A remarkable recent experiment has observed Mott insulator and proximate superconductor phases in twisted bilayer graphene when electrons partly fill a nearly flat mini-band that arises a `magic' twist angle. However, the nature of the Mott insulator, origin of superconductivity and an effective low energy model remain to be determined. We propose a Mott insulator with intervalley coherence that spontaneously breaks U(1) valley symmetry, and describe a mechanism that selects this order over the competing magnetically ordered states favored by the Hunds coupling. We also identify symmetry related features of the nearly flat band that are key to understanding the strong correlation physics and constrain any tight binding description. First, although the charge density is concentrated on the triangular lattice sites of the moir$\\text{e }$ pattern, the Wannier states of the tight-binding model must be centered on different sites which form a honeycomb lattice. Next, spatially localizing electrons derived from the nearly flat band necessarily breaks valley and other symmetries within any mean-field treatment, which is suggestive of a valley-ordered Mott state, and also dictates that additional symmetry breaking is present to remove symmetry-enforced band contacts. Tight-binding models describing the nearly flat mini-band are derived, which highlight the importance of further neighbor hopping and interactions. We discuss consequences of this picture for superconducting states obtained on doping the valley ordered Mott insulator. We show how important features of the experimental phenomenology may be explained and suggest a number of further experiments for the future. We also describe a model for correlated states in trilayer graphene heterostructures and contrast it with the bilayer case.

Origin of Mott Insulating Behavior and Superconductivity in Twisted Bilayer Graphene

Low-frequency and Moiré–Floquet engineering: A review

We derive effective Floquet Hamiltonians for twisted bilayer graphene driven by circularly polarized light in two different regimes beyond the weak-drive, high-frequency regime. First, we consider a driving protocol relevant for experiments with frequencies smaller than the bandwidth and weak amplitudes and derive an effective Hamiltonian, which through a symmetry analysis, provides analytical insight into the rich effects of the drive. We find that circularly polarized light at low frequencies can selectively decrease the strength of AA-type interlayer hopping while leaving the AB-type unaffected. Then, we consider the intermediate frequency and intermediate-strength drive regime. We provide a compact and accurate effective Hamiltonian which we compare with the Van Vleck expansion and demonstrate that it provides a significantly improved representation of the exact quasienergies. Finally, we discuss the effect of the drive on the symmetries, Fermi velocity, and the gap of the Floquet flat bands.

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Effective Floquet Hamiltonians for periodically driven twisted bilayer graphene

We introduce an approach that allows one complete control over the modulation of the effective twist angle change in few-layer van der Waals heterostructures by irradiating them with longitudinal waves of light at the end of a waveguide. As a specific application, we consider twisted bilayer graphene and show that one can tune the magic angles to be either larger or smaller, allowing in situ experimental control of the phase diagram of this and other related materials. A waveguide allows one to circumvent the free-space constraints on the absence of longitudinal electric field components of light. We propose to place twisted bilayer graphene at a specific location at the exit of a waveguide, such that it is subjected to purely longitudinal components of a transverse magnetic mode wave.

Floquet engineering of interlayer couplings: Tuning the magic angle of twisted bilayer graphene at the exit of a waveguide

Due to strong Coulomb interactions, two-dimensional (2D) semiconductors can support excitons with large binding energies and complex many-particle states. Their strong light-matter coupling and emerging excitonic phenomena make them potential candidates for next-generation optoelectronic and valleytronic devices. The relaxation dynamics of optically excited states are a key ingredient of excitonic physics and directly impact the quantum efficiency and operating bandwidth of most photonic devices. Here, we summarize recent efforts in probing and modulating the photocarrier relaxation dynamics in 2D semiconductors. We classify these results according to the relaxation pathways or mechanisms they are associated with. The approaches discussed include both tailoring sample properties, such as the defect distribution and band structure, and applying external stimuli such as electric fields and mechanical strain. Particular emphasis is placed on discussing how the unique features of 2D semiconductors, including enhanced Coulomb interactions, sensitivity to the surrounding environment, flexible van der Waals (vdW) heterostructure construction, and non-degenerate valley/spin index of 2D transition metal dichalcogenides (TMDs), manifest themselves during photocarrier relaxation and how they can be manipulated. The extensive physical mechanisms that can be used to modulate photocarrier relaxation dynamics are instrumental for understanding and utilizing excitonic states in 2D semiconductors. Electrons and positively charged regions in semiconductors known as holes can form tightly bound states called excitons, offering new opportunities in optoelectronics and in ‘valleytronics,’ which exploits the effects of valleys and peaks in an energy landscape. The excitons display particle-like properties, so are described as quasiparticles. Fengqiu Wang and colleagues at Nanjing University, in China, review many technical aspects of the creation and control of excitons in single layer (2D) semiconductor sheets. The restrictions of 2D materials promote unique exciton behavior and strong light-matter interactions. The authors focus on the ability of excitons to act as photocarriers of absorbed light energy, and on the relaxation processes that can release the energy. Learning how to control exciton formation, interactions and relaxation will be crucial for using them to develop novel optoelectronic and photonic devices.

/pdf/modulation-of-photocarrier-relaxation-dynamics-in-two-48mwls7txa.pdf

Modulation of photocarrier relaxation dynamics in two-dimensional semiconductors

The growth of wafer-scale single-crystal two-dimensional transition metal dichalcogenides (TMDs) on insulating substrates is critically important for a variety of high-end applications1–4. Although the epitaxial growth of wafer-scale graphene and hexagonal boron nitride on metal surfaces has been reported5–8, these techniques are not applicable for growing TMDs on insulating substrates because of substantial differences in growth kinetics. Thus, despite great efforts9–20, the direct growth of wafer-scale single-crystal TMDs on insulating substrates is yet to be realized. Here we report the successful epitaxial growth of two-inch single-crystal WS2 monolayer films on vicinal a-plane sapphire surfaces. In-depth characterizations and theoretical calculations reveal that the epitaxy is driven by a dual-coupling-guided mechanism, where the sapphire plane–WS2 interaction leads to two preferred antiparallel orientations of the WS2 crystal, and sapphire step edge–WS2 interaction breaks the symmetry of the antiparallel orientations. These two interactions result in the unidirectional alignment of nearly all the WS2 islands. The unidirectional alignment and seamless stitching of WS2 islands are illustrated via multiscale characterization techniques; the high quality of WS2 monolayers is further evidenced by a photoluminescent circular helicity of ~55%, comparable to that of exfoliated WS2 flakes. Our findings offer the opportunity to boost the production of wafer-scale single crystals of a broad range of two-dimensional materials on insulators, paving the way to applications in integrated devices. A dual-coupling-guided growth mechanism enables the realization of wafer-scale single-crystal WS2 on vicinal a-plane sapphire.

Dual-coupling-guided epitaxial growth of wafer-scale single-crystal WS2 monolayer on vicinal a-plane sapphire.

https://iopscience.iop.org/article/10.1088/1674-1056/ab3e46/pdf

Emerging properties of two-dimensional twisted bilayer materials

https://iopscience.iop.org/article/10.1088/1674-1056/ab99ba/pdf

Modulation of carrier lifetime in MoS2 monolayer by uniaxial strain

Tunable and highly sensitive temperature sensor based on graphene photonic crystal fiber

The great challenge for the growth of non-centrosymmetric 2D single crystals is to break the equivalence of antiparallel grains. Even though this pursuit has been partially achieved in boron nitride and transition metal dichalcogenides (TMDs) growth, the key factors that determine the epitaxy of non-centrosymmetric 2D single crystals are still unclear. Here we report a universal methodology for the epitaxy of non-centrosymmetric 2D metal dichalcogenides enabled by accurate time sequence control of the simultaneous formation of grain nuclei and substrate steps. With this methodology, we have demonstrated the epitaxy of unidirectionally aligned MoS2 grains on a, c, m, n, r and v plane Al2O3 as well as MgO and TiO2 substrates. This approach is also applicable to many TMDs, such as WS2, NbS2, MoSe2, WSe2 and NbSe2. This study reveals a robust mechanism for the growth of various 2D single crystals and thus paves the way for their potential applications. 

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Chen Huang

Papers

Dual-coupling-guided epitaxial growth of wafer-scale single-crystal WS2 monolayer on vicinal a-plane sapphire.

Emerging properties of two-dimensional twisted bilayer materials

Modulation of carrier lifetime in MoS2 monolayer by uniaxial strain

Tunable and highly sensitive temperature sensor based on graphene photonic crystal fiber

Universal epitaxy of non-centrosymmetric two-dimensional single-crystal metal dichalcogenides