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Twist-angle two-dimensional superlattices and their application in (opto)electronics

Kaiyao Xin1, 3, Xingang Wang1, 3, Kasper Grove-Rasmussen2, 3, and Zhongming Wei1, 3,

+ Author Affiliations

 Corresponding author: Kasper Grove-Rasmussen, k_grove@nbi.ku.dk; Zhongming Wei, zmwei@semi.ac.cn

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Abstract: Twist-angle two-dimensional systems, such as twisted bilayer graphene, twisted bilayer transition metal dichalcogenides, twisted bilayer phosphorene and their multilayer van der Waals heterostructures, exhibit novel and tunable properties due to the formation of Moiré superlattice and modulated Moiré bands. The review presents a brief venation on the development of “twistronics” and subsequent applications based on band engineering by twisting. Theoretical predictions followed by experimental realization of magic-angle bilayer graphene ignited the flame of investigation on the new freedom degree, twist-angle, to adjust (opto)electrical behaviors. Then, the merging of Dirac cones and the presence of flat bands gave rise to enhanced light-matter interaction and gate-dependent electrical phases, respectively, leading to applications in photodetectors and superconductor electronic devices. At the same time, the increasing amount of theoretical simulation on extended twisted 2D materials like TMDs and BPs called for further experimental verification. Finally, recently discovered properties in twisted bilayer h-BN evidenced h-BN could be an ideal candidate for dielectric and ferroelectric devices. Hence, both the predictions and confirmed properties imply twist-angle two-dimensional superlattice is a group of promising candidates for next-generation (opto)electronics.

Key words: twist angleMoiré superlatticetwo-dimensional(opto)electronics



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Fig. 1.  (Color online) Merging of two Dirac cones and the presence of flat bands. (a) Twisted Brillouin zones from upper and lower graphene sheets (colored by red black and red) with θ. (b) Schematic of merging of the two Dirac cones between Ka and Kb points (left) in (a) and the corresponding distribution of density of states (right). Reproduced with permission[36]. Copyright 2012, American Physical Society. (c) Theoretical simulation on the band structure of TBLG at 1.6°, 1.3° and 1.0° by tight-binding calculations, leading to the presence of flat bands at twist-angle of 1.6° and 1.3°. Reproduced with permission[38]. Copyright 2010, American Physical Society. (d) Electric-field tunable VHSs in two merging Dirac cones observed by nanoARPES. Reproduced with permission[41]. Copyright 2020, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. (e) Flat bands in TBLG near the magic-angle and their local density of states through mean-field theory. Reproduced with permission[45]. Copyright 2018, American Physical Society.

Fig. 2.  (Color online) Fabrication methods and synthesis routes of twist-angle 2D superlattices. ① One-step growth of twisted superlattice by chemical vapor deposition; ② Fabrication of component 1 (single-layer or several layers) by CVD; ③ Fabrication of component 1 by mechanical exfoliation; ④ Transfer of the product from synthesis substrate to device substrate by dry or wet transfer methods; ⑤ Adjusting the twist-angle of component 1 and component 2 which stay on device substrate and transfer mediate respectively; ⑥ Compaction of component 1 and component 2 to form twist-angle 2D superlattice.

Fig. 3.  (Color online) Moiré superlattices, interlayer coupling and the behavior of interlayer excitons in Moiré potentials. (a) Twist-angle-dependent Moiré pattern of TBG. Reproduced with permission[86]. Copyright 2015, American Physical Society. Mapping of potential difference in ABAB and ABCA stacking modes (top) and potential fluctuation along the certain direction marked by red color (bottom) measured by amplitude modulated scanning Kelvin probe microscopy (AM-SKPM) (b) and frequency modulated SKPM (FM-SKPM) (c), respectively. Reproduced with permission[84]. Copyright 2021, American Chemical Society. (d) Schematic of Moiré potentials resulted from Moiré pattern, containing saddles and wells. Reproduced with permission[45]. Copyright 2018, American Physical Society. (e) Moiré superlattice of rigid-lattice MoSe2/WSe2 at 0°+δ. (f) Theoretical calculation of stacking energy, showing an identical energy of AB and BA stacking modes. (g) The evidence of superlattice reconstruction based on observed alternant triangular regions; while rigid-lattice pattern of MoSe2/WSe2 at 60°+δ theoretically showed similar smoothly boundary (h), and hexagonal reconstruction (j) resulting from the single minimum of stacking energy reduction in ABBA mode (i). Reproduced with permission[69]. Copyright 2020, American Chemical Society.

Fig. 4.  (Color online) (a) Moiré periodic potential wells formed in MoSe2/WSe2 twisted heterostructure which would influence the transport process of excitons. (b) Localized excitons in Moiré periodic potential wells at ultra-low temperature of 4 K. Reproduced with permission[88]. Copyright 2021, American Chemical Society. (c) PL spectra of monolayer and twisted bilayer WS2 with various twist-angles. (d) The position of PL peaks of A (red dots) and I (blue dots) at various twist-angles. (e) and (f) are the E2g and A1g peaks in Raman spectra with different twist-angle, which reflect intralayer vibration and interlayer vibration, respectively, being summarized in (g). (h) The distance between E2g and A1g peaks as a function of twist-angle, indicating the interlayer coupling strength. Reproduced with permission[89]. Copyright 2019, American Chemical Society.

Fig. 5.  (Color online) The merging of two Dirac cones and the presence of DOS gap. (a) The DOS gap is established between two VHSs and hence create the photoexcited transition route. (b) Schematic of the merging Dirac cones with other two operating directions of ARPES spectra to the TBG. (c) Stacking plot of constant-energy contours measured by ARPES, showing the merging of Dirac cones. The band structures in Cut 1 and Cut 2 from (b) are shown in (d) and (e), respectively, where VHSs are marked by red arrows. (f) DOS gap (2EVHS) as a function of twist-angle. Reproduced with permission[66]. Copyright 2016, The Author(s).

Fig. 6.  (Color online) Selectively enhanced photoresponsivity of TBG based on a tunable DOS gap. (a) Schematic of a TBG-based photodetector whose channel consists of two TBG with different twist-angle of θ1 = 7° and θ2 = 13°, respectively. (b) The corresponding optical image of the device in which the dashed circle A and B represent 7° and 13° regimes. (c) Raman G-band intensity mapping under a 532 nm (2.33 eV) laser. (d) Scanning photocurrent distribution of the same device in planform (top) and stereogram (bottom). (e) Twist-angle-dependent the position of photocurrent maximum peaks responding to different photon energy. Scale bars: 5 μm (all). Reproduced with permission[66]. Copyright 2016, The Author(s). (f) Schematic of the device consisting of TBG at 10° and monolayer graphene. (g) Raman G-band intensity mapping of the same device under 633 nm (1.96 eV) laser. (h) Scanning photocurrent distribution of the device in which strong photoresponsivity almost took place in the TBG region. Significantly enhanced G-band intensity in Raman spectra of 13° TBG under 633 nm laser (i) and 10° TBG under 532 nm laser (j), respectively. Reproduced with permission[67]. Copyright 2016, American Chemical Society.

Fig. 7.  (Color online) (a) Schematic of a TBG-based photodetector with metal–graphene–metal architecture (MGM), and the inset shows a zoom of the central region at the MGM junction. (b) Model of the device and the corresponding energy structure. (c) Current as a function of bias voltage of TBG at 10° at the left and right side under different polarized radiation, and the inset is the dark current fluctuation. (d) Different photovoltage of 10° TBG under lasers with different polarization modes. (e) The photovoltage as a function of polarization angle at the left and right MGM junctions with sine fitting. (f) The linear relationship between incident power and photovoltage intensity at different positions under different polarized lasers. Reproduced with permission[78]. Copyright 2016, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. (g) Three types of graphene quantum dots and twisted bilayer graphene quantum dot. (h) Energy gap as a function of rotation angle for A-TGQD with different size (top) and for Z-TGQD with various size (bottom). (i) Further analysis on Z-TGQD-7 on twist-angle-dependent energy gap (top) and the model of stacking configurations at four rotation angles (bottom). Reproduced with permission[96]. Copyright 2019, Elsevier B.V. All rights reserved.

Fig. 8.  (Color online) (a) Schematic of a TBG-based Terahertz photodetector. (b) Photovoltage as a function of the azimuth angle of the incident light. (c) Fluctuation of photovoltage intensity caused by a tunable filling level of the multiple relatively flat bands through gate bias. (d) Gate-bias-dependent circular photovoltage at bulk (offset by 90 nV/mW for visibility) and edge, and longitudinal resistance under the control of gate bias. The top two inset images are polarization-dependent photovoltage signals and the bottom inset shows an experimental measurement. Reproduced with permission[79]. Copyright 2020, American Chemical Society. (e) Optical microscope image of star-like TBGs (top) and the image of the one marked by the black arrow (bottom), in which colorful circles represent TBG with different twist-angle and the black circle represents monolayer graphene. (f) Significantly enhanced G-band intensity in Raman spectra of the green region under 532 nm laser, indicating the TBG at around 12°. (g) Schematic of band structure and third-harmonic generation process when the DOS gap matches well with the three-photon energy. (h) Tendency of THG intensity with respect to I2D/IG ratio. Reproduced with permission[76]. Copyright 2021, The Author(s).

Fig. 9.  (Color online) Chirality-induced giant unidirectional magnetoresistance in TBG at 1.5°. (a) In-plane external magnetic field will break the time-reversion symmetry on the TBG with chirality caused by twisting, leading to band structure changing from symmetric (b, left) to asymmetric (b, right) and unidentical carrier velocity along the opposite direction. (c) The band structure of TBG under 10 T magnetic field (orange line) and without magnetic field (red line). (d) Schematic of the device under in-plane I//B. Electronic structure of the TBG in the case (d) and corresponding direction-induced conduction difference $ \Delta G={G}_{\to }-{G}_{\leftarrow } $ (f). (g) Calculated unidirectional magnetoresistance at η = 0.1 (blue dashed line) and 1 (red solid line), respectively, where η is dephasing parameter. Reproduced with permission[97]. Copyright 2021, The Authors.

Fig. 10.  (Color online) Weakened interlayer coupling of TBTMDs and optimized rectifying behavior. (a) Schematic of a bilayer heterojunction WSe2/MoSe2 with different twist-angle including 0°, 15° and 30° under incident light with various wavelengths. (b) Band structure of 0° (top row) and 15° (bottom row) WSe2/MoSe2 bilayer heterojunction under zero bias. (c) and (d) show spectral responsivity with raw and median values of three devices with 0°, 15° and 30° under IR (850 nm) and UV (365 nm) luminescence, respectively. (e) and (f) show external quantum efficiency (EQE) with average and median values of the three devices under 850 nm and 365 nm radiation, respectively. Reproduced with permission[98]. Copyright 2019, American Chemical Society. (g) Electrical transfer curves of a 30° twisted bilayer MoS2 field effect transistor, the inset is the optical image of the device array, scalebar is 400 μm. (h) Electrical output curves of a 30° twisted bilayer MoS2 FET. (i) The statistic distribution of the on/off ratio of 30° (red dots) and 0° (blue dots) twisted bilayer MoS2 FET. (j) Field effect mobility measured in twisted bilayer and trilayer MoS2 FET, where 0° and 30° represent the twist-angle in bilayer sample and (0°, 30°) means two relative twist-angles between each two layers are 0° and 30°, respectively, in a trilayer system. Reproduced with permission[77]. Copyright 2020, The Author(s).

Fig. 11.  (Color online) (a) Schematic of a cross-stacked bilayer black phosphorus (BP). (b) Significant influence on the effective mass of holes along zigzag and armchair direction in BP under external electric field. Reproduced with permission[100]. Copyright 2016, American Chemical Society. (c) The schematic of cruciform few-layer BP (CBP) device without twisting but adjacent electrodes connected. (d) The difference in the band structure and Fermi levels along AC and ZZ directions induced by anisotropy in BP (top) and the formation of orientation barrier from the bands bending (bottom). (e) Cross-stacked few-layer BP junction (CBPJ) with adjacent electrodes connected. (f) Vertical-stacked BP (VBP) with only two opposite terminals connected. (g) Photoresponse under incident light with polarization state along the AC (red) and ZZ (blue) direction and intrinsic rectification curve (black). The top-left inset showed an optical image of the CBP device while the bottom-right inset showed the polarization-dependent photocurrent. (h) Photoresponse (red) and intrinsic rectification features (black) of CBPJ. The top-left inset showed millisecond-level photoresponse under pulse light while the bottom-right inset revealed incident-power-dependent photocurrent with photoresponsivity of 4.6 mA/W at 50 μW. (i) Photoresponse (red) and intrinsic rectification features (black) of VBP under incident light with certain polarization state. Reproduced with permission[73]. Copyright 2017, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. (j) Schematic of a vertically cross-stacked BP junction under laser illumination. (k) Top: schematic of the top view of B1-B2 two terminal device; middle: pristine energy band and Fermi level distribution with bandgap of 0.57 eV; bottom: after thermodynamically equilibrium, a p-p-p lateral junction was formed with orientation barrier of 0.05 eV. (l) The stacking-morphology-dependent carrier transportation processes. Reproduced with permission[74]. Copyright 2018, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Fig. 12.  (Color online) (a) Band structure determined by twist-angle of 0°, 26.02°, 71.61°, 110.54°, 130.39° and 149.01° of twisted bilayer black phosphorus (TBBP). (b) Bandgap as a function of twist-angle. (c) Rotated energy defined as the difference between E(θ°) and E(0°) influenced by rotated angle. (d) Absorption coefficient of the bilayer phosphorene with six twist-angles under incident radiation with various energy and different polarization along xx direction (top) and yy direction (bottom). Reproduced with permission[102]. Copyright managed by AIP Publishing. (e) Electron cloud of nitrogen atoms (colored gray) induced by orbital hybridization between nitrogen and boron atoms (colored green) and the formation of polarization in AB (left) and BA (right) stacking. (f) The resistance of graphene as a function of the external electric field (VT/dT) where VT and dT is the top gate voltage and the thickness of the top dielectric layer, respectively. Blue and red arrows represent the opposite scanning directions of the top gate voltage. The left inset shows the schematic of the device and the right inset is the optical image of the device. (g) The hysteresis in ferroelectricity of the parallel stacked bilayer h-BN which was reflected by the staggered two peaks of RXX,U during opposite scanning of bottom gate voltage. The inset is the enlarged plot around 0.2 V/nm. (h) The left figure: RXX,U measured through upper contacts (shown in lower left inset) as a function of top and bottom electric field, where the white dashed arrow and solid arrow represents the slow scanning and fast scanning direction, respectively. The higher left inset and lower right inset shows the controllable reversion of polarization. The right figure: RXX,L measured through lower contacts as a function of both two gate electric field. The left inset depicts the pinning of domain wall during the reversion of stacking mode and the right inset describes the relevant resistance peak assigned by the three red arrows on its left. (i) Gradual changing of the stacking mode in Moiré scale (inset schematics), resulting in a gradual reversion of polarization and the resistance detected by graphene rather than abrupt shift in (d). (j) Outstanding stability of polarization after one month at room temperature. Reproduced with permission[75]. Copyright 2021, American Association for the Advancement of Science.

Table 1.   Primary 2D materials for twisting with their typical band structure and important physical properties.

2D twist systemTwist-angleBand structurePhysical propertyRef.
Non-magic-angleFormation of DOS gap[66, 67]
Formation of Moiré bandgap[68]
GrapheneMagic-angleCorrelated insulating state[43]
Unconventional superconductivity[44]
Pomeranchuk effect[50]
Integer quantum Hall effect[53]
Josephson effect[54, 55]
TMDsNo magic-angleAtomic reconstruction[69]
Interlayer hybridization[7072]
Correlated electronic state[58, 59]
Superconductivity[62]
BP90°Orientation barrier[73]
Rectification effect[74]
h-BN0.6°N/ATunable ferroelectricity[75]
N/A: Not available
DownLoad: CSV

Table 2.   Collection of primary devices and their (opto)electrical property parameters.

2D twist systemTwist-angleOptoelectronic ElectronicRef.
WavelengthPhotoresponsivity Rectification ratioOn/Off ratio
Graphene0.6°432 μm~ 80 mV/W N/AN/A[79]
1.81°1200 nm26 mA/WN/AN/A[68]
10°633 nm/48°2.2 V/WN/AN/A[78]
10°633 nm2.5 mA/WN/AN/A[67]
12°532 nm/52°1.6 V/WN/AN/A[78]
13°532 nm1 mA/WN/AN/A[66]
MoS230°N/AN/AN/A108[77]
MoSe2/WSe215°365 nm2 A/WN/AN/A[98]
60°926 nmN/AN/AN/A[69]
BP90°532 nm4.6 mA/W115N/A[73]
N/A: Not available
DownLoad: CSV
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    Received: 23 July 2021 Revised: 24 September 2021 Online: Accepted Manuscript: 01 November 2021Uncorrected proof: 04 November 2021Published: 04 January 2022

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      Kaiyao Xin, Xingang Wang, Kasper Grove-Rasmussen, Zhongming Wei. Twist-angle two-dimensional superlattices and their application in (opto)electronics[J]. Journal of Semiconductors, 2022, 43(1): 011001. doi: 10.1088/1674-4926/43/1/011001 K Y Xin, X G Wang, K Grove-Rasmussen, Z M Wei, Twist-angle two-dimensional superlattices and their application in (opto)electronics[J]. J. Semicond., 2022, 43(1): 011001. doi: 10.1088/1674-4926/43/1/011001.Export: BibTex EndNote
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      Kaiyao Xin, Xingang Wang, Kasper Grove-Rasmussen, Zhongming Wei. Twist-angle two-dimensional superlattices and their application in (opto)electronics[J]. Journal of Semiconductors, 2022, 43(1): 011001. doi: 10.1088/1674-4926/43/1/011001

      K Y Xin, X G Wang, K Grove-Rasmussen, Z M Wei, Twist-angle two-dimensional superlattices and their application in (opto)electronics[J]. J. Semicond., 2022, 43(1): 011001. doi: 10.1088/1674-4926/43/1/011001.
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      Twist-angle two-dimensional superlattices and their application in (opto)electronics

      doi: 10.1088/1674-4926/43/1/011001
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      • Kaiyao Xin:received his BSc in Material Physics from Southwest University in 2020 and he is currently pursuing his MS in Nanoscience and Technology at Institute of Semiconductors, Chinese Academy of Sciences; Sino-Danish College, University of Chinese Academy of Sciences; and University of Copenhagen, under the supervision of Prof. Zhongming Wei and Prof. Kasper Grove-Rasmussen. His research interests include low-dimensional materials and their (opto)electronic devices
      • Xingang Wang:received his bachelor Engineering degree in 2018 from Qingdao University. He is currently a masters candidate at Nanoscience and Technology at Institute of Semiconductors, Chinese Academy of Sciences; Sino-Danish College, University of Chinese Academy of Sciences; and University of Copenhagen, under the supervision of Prof. Zhongming Wei and Prof. Kasper Grove-Rasmussen. His research focuses on the syntheses of 2D layered materials and their related electronic and photoelectric properties
      • Kasper Grove-Rasmussen:received his PhD in 2006 from the University of Copenhagen supervised by Prof. Poul Erik Lindelof. During his postdoc years, he stayed at NTT Basic Research Laboratories, Atsugi, Japan and was a visiting researcher at Harvard University, US. He is currently an Associate Professor at the Center for Quantum Devices at the Niels Bohr Institute, University of Copenhagen, Denmark. From 2013 he has also been involved in the Sino-Danish Center. His research is focused on quantum transport and electronic properties of low-dimensional normal and hybrid superconducting systems involving e.g., carbon nanotubes and semiconductor nanowires
      • Zhongming Wei:received his BS degree from Wuhan University (China) in 2005, and Ph.D. from Institute of Chemistry, Chinese Academy of Sciences in 2010 under the supervision of Prof. Daoben Zhu and Prof. Wei Xu. From August 2010 to January 2015, he worked as a postdoctoral fellow and then Assistant Professor in Prof. Thomas Bjørnholm's group at University of Copenhagen, Denmark. Currently, he is working as a Professor at Institute of Semiconductors, Chinese Academy of Sciences. His research interests include low-dimensional semiconductors and their optoelectronic devices
      • Corresponding author: k_grove@nbi.ku.dkzmwei@semi.ac.cn
      • Received Date: 2021-07-23
      • Revised Date: 2021-09-24
      • Published Date: 2022-01-10

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