Author Affiliations
1Advanced Research Institute of Multidisciplinary Science, Beijing Institute of Technology, Beijing 100081, China2Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China3School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China4School of Integrated Circuits and Electronics, MIIT Key Laboratory for Low-Dimensional Quantum Structure and Devices, Beijing Institute of Technology, Beijing 100081, China5BIT Chongqing Institute of Microelectronics and Microsystems, Chongqing 401332, Chinashow less
Fig. 1. (Color online) Schematic illustration of the topics of this review, including the fabrication methods and several distinctive properties of the twisted moiré materials
[4–6]. ([4] Copyright 2018, American Physical Society. [5] Copyright 2018, American Physical Society. [6] Copyright 2021, Nature Publishing Group (NPG).)
Fig. 2. (Color online) Mechanism of Au-film-assisted exfoliation technology and some examples of exfoliated 2D crystals. (a) Part of the periodic table, showing the elements involved in most 2D materials between groups 4 (IVB) and 17 (VIIA). Most of the layered crystals are composed of the elements with pink and green colors, which have strong interaction with Au. (b) Schematic of the interaction mechanism between layered crystal and Au. Once the interface interaction energy is larger than the interlayer interaction, monolayer flakes can be exfoliated. (c) Schematic illustration of the Au-film-assisted exfoliation process. (d) Optical images of large exfoliated 2D flakes
[50]. Copyright 2022, Nature Publishing Group (NPG).
Fig. 3. (Color online) Ag-assisted exfoliation procedures and optical images of exfoliated samples. (a) Schematic illustration of the exfoliation procedures. (b) Exfoliated macroscopic MoS
2 and WS
2 on 15 nm Ag film supported by SiO
2/Si substrates, and bulk crystals on PDMS tapes. (c) Exfoliated macroscopic MoS
2 supported by sapphire substrates. (d) Exfoliated MoS
2 supported by elastic PET substrates. (e) Exfoliated MoS
2 on Ag/epoxy/glass slide substrate. (f) Optical microscope images of some 2D crystals exfoliated on 15 nm Ag film, including MoS
2, WS
2, 1T-WTe
2, and BP. (g) Optical microscope images of exfoliated millimeter size 2D crystals on 5 nm Ag film, including ReSe
2, Fe
3GeTe
2, FeSe, and TaS
2. (h, i) Optical microscope images of exfoliated millimeter size MoS
2 on sapphire substrate and TS Ag, respectively. (j) Optical microscope and PL mapping images of exfoliated monolayer WS
2 on 15 nm Ag film with hole array, the scale bars in the two images are 40 and 20
μm, respectively
[51]. Copyright 2022, Wiley Online Library.
Fig. 4. (Color online) Fabrication process and characterization of suspended 2D materials. (a) Schematic images for preparing suspended samples. (b–d) Optical images of exfoliated graphene, MoS
2 and WSe
2 on different patterned substrates, including rectangle, Hall bar and circular hole structures. (e) PL mapping image of suspended monolayer WSe
2[48]. Copyright 2022, Wiley Online Library.
Fig. 5. (Color online) Tear-rotate-stack method for fabricating 2D twisted heterostructure. (a) Schematic of cutting the 2D materials with femtosecond laser to get the straight edge for twist angle reference
[54]. Copyright 2016, Wiley Online Library. (b) Preparing the twisted bilayer graphene with desired twist angle using the tear-rotate-stack method
[53]. Copyright 2017, National Academy of Sciences (NAS). (c) The tear-rotate-stack method to fabricate the twisted MoS
2 homostructures from the as-grown wafer MoS
2 monolayer. (d) Optical image of 30° twisted bilayer MoS
2[55]. Copyright 2020, Nature Publishing Group (NPG).
Fig. 6. (Color online) Schematic illustration of the band structure and Hubbard model simulation of the TMD moiré systems. (a) showing the narrowing of bandwidth with a larger wavelength (λ) of the periodic potential well for 1D lattice in the nearly-free electron approximation. The additional periodic potential folds the bands into a mini-Brillouin zone with boundary at ±π/λ. The lowest band (orange) becomes narrower with the bandwidth tuned by λ. (b) Typical band alignment of angle-aligned heterobilayers and AB stacked homobilayers with SU(2) and SU(4) symmetry, respectively. (c) Schematic illustration of the inter-site hopping termt, on-site Coulomb repulsionU, and inter-site Coulomb repulsionV. (d) Quantum phase diagram of the half-filled triangular lattice.
Fig. 7. (Color online) Simulation of Hubbard model in the strong correlation limit. (a) Rydberg sensing of the abundant correlated insulating states in WSe
2/WS
2 described by a single-band extended Hubbard model with SU(2) symmetry. (b) Charge configuration at several typical fillings in (a)
[78]. (c) Electric-field-controlled layer polarization of t-WSe
2 (mapped to a SU(4) bilayer Hubbard model) probed by the moiré exciton resonance. The dashed line denotes the boundary of fully polarized states (|
P| = 1, in blue). (d) Doping dependence of MCD (proportional to sample magnetization) with
P = 0 (blue) and
P = 1 (black)
[84]. The vanishing magnetization at
ν = 2,
P = 1 is related to the formation of antiferromagnetic order. (e) Charge/spin configuration of an excitonic insulator and an antiferromagnetic insulator in AB-stacked t-WSe
2.
Fig. 8. (Color online) Hubbard model physics with an intermediate correlation
[87]. (a) Longitudinal resistance
ρxx at
T = 20 K,
B = 0 T in angle-aligned 3L-MoTe
2/WSe
2. A resistance peak is discovered at
ν = 1. (b) Evolution of the gates-dependent
ρxx as a function of temperature. (c) Temperature dependence of
ρxx at
ν = 1 and
D = 1.313 V/nm. At low temperatures, the
ρxx accords well with the blue dashed curve (∝
T2) denoting a Fermi-liquid behavior. (d) Magnetic-field dependence of the
ν = 1 resistance at
T = 0.3 K. Sharp resistance peaks occur above the critical magnetic field
Bc ≈ 6 T. (e) Phase diagram of 3L-MoTe
2/WSe
2 at half filling.
Fig. 9. (Color online) Kane–Mele–Hubbard model in AB stacked WSe
2/MoTe
2[6]. (a) Schematic illustration of the electric-field-induced topological phase transitions. (b) Longitudinal resistance
Rxx at
T = 300 mK,
B = 0 T, with the green dashed circle denoting the quantum anomalous Hall region. (c) Hall (
Rxy) and (d) longitudinal (
Rxx) resistances versus
B-field in the QAH region. Quantized
Rxy and vanishing
Rxx are observed at low temperatures. (e) Electric-field dependence of
Rxx at
ν = 1 under zero magnetic field at varying temperatures. (f) Electric-field dependence of the extracted charge gap (∆
C by thermal activation fits to the resistance data, ∆
tr by direct compressibility measurements) at
ν = 1 from the Mott insulating region to the QAH region and the metallic region.