes are marked by red and black arrows, respectively. The twisted angle is ~47° determined by the polarized Raman spectroscopy (see Supplementary Fig. 10). The thicknesses of the top and bottom flakes are 28 and 14 nm, respectively, determined by AFM (see Supplementary Fig. 10). Then, we performed photocurrent characterizations using electrode pair 2–4 of which carrier collection direction is close to the C_x direction at zero voltage bias. As shown in Fig. 5b, d, the unchanged polarity of photocurrent is observed in the twisted region, which is distinct from that in extrinsic photovoltaic effects, such as a built-in electric field in Schottky junctions and photo-thermoelectric effect. For the Schottky junction effect, the directions of build-in electric fields near two electrodes are opposite, which will lead to opposite photocurrents (see Supplementary Fig. 11). For the photo-thermoelectric effect, the temperature of carriers and lattice under light spot will rise up and form the temperature gradient, leading to the diffusion of carriers to electrodes. If the light spot is in the middle of the channel, photo-thermoelectric-effect-driven carriers would diffuse to and be collected by two electrodes at the same probability, leading to a vanishing photocurrent. Hence, a photo-thermoelectric effect also shows maximum photocurrent near electrodes and vanishing value in the middle of the channel, similar to that of the Schottky effect. In our mid-infrared photocurrent measurement, the influence of the Schottky junction and photo-thermoelectric effects cannot be fully removed due to the large light spot of the mid-infrared light source. However, we have tried to minimize the contribution from these two extrinsic effects by putting the light spot in the middle of the channel. In addition, the BPVE phenomenon persists over a broad spectral band up to 4 μm (see Fig. 5f). Two photocurrent peaks near 520 nm and 2.6 μm can be observed. These photocurrent peaks match well with the absorption peaks of twisted BP as shown in Supplementary Fig. 12. On the contrary, photocurrents measured by electrode pair 1–3 (close to the C_y direction) show conventional profile with vanishing value near the middle of channel and opposite polarity near two electrodes (see Fig. 5c, e), indicating that Schottky junction effect at metal-semiconductor interface or photo-thermoelectric effect dominate the electron-pair separation process. All these experimental results show excellent agreement with the theoretical prediction in Fig. 4.

Fig. 5. Observation of BPVE in twisted BP at room temperature.

a Optical image of a twisted BP photodetector (Sample PA) with twisted angle α ~ 47°. The top and bottom BP are enclosed by the red and black dashed lines, respectively. Red and black arrows show the armchair directions of top and bottom BP, respectively. The scale bar is 10 μm. b, c Photocurrent mapping at zero voltage bias for electrode pairs 2–4 (b) and 1–3 (c), respectively. The excitation wavelength is 520 nm. d Photocurrent for electrode pair 2–4 along the dashed line in (b). e Photocurrent for electrode pair 1–3 along the dashed line in (c). f Experimentally measured wavelength-dependent responsivity for electrode pair 2–4 at zero voltage bias. The excitation sources are lasers for 0.4–1.7 μm wavelengths and a blackbody radiation source for wavelengths over 2 μm.

Compared with previous published works on BP photodetectors utilizing conventional photovoltaic effect (see Supplementary Table 2), the BPVE responsivity of twisted BP is not high which could be attributed to following reasons. Firstly, the BPVE mainly affects photocarriers near the twisted interface. The photocarriers generated away from twisted interface scarcely contribute to the BPVE photocurrent. Secondly, the interfacial charge polarization in twisted BP is not strong enough to generate significant photocurrent.

Influence of twisted angles

In total, we have fabricated over 24 samples with various twisted angles to repeat these phenomena in twisted BP. Figure 6a–c shows the PL spectra of 3 representative samples with different twist angles, which are 75° (Sample LB), 30° (Sample LC), and 6° (Sample LD). The top BP has a smaller thickness compared with the bottom BP in all samples. The laser excitation direction is along the armchair direction of bottom BP flakes, and the PL detection direction is along the zigzag direction of bottom BP flakes. We find that pronounced photon emissions along the zigzag direction of bottom BP only appear in samples with large twisted angles (Sample LB and LC). For Sample LD with small twisted angles 6°, there is no PL signal in twisted region along the zigzag direction of bottom BP. Figure 6e–g shows measured photocurrents near C_x direction of 3 representative samples with twist angles of 78° (Sample PB), 10° (Sample PC), and 0° (Sample PD). Contrary to the observation in PL samples, BPVE is more obvious in small twisted angles. These observations agree with our theoretical calculations that spontaneous polarization is stronger at smaller twisted angles (see Fig. 4e), which enhances the electron-hole pair separation process and suppresses the electron-hole recombination process, leading to stronger photocurrents and lower photon emission densities. Supplementary Fig. 13 further shows the PL spectra of Sample LD without a polarizer at the detection side. The lower PL intensity in the twisted region than that in individual BP could be attributed to the enhanced electron-hole separation process at a small twisted angle of 6°. Optical images and measured thickness of Sample LB, LC, LD, PB, PC, and PD are further shown in Supplementary Fig. 14.

Fig. 6. PL spectra and BPVE in twisted BP with various twisted angles at room temperature.

a–c PL spectra of twisted BP structure and individual top BP and bottom BP flakes with twist angles 75° (a), 30° (b), and 6° (c) in the same characterization condition. The laser excitation direction is along the armchair direction of bottom BP flakes, and the detection direction is along the zigzag direction of bottom BP flakes. “×3” indicates that the PL intensity is multiplied by three times. d–f Photocurrents near the C_x direction of twisted BP photodetectors with twist angles of 78° (d), 10° (e), and 0° (f) in the same characterization condition.

Then, we discuss the possible range of twisted angles for generating BPVE. Firstly, at the twisted angle of 90°, the distribution of differential charge densities is centrosymmetric, as shown in Fig. 4g, which leads to vanishing polarization. Secondly, at the twisted angle of 0°, the centrosymmetry of the lattice is broken if there exists an interlayer shift between top and bottom BP which supports the generation of BPVE (see theoretical calculations in Supplementary Fig. 15). If there is no interlayer shift, the lattice possesses centrosymmetry, and BPVE is not allowed in the system. Thirdly, at other twisted angles, since the centrosymmetry of the lattice does not exist near the twisted interface, the system should support BPVE in theory. However, the existence of BPVE does not guarantee that the induced photocurrent is large enough to be experimentally detected. For example, for Sample PB with the twist angle of 78°, the BPVE-induced photocurrents can not be distinguished from photocurrents induced by conventional photovoltaic effect and photo-thermoelectric effect probably due to its smaller amplitude (see Fig. 6d). Another example is about monolayer WSe₂ and MoS₂ whose lattice also do not possess centrosymmetry. No BPVE photocurrent has been observed in monolayer WSe₂ and MoS₂ yet⁵ since the photocurrent intensity also depends on the second-order nonlinear tensor and other factors. In summary, we are only confident to claim that at a twisted angle of 90° and 0° without any interlayer shift, BPVE does not exist.

Discussion

Here, we discuss some other effects that might contribute to the observed abnormal PL spectra and interfacial BPVE in twisted BP. Interfacial bubbles, which can induce tensile strain, are inevitable during the fabrication process of twisted BP^51,52. Tensile strain can enlarge the bandgap and blueshift the PL spectra of BP³³, while in our twisted BP sample, the newly emerged PL peak is at the lower energy position. We guess that PL spectra from the bubble region might be mixed with the higher energy PL spectra of the top BP flake. We further measured the PL spectra of Sample LA at different positions with various bubble intensities. They all show similar spectral shapes and broad features (see Supplementary Figs. 16 and 17). For twisted hBN/BP/BP trilayer where hBN serves as protection layers, bubbles seem to be very dense. In fact, a large proportion of bubbles are introduced in the hBN/BP interface after transferring hBN to BP/BP, as demonstrated in Supplementary Fig. 18. Those bubbles in the hBN/BP interface only induce strain in the hBN layer, which does not contribute to the mid-infrared light spectra. In addition, previous studies on PL spectra of strained BP show perfect linear dichroism with vanishing intensities along the zigzag direction, the same as that in pristine BP⁵³. Hence, we believe that the symmetry engineering of twisted interface plays a key role in the observation of abnormal light emission and unipolar photocurrents in twisted BP.

BP might also experience thermal expansion-induced strain at room temperature³⁴. We further performed DFT calculations of the band structures of a 3 L/4 L twisted BP under strain. The tensile strain of 1% along the diagonal direction (x-directional strain of 0.707% and y-directional strain of 0.707%) is used for simulations of thermal expansion-induced strain in BP. The calculation results are shown in Supplementary Fig. 19. Firstly, the bandgap increases in the presence of tensile strain. Secondly, the indirect bandgap still preserves under tensile strain. Thirdly, electronic states in CB_ID and VB_B are still located in the bottom BP. Lastly, the CB_D band moves upwards. In conclusion, although strain can alter the band structure of twisted BP, the indirect optical transitions from CB_ID to VB_B still persist and only occur in the bottom BP (the thicker side). On the one hand, the lattice of individual BP possesses centrosymmetry which suppresses the generation of BPVE. It is true that the large thermal expansion coefficient could generate uniform in-plane strain in BP at room temperature³⁴. However, if the in-plane strain is uniform in BP, the lattice is still centrosymmetric, for which BPVE is not allowed. That’s the reason why non-uniform strain (strain gradient) is needed to break the centrosymmetry of the 2H-MoS₂ lattice to generate BPVE in MoS₂⁴⁷. We further fabricated a single BP device and studied its photocurrent at zero bias at room temperature. As shown in Supplementary Fig. 20, photocurrent measurements show a traditional photovoltaic effect profile in the single BP flake. This indicates that thermal-expansion-induced in-plane strain cannot induce detectable BPVE photocurrents.

In conclusion, we show that the twisted strategy is a promising approach for controlling the recombination and separation of electron-hole pairs. Firstly, a lower photon energy PL peak and its indirect nature were revealed in twisted BP systems. Importantly, photon emission was enabled with polarization along the zigzag direction of the bottom BP (thicker side), which was symmetrically forbidden in individual BP. Then, we demonstrated that BPVE could occur in twisted structures with a broad range of twist angles and thickness of BP flakes. This could simplify the fabrication of twisted structures, expanding the possibilities beyond the use of single or bi-layer vdW materials. Last but not least, this strategy might be extended to other vdW twisted systems (see some preliminary results in Supplementary Fig. 21).

Methods

Sample preparation

BP samples were mechanically exfoliated on silicon substrates covered with 300 nm-thick SiO₂ through the standard mechanical exfoliation method. Firstly, BP and hBN flakes were mechanically exfoliated on PDMS/glass substrates. Secondly, the bottom BP was aligned and transferred onto the SiO₂/Si substrate under an optical microscope⁵⁴. Then, the same method was used to transfer the top BP onto the bottom one and coat the twisted BP with hBN flakes. Finally, the samples were annealed at 200 °C for 20 min to increase the vdW interactions between flakes. All the above processes involving BP were performed in a nitrogen-filled glovebox to prevent oxidation and photodegradation.

Optical characterizations

PL spectra of twisted BP were characterized using a Fourier transform infrared (FTIR) spectrometer and an infrared microscope (Bruker Invenio-R and Hyperion-1000) with an external lock-in amplifier (model SR830). A chopped laser with a 572 Hz chopper frequency, 532 nm wavelength, and ~25 μm spot radius was used as an excitation source. The PL signal was collected via 15× objective and further analyzed by FTIR spectrometer. The infrared polarizer in the detection path was used to measure polarization-resolved PL, and the polarization of the incident laser was modulated by a half-wavelength plate. The temperature-dependent measurements were performed in an optical vacuum chamber with incident laser power of 80 W cm⁻². The photocurrent mapping was performed in a vacuum chamber mounted on the MStarter-200 testing system. A laser with 520 nm wavelength, 1 μm spot radius, and 300 μW power was used as the excitation source for mapping. The step length is 1 μm in the mapping test. An external lock-in amplifier (model SR830) was used to filter the noise photocurrent at 200 Hz frequency. The mid-infrared photocurrent tests were characterized using the Bruker FTIR spectrometer and the Hyperion infrared microscope. The excitation source is an internal blackbody radiation source in FTIR. The light spectrum of the source is shown in Supplementary Fig. 22. Samples were mounted on the infrared microscope stage. The light was chopped with a frequency of 604 Hz and was focused on the device with a diameter of ~100 μm. The amplitude and phase of the photocurrent signal were collected by a lock-in amplifier. The output signal from the lock-in amplifier was sent back to FTIR to transform the signal from the frequency domain to the wavelength domain. The schematic setup is further shown in Supplementary Fig. 23.

Theoretical calculation

We employed the Vienna ab initio simulation package (VASP), implemented with density functional theory (DFT), to optimize the crystal structure and calculate the fundamental electronic properties⁵⁵. The self-consistent calculations were performed using a k-mesh of size 12 × 12 × 1 for the 3-layer BP flake, 5 × 5 × 1 for the BP heterostructure with twisted angle of 90°, and 2 × 2 × 1 for the BP heterostructure with twisted angle of 36.87°. The energy cutoff was set at 500 eV, and the tolerance for the total energy convergence was set to be smaller than 10⁻⁴ eV. The generalized gradient approximation of the Perdew–Burke–Ernzerhor form for the exchange-correlation functional was used for all DFT calculations⁵⁶.

Author contributions

X. C. conceived and supervised the projects. S. C. and Z. L. fabricated twisted BP samples with the assistance of S. W., H. W., Y. Z., and G. L. S. C. characterized photoluminescence of twisted BP with the assistance of H. W., J. M., and H. Z.. Z. L. performed photocurrent measurement with the assistance of J. M. and L. W.. X.L. Y. did the theoretical calculations. X. C., S. C., and X.L. Y. proposed the mechanisms. S. C. and Z. L. did AFM characterizations with the assistance of Y. W. and C. C.. X. C., J. M., S. C., and Z. L. drafted the paper with the assistance of X.L. Y., H. Z., and T. W.. All authors discussed and commented the paper.

Peer review

Peer review information

Nature Communications thanks Song Zhu and the other, anonymous, reviewers for their contribution to the peer review of this work. A peer review file is available.

Data availability

Relevant data supporting the key findings of this study are available within the article and the Supplementary Information file. All raw data generated during the current study are available from the corresponding authors upon request.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-024-53125-4.