As shown in Fig. 3(a), it has been reported that within a broad range (from 1° to 10°) of twist angles, two robust new van Hove singularities arise owing to the hybridization of the energy bands of these two layers.^[25–27] The energy level of the two van Hove singularities can be obtained by scanning tunneling spectroscopy (STS), while the experimental results of the energy separation between them ( ) accord with the theoretical prediction (based on the continuum model)^[28,29]

Fig. 3.

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Fig. 3. Physical properties of twisted bilayer graphene. (a) Schematic illustration and STS results of the new van Hove singularities of twisted bilayer graphene. The interlayer interaction leads to the formation of van Hove singularities, and they correspond to the two peaks in STS measurements. The relation between the singularity energy separation and the twist angle is also shown. Reprinted with permission from Ref. [27]. Copyright 2012, American Physical Society. (b) Left, calculated band structure and density of states of twisted bilayer graphene with twist angle . Top right, two-probe longitudinal conductance results of twisted bilayer graphene with twist angle . Insulating states have been marked by background color. Bottom right, four-probe longitudinal resistance results of two twisted bilayer graphene samples with twist angles and . Reprinted with permission from Ref. [7]. Copyright 2018, Nature Publishing Group. (c) Left: illustration of quasicrystal twisted bilayer graphene. Top right: ARPES results of quasicrystal twisted bilayer graphene. Bottom right: illustration of Umklapp scattering process, which is responsible for the extra scattering points in the ARPES. Reprinted with permission from Ref. [51]. Copyright 2018, American Association for the Advancement of Science.

In 2010, Morell et al. predicted the occurrence of flat bands (simultaneously, zero Fermi velocity at Dirac point) in twisted bilayer graphene using tight-binding calculations, which probably means the existence of strong electron–electron interaction.^[35] In 2011, Bistritzer et al. solved the continuum Dirac model for twisted bilayer graphene and also found a flat band for a series of the so-called magic angles,^[18] which was partly (only for the largest twist angle) convinced in 2015 using STS by Yin et al.^[36] Later, Cao et al. successfully realized the material system and made various electrical measurements on it.^[6,7] At first, they found that the conductance of twisted bilayer graphene becomes zero with the moiré band half-filled and attributed this to the formation of a Mott insulator, which can be explained in rough as the consequence of the split of the moiré band caused by the repulsion of the two electrons in the same orbital state with different spins (Hubbard model).^[37,38] Then they made more careful measurements (four-probe resistance and observed an unconventional superconducting state whose doping density is slightly away from the lower Mott-insulator state (Fermi level ) with the critical temperature below 1.7 K. The band structure, the two-probe conductance results, and the four-probe resistance results are shown in Fig. 3(c). As they have pointed out, such tunable system offers a brand-new platform to study unconventional superconductivity, which has attracted many researchers to do related work on it (e.g., a superconducting state is also observed at a twist angle slightly larger than 1.1° under higher pressure).^[39–48]

The twist angles mentioned above are mostly small angles. As for large twist angles, the interaction between two layers is usually weak.^[49,50] Ahn et al. fabricated twisted bilayer graphene with a twist angle of exactly 30°, which forms a graphene quasicrystal with dodecagonal quasicrystalline order and anomalous interlayer interaction is found by angle-resolved photoemission spectra of the system.^[51] Extra scattering points owing to Umklapp scattering process of the two layers are shown in Fig. 3(b). Yao et al. have also reported successful growth of such graphene quasicrystal and investigated the emergence of mirrored Dirac cones.^[52] They identified that these mirrored Dirac cones are a consequence of the interlayer interaction showing its importance in the incommensurate structure which had been overlooked before.

In addition to the band structure of electrons, electron–phonon coupling is also a fundamental interaction that affects a broad range of phenomena in condensed matter physics, such as electron mobility, and is responsible for conventional superconductivity.^[53] In multilayer structures, the interaction can involve intralayer electron–phonon interaction or interlayer electron–phonon interaction (Figs. 4(a) and 4(b)). Eliel et al. reported the ability of Raman spectroscopy to probe and distinguish interlayer and intralayer interactions in graphene-based heterostructures.^[54] As shown in Figs. 4(c) and 4(d), they measured Raman spectra in two samples of twisted bilayer graphene with twist angles and 13° recorded with the 2.18 eV and 2.41 eV laser lines, respectively. The frequencies of these phonons depend on the twisting angle θ.^[55–63] In addition, they made multiple-excitation Raman measurements using multiple laser lines and found that the results show different dependence on the incident photon energy (Figs. 4(e) and 4(f)). Bilayer graphene and graphene/hBN samples with different twist angles also show similar results.

The theoretical results of twisted bilayer graphene mentioned above are all based on a common assumption that the lattice structure of either layer does not change significantly despite the interlayer interaction. However, Yoo et al. reported that this is not the case.^[45] In Fig. 4(g), the transmission electron microscope (TEM) dark-field images are obtained by selecting the diffraction peak from a series of twisted bilayer graphene samples with multiple twist angles. In these images, different contrasts stand for totally different stacking order (AB/BA) domains, and for the twisted bilayer graphene sample with 0.1° twist angle, the sharp boundaries indicate the existence of atomic reconstruction, in contrast to the relatively continuous distribution of stacking order if not reconstructed. As the twist angle increases, the boundaries become blurry, which represents the weakening of interlayer interaction. Based on this discovery, they recalculated the band structure of twisted bilayer graphene with small twist angles and found that a simple moiré band description breaks down and the secondary Dirac bands appear when the twist angle .

Fig. 4.

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Fig. 4. Electron–phonon coupling and atomic reconstruction in 2D twisted bilayer materials. (a) and (b) Schematics of interlayer electron–phonon process where a phonon with momentum connects the states and of different layer (a) and intralayer electron–phonon process where both states and are from the same layer. (c) and (d) Raman spectra of twisted bilayer graphene with and 13° measured with the 2.18 eV and 2.41 eV laser lines, respectively. The vertical coordinate corresponds to the ratio of the peak intensities of the Raman spectra in twisted bilayer graphene and monolayer graphene. (c) The peak around 1620 cm−1 is called La and stems from intralayer electron–phonon scattering process and (d) the peak at 1480 cm−1 is called Te and stems from the interlayer electron–phonon scattering process. (e) and (f) Excitation Raman maps of twisted bilayer graphene with (e) and 13° (f) measured under different laser energy excitations. Reprinted with permission from Ref. [54]. Copyright 2019, Nature Publishing Group. (g) TEM dark-field images of twisted bilayer graphene with different twist angles obtained by selecting diffraction peak ( . Different contrast stands for different stacking order (AB/BA). Reprinted with permission from Ref. [45]. Copyright 2019, Nature Publishing Group.

Liu et al. investigated photoluminescence and Raman spectra of 44 MoS₂ bilayers with different twist angles (Figs. 6(a) and 6(b)).^[80] They reported that the A exciton recombination photoluminescence peak position (peak I in Fig. 6(c)) remains the same for all bilayers with different twist angles, but photoluminescence intensity decreases significantly compared with the monolayer one. For the bilayer case, a lower-energy peak appears (peak II in Fig. 6(c)), which corresponds to an indirect bandgap recombination resulting from the interlayer electronic coupling. They found that the indirect bandgap varies with twist angle. AA/AB stacking bilayers have smaller bandgap than that of twist ones, indicating stronger interlayer electronic coupling. In addition, Raman spectra of MoS₂ monolayer and bilayers with different twist angles have been investigated to identify the effective interlayer mechanical coupling, that is, larger separation between two Raman peaks ( ) means stronger coupling strength (Fig. 6(d)). This twist-angle-dependent coupling is attributed to the varied interlayer distance in van der Waals coupled 2D atomic-layered materials due to steric effect: the increase of the interlayer distance will weaken the coupling strength. From their experimental results, AA or AB stacking MoS₂ bilayer has stronger electronic and mechanical coupling than the twist angles ones. This conclusion is also suitable for other TMD bilayers.^[81–83]

Fig. 6.

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Fig. 6. Electronic and mechanical coupling in twisted MoS2 bilayer. (a) Schematics of MoS2 bilayers with different stacking configurations. Green spheres are Mo atoms; yellow sphere are S atoms. (a) Optical images of a MoS2 monolayer and twisted bilayers with different twist angles. (c) Photoluminescence and (d) Raman spectra of MoS2 monolayer and bilayers with different twist angles. Reprinted with permission from Ref. [80]. Copyright 2014, Nature Publishing Group.

TMD heterostructures are of particular interests because many of them form type II heterojunctions, which facilitate the efficient separation of photoexcited electrons and holes and therefore exhibit great potential in the applications of photodetectors, photovoltaics, and sensors. This separation in MoS₂/WS₂ bilayers could take place within 50 fs upon photoexcitation due to strong interlayer coupling.^[84–86] As the interlayer coupling in 2D heterostructure materials varies with interlayer twist angles, Ji et al. have investigated how the interlayer charge transfer in MoS₂/WS₂ bilayers evolves with different stacking configurations (Fig. 7(a)).^[87] In Fig. 7(b), two obvious peaks in MoS₂/WS₂ bilayers photoluminescence spectra correspond to direct A-exciton transitions from MoS₂ (peak I) and WS₂ (peak II), respectively. Intensity of Peak I in the heterostructures is 1/5 of that in MoS₂ monolayer indicating strong interlayer electronic coupling and efficient electron–hole separation. The transient absorption spectra of MoS₂ and MoS₂/WS₂ bilayers with different twist angles are shown in Fig. 7(c). Interestingly, they observed that the rise time of MoS₂/WS₂ bilayers with different twist angles only varies slightly, suggesting that the charge transfer time is robust and stacking independent. This robust ultrafast charge transfer is contrary to time-dependent density functional theory simulations and naive thinking that stronger interlayer coupling induces faster charge transfer.^[88] In Fig. 7(d), scanning transmission electron microscopy (STEM) image of an AA stacking MoS₂/WS₂ bilayer indicates that in addition to the energy-favourable AA₁ stacking, there exists high-energy stacking of AA₃ due to interlayer stretching and shifting. The existence of multiple parallel charge transfer channels results in the robust ultrafast stacking-independent charge transfer, as the measured charge transfer time is mainly determined by the fastest channel (Fig. 7(e)). Same results have also be reported by Zhu et al.^[89]

Fig. 7.

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Fig. 7. Stacking-independent ultrafast charge transfer in TMD heterostructures. (a) Band alignment of MoS2/WS2 bilayers. After pumping MoS2 A-exciton with ultrafast laser, the electron remains in MoS2 while the hole will transfer to a lower energy at WS2, resulting in an efficient electron–hole separation. (b) Photoluminescence spectra of MoS2 monolayer and MoS2/WS2 bilayers. The two obvious peaks in MoS2/WS2 bilayers correspond to direct A-exciton transitions from MoS2 (peak I) and WS2 (peak II), respectively. (c) Transient absorption spectra of MoS2/WS2 bilayers by selectively probing with a higher energy light at WS2 A-exciton resonance. (d) TEM image of an AA stacking MoS2/WS2 bilayer. In addition to the energy-favorable AA1 stacking, there exists high-energy state of AA3 stacking due to interlayer stretching and shifting. (e) Schematic of charge transfer process at the interface of AA stacking MoS2/WS2 bilayers, where multi-channels coexist. The apparent transfer time is mainly determined by the fastest channel. Reprinted with permission from Ref. [87]. Copyright 2017, American Chemical Society.

In TMD bilayers, there exists a moiré periodic potential as well, so electron–phonon coupling and phonon–phonon interactions can be affected. Lin et al. discovered that the moiré periodic potential in twisted MoS₂ bilayer can modify the properties of phonons in its MoS₂ monolayer constituent to generate Raman modes related to moiré phonons.^[90] They measured the Raman spectra in the region of 50–425 cm⁻¹ of the twisted MoS₂ bilayers with twist angles ranging from 9° to 49° under the excitation energy E=2.54 eV. Apart from those modes observed in all twisted MoS₂ bilayers independent of θ like longitudinal acoustic (LA) and transverse acoustic (TA) modes, they observed seven series of θ-dependent Raman modes (Figs. 8(a) and 8(b)). It can be attributed to that there are seven moiré phonons in the twisted MoS₂ bilayer. These phonons originate from the phonons in monolayer constituents with the basic vectors of moiré reciprocal lattices folded onto the zone center due to the modulation of the periodic moiré potentials (Figs. 8(c) and 8(d)). Due to the weak interlayer coupling in twisted MoS₂ bilayer, the phonon dispersions of the monolayer constituents can be probed by the θ-dependent frequency of moiré phonons. In addition, all these moiré phonons exhibit a mirror behavior with regard to θ =30°.

Fig. 8.

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Fig. 8. Moiré phonons in twisted MoS2 bilayer. (a) and (b) Raman spectra of twisted MoS2 bilayer in the regions of (a) 50–365 cm−1 and (b) 370–425 cm−1. The Raman modes in different phonon branches are represented by different shapes and color symbols. The Raman spectra of monolayer MoS2 and 3R-bilayer MoS2 (θ =0°) are plotted for comparison. (c) and (d) The comparison of calculated and experimental frequencies of moiré phonons dependent on θ (c) and (d), is the magnitude of the basic vector of the moiré reciprocal lattices. Reprinted with permission from Ref. [90]. Copyright 2018, American Chemical Society.

Exciton is the particle-like entity that formed by an electron bound to a hole.^[91] Moiré excitons are excitons whose energy levels are quantized arising from the lateral confinement imposed by the deep moiré potential.^[8,11] Jin et al. reported experimental observation of moiré excitons in WSe₂/WS₂ bilayers.^[8] The optical photograph and schematic diagram are shown in Figs. 9(a) and 9(b), and the WSe₂/WS₂ bilayers are encapsulated in thin hBN layers for protection. The twist angle is identified by the STEM image in Fig. 9(c), which shows a uniform triangular lattice pattern with a well-defined periodicity of about 8 nm. In the WSe₂/WS₂ bilayers with near-zero twist angle, WSe₂ A exciton state splits to three prominent peaks (labelled as I, II, and III, respectively) corresponding to distinct moiré exciton states, while only a single resonance peak appears in large twist angle heterostructures (Fig. 9(d)). They found that the gate-dependent behaviors of these moiré exciton states are distinct from that of the A exciton in WSe₂ monolayers and WSe₂/WS₂ bilayers with large twist angles (Fig. 9(e)). These phenomena can be fully described by a theoretical model in which the moiré periodic potential (250 meV) is much stronger than the exciton kinetic energy (8 meV) and generates multiple flat exciton minibands. Other three groups also reported the observation of moiré excitons in TMD heterostructures at the same time.^[9–11] These observations provide a promising platform for exploring several theoretical proposals related to quantum photonics, such as topological excitons, giant spin–orbit coupling, and entangled photon sources.

Fig. 9.

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Fig. 9. Moiré excitons in twisted TMD heterostructures. (a) and (b) Optical microscopy image (a) and side-view illustration (b) of a representative heterostructure with a near-zero twist angle. (c) A zoomed-in image of atomic-resolution STEM of near-zero twist angle WSe2/WS2 bilayers showing the moiré superlattice. The two superlattice vectors are labelled. (d) Reflection contrast spectrum of near-zero twist angle WSe2/WS2 bilayers (top) compared to a large twist angle one (bottom). (e) Reflection contrast spectra in the range between 1.6 eV and 1.8 eV of the WSe2. A exciton upon electron doping. The electron concentration is noted for each spectrum in units of cm−2. Reprinted with permission from Ref. [8]. Copyright 2019, Nature Publishing Group.