Interaction effects and superconductivity signatures in twisted double-bilayer WSe2

CVD Synthesis of Twisted Bilayer WS2 with Tunable Second Harmonic Generation

The introduction of rotational freedom by twist angles in twisted bilayer (TB) transition metal dichalcogenides (TMDCs) can tailor the inherent properties of the TMDCs, which provides a promising platform to investigate the exotic physical properties. However, direct synthesis of high-quality TB-TMDCs with full twist angles is significantly challenging due to the substantial energy barriers during crystal growth. Here, a modified chemical vapor deposition strategy is proposed to synthesize TB-WS2 with a wide twist angle range from 0° to 120°. Utilizing a tilted SiO2/Si substrate, a gas flow disturbance is generated in the furnace tube to create a heterogeneous concentration gradient of the metal precursor, which provides an extra driving force for the growth of TB-WS2. The Raman and photoluminescence results confirm a weak interlayer coupling of the TB-WS2. High-quality periodic Moiré patterns are observed in the scanning transmission electron microscopy images. Moreover, owing to the strong correlation between the nonlinear optical response and the twisted crystal structure, tunable second harmonic generation behaviors are realized in the TB-WS2. This approach opens up a new avenue for the direct growth of high-crystalline-quality and pristine TB-TMDCs and their potential applications in nonlinear optical devices.

Simultaneously Regulated Highly Polarized and Long-Lived Valley Excitons in WSe2/GaN Heterostructures

Interlayer excitons, with prolonged lifetimes and tunability, hold potential for advanced optoelectronics. Previous research on the interlayer excitons has been dominated by two-dimensional heterostructures. Here, we construct WSe2/GaN composite heterostructures, in which the doping concentration of GaN and the twist angle of bilayer WSe2 are employed as two ingredients for the manipulation of exciton behaviors and polarizations. The exciton energies in monolayer WSe2/GaN can be regulated continuously by the doping levels of the GaN substrate, and a remarkable increase in the valley polarizations is achieved. Especially in a heterostructure with 4°-twisted bilayer WSe2, a maximum polarization of 38.9% with a long lifetime is achieved for the interlayer exciton. Theoretical calculations reveal that the large polarization and long lifetime are attributed to the high exciton binding energy and large spin flipping energy during depolarization in bilayer WSe2/GaN. This work introduces a distinctive member of the interlayer exciton with a high degree of polarization and a long lifetime.

Influence of Atomic Relaxations on the Moiré Flat Band Wave Functions in Antiparallel Twisted Bilayer WS2

Twisting bilayers of transition metal dichalcogenides gives rise to a moiré potential resulting in flat bands with localized wave functions and enhanced correlation effects. In this work, scanning tunneling microscopy is used to image a WS2 bilayer twisted approximately 3° off the antiparallel alignment. Scanning tunneling spectroscopy reveals localized states in the vicinity of the valence band onset, which is observed to occur first in regions with S-on-S Bernal stacking. In contrast, density functional theory calculations on twisted bilayers that have been relaxed in vacuum predict the highest-lying flat valence band to be localized in regions of AA' stacking. However, agreement with experiment is recovered when the calculations are performed on bilayers in which the atomic displacements from the unrelaxed positions have been reduced, reflecting the influence of the substrate and finite temperature. This demonstrates the delicate interplay of atomic relaxations and the electronic structure of twisted bilayer materials.

Pressure-Induced Dynamic Tuning of Interlayer Coupling in Twisted WSe2/WSe2 Homobilayers

Moiré superlattices induced by twisted van der Waals (vdW) heterostructures or homostructures have recently gained significant attention due to their potential to generate exotic strong-correlation electronic and phonon phenomena. However, the lack of dynamic tuning for interlayer coupling of moiré superlattices hinders a thorough understanding and development of the moiré correlation state. Here, we present a dynamic tuning method for twisted WSe2/WSe2 homobilayers using a diamond anvil cell (DAC). We demonstrate the powerful tuning of interlayer coupling and observe an enhanced response to pressure for interlayer breathing modes and the rapid descent of indirect excitons in twisted WSe2/WSe2 homobilayers. Our findings indicate that the introduction of a moiré superlattice for WSe2 bilayers gives rise to hybridized excitons, which lead to the different pressure-evolution exciton behaviors compared to natural WSe2 bilayers. Our results provide a novel understanding of moiré physics and offer an effective method to tune interlayer coupling of moiré superlattices.

Recent Advances in Moiré Superlattice Systems by Angle-Resolved Photoemission Spectroscopy

The last decade has witnessed a flourish in 2D materials including graphene and transition metal dichalcogenides (TMDs) as atomic-scale Legos. Artificial moiré superlattices via stacking 2D materials with a twist angle and/or a lattice mismatch have recently become a fertile playground exhibiting a plethora of emergent properties beyond their building blocks. These rich quantum phenomena stem from their nontrivial electronic structures that are effectively tuned by the moiré periodicity. Modern angle-resolved photoemission spectroscopy (ARPES) can directly visualize electronic structures with decent momentum, energy, and spatial resolution, thus can provide enlightening insights into fundamental physics in moiré superlattice systems and guides for designing novel devices. In this review, first, a brief introduction is given on advanced ARPES techniques and basic ideas of band structures in a moiré superlattice system. Then ARPES research results of various moiré superlattice systems are highlighted, including graphene on substrates with small lattice mismatches, twisted graphene/TMD moiré systems, and high-order moiré superlattice systems. Finally, it discusses important questions that remain open, challenges in current experimental investigations, and presents an outlook on this field of research.

Robust ferromagnetism in two-dimensional GeC/CrN heterobilayers

We have investigated the electronic and finite temperature magnetic properties of germanium carbide (GeC) and ferromagnetic chromium nitride (CrN) heterobilayers by using first-principles calculations based on density functional theory with Hubbard U correction and an effective anisotropic Heisenberg spin model. The dynamical stability of different stacking formations of heterobilayers is ensured by considering the phonon spectra. All the stacking patterns show half-metallicity with an out-of-plane easy-axis ferromagnetic ground state. We find a high Curie temperature for GeC/CrN heterobilayers within the random phase approximation (RPA). In addition to the symmetric stackings, i.e., AA and AB, the electronic properties of non-symmetric stackings at three different twist angles are also analyzed. The electronic structure analysis of twisted structures demonstrates that the half-metallicity of the GeC/CrN heterobilayer is stack independent. Furthermore, we have investigated the electronic properties, magnetic anisotropy energy, Curie temperature, and spin wave spectrum in the presence of biaxial strain. It is shown that the compressive strain dramatically reduces the magnetic anisotropy energy of the GeC/CrN heterobilayer and Curie temperature, but the Curie temperature still remains well above room temperature for all strain values. The increasing values of tensile strain reduce the magnetic exchange while it increases the magnetic anisotropy energy of the heterobilayer system which enhances the Curie temperature of the structures. The monolayer CrN on the GeC with a wide band gap and commensurate lattice together with a high Tc value can be a feasible candidate for future spintronic applications.

Twist-Induced Modification in the Electronic Structure of Bilayer WSe2

The recent discovery of strongly correlated phases in twisted transition-metal dichalcogenides (TMDs) highlights the significant impact of twist-induced modifications on electronic structures. In this study, we employed angle-resolved photoemission spectroscopy with submicrometer spatial resolution (μ-ARPES) to investigate these modifications by comparing valence band structures of twisted (5.3°) and nontwisted (AB-stacked) bilayer regions within the same WSe2 device. Relative to the nontwisted region, the twisted area exhibits pronounced moiré bands and ∼90 meV renormalization at the Γ-valley, substantial momentum separation between different layers, and an absence of flat bands at the K-valley. We further simulated the effects of lattice relaxation, which can flatten the Γ-valley edge but not the K-valley edge. Our results provide a direct visualization of twist-induced modifications in the electronic structures of twisted TMDs and elucidate their valley-dependent responses to lattice relaxation.

Flat Γ Moiré Bands in Twisted Bilayer WSe_{2}

The recent observation of correlated phases in transition metal dichalcogenide moiré systems at integer and fractional filling promises new insight into metal-insulator transitions and the unusual states of matter that can emerge near such transitions. Here, we combine real- and momentum-space mapping techniques to study moiré superlattice effects in 57.4° twisted WSe_{2} (tWSe_{2}). Our data reveal a split-off flat band that derives from the monolayer Γ states. Using advanced data analysis, we directly quantify the moiré potential from our data. We further demonstrate that the global valence band maximum in tWSe_{2} is close in energy to this flat band but derives from the monolayer K states which show weaker superlattice effects. These results constrain theoretical models and open the perspective that Γ-valley flat bands might be involved in the correlated physics of twisted WSe_{2}.

Orbital Fulde-Ferrell Pairing State in Moiré Ising Superconductors

In this Letter, we study superconducting moiré homobilayer transition metal dichalcogenides where the Ising spin-orbit coupling (SOC) is much larger than the moiré bandwidth. We call such noncentrosymmetric superconductors, moiré Ising superconductors. Because of the large Ising SOC, the depairing effect caused by the Zeeman field is negligible and the in-plane upper critical field (B_{c2}) is determined by the orbital effects. This allows us to study the effect of large orbital fields. Interestingly, when the applied in-plane field is larger than the conventional orbital B_{c2}, a finite-momentum pairing phase would appear which we call the orbital Fulde-Ferrell (FF) state. In this state, the Cooper pairs acquire a net momentum of 2q_{B}, where 2q_{B}=eBd is the momentum shift caused by the magnetic field B and d denotes the layer separation. This orbital field-driven FF state is different from the conventional FF state driven by Zeeman effects in Rashba superconductors. Remarkably, we predict that the FF pairing would result in a giant superconducting diode effect under electric gating when layer asymmetry is induced. An upturn of the B_{c2} as the temperature is lowered, coupled with the giant superconducting diode effect, would allow the detection of the orbital FF state.

Tunable spin and valley excitations of correlated insulators in Γ-valley moiré bands

Moiré superlattices formed from transition metal dichalcogenides support a variety of quantum electronic phases that are highly tunable using applied electromagnetic fields. While the valley degree of freedom affects optoelectronic properties in the constituent transition metal dichalcogenides, it has yet to be fully explored in moiré systems. Here we establish twisted double-bilayer WSe₂ as an experimental platform to study electronic correlations within Γ-valley moiré bands. Through local and global electronic compressibility measurements, we identify charge-ordered phases at multiple integer and fractional moiré fillings. By measuring the magnetic field dependence of their energy gaps and the chemical potential upon doping, we reveal spin-polarized ground states with spin-polaron quasiparticle excitations. In addition, an applied displacement field induces a metal-insulator transition driven by tuning between Γ- and K-valley moiré bands. Our results demonstrate control over the spin and valley character of the correlated ground and excited states in this system.

Quantum Phase Diagram and Spontaneously Emergent Topological Chiral Superconductivity in Doped Triangular-Lattice Mott Insulators

The topological superconducting state is a highly sought-after quantum state hosting topological order and Majorana excitations. In this Letter, we explore the mechanism to realize the topological superconductivity (TSC) in the doped Mott insulators with time-reversal symmetry (TRS). Through large-scale density matrix renormalization group study of an extended triangular-lattice t-J model on the six- and eight-leg cylinders, we identify a d+id-wave chiral TSC with spontaneous TRS breaking, which is characterized by a Chern number C=2 and quasi-long-range superconducting order. We map out the quantum phase diagram with by tuning the next-nearest-neighbor (NNN) electron hopping and spin interaction. In the weaker NNN-coupling regime, we identify a pseudogaplike phase with a charge stripe order coexisting with fluctuating superconductivity, which can be tuned into d-wave superconductivity by increasing the doping level and system width. The TSC emerges in the intermediate-coupling regime, which has a transition to a d-wave superconducting phase with larger NNN couplings. The emergence of the TSC is driven by geometrical frustrations and hole dynamics which suppress spin correlation and charge order, leading to a topological quantum phase transition.

Thermodynamic Characteristic for a Correlated Flat-Band System with a Quantum Anomalous Hall Ground State

While the ground-state phase diagram of the correlated flat-band systems has been intensively investigated, the dynamic and thermodynamic properties of such lattice models are less explored, but it is the latter which is most relevant to the experimental probes (transport, quantum capacitance, and spectroscopy) of the quantum moiré materials such as twisted bilayer graphene. Here we show, by means of momentum-space quantum Monte Carlo and exact diagonalization, in chiral limit there exists a unique thermodynamic characteristic for the correlated flat-band model with interaction-driven quantum anomalous Hall (QAH) ground state, namely, the transition from the QAH insulator to the metallic state takes place at a much lower temperature compared with the zero-temperature single-particle gap generated by the long-range Coulomb interaction. Such low transition temperature comes from the proliferation of excitonic particle-hole excitations, which transfers the electrons across the gap between different topological bands to restore the broken time-reversal symmetry and gives rise to a pronounced enhancement in the charge compressibility. Future experiments, to verify such generic thermodynamic characteristics, are proposed.

Laser Shock-Induced Nano-Twist of Transition Metal Dichalcogenides

Mechanical strain, such as stretching, compression, bending, and rotation, significantly alters the photonic and electronic properties of 2D materials. The laser shock process, which allows 2D materials to deform at an ultrahigh strain rate, is a promising technology for alleviating the low strain transfer efficiency caused by the low interfacial bonding strength of the layered 2D materials. However, the mechanical strain introduced by shock waves is currently limited to uniaxial compression or bending deformation, and the monotonic strain patterns constrain the strain diversity and performance expansion space of 2D materials. This work proposed a novel strategy for nano-twist manufacturing using laser shock processing, based on partial interfacial decoupling behavior. Apart from the conventional uniaxial strain, we demonstrated experimentally and theoretically that the manufacturing of nano-twist allows the introduction of interlayer tensile and rotational strains in TMDCs. The microstructure and properties of the strained 2D materials were investigated. Furthermore, the dynamic deformation response of WSe₂ during the shock process was studied using molecular dynamics simulations. The correlation between the laser shock-induced dynamic loading process, interfacial behavior, and deformation behavior of 2D materials was comprehensively explored. The primary contribution of this study lies in the introduction of diversified strain modes through nano-twist manufacturing by the laser shock process, which is expected to provide a convenient nano-twist fabrication process for the strain engineering and twistronics fields.

Reproducibility in the fabrication and physics of moiré materials

Overlaying two atomic layers with a slight lattice mismatch or at a small rotation angle creates a moiré superlattice, which has properties that are markedly modified from (and at times entirely absent in) the 'parent' materials. Such moiré materials have progressed the study and engineering of strongly correlated phenomena and topological systems in reduced dimensions. The fundamental understanding of the electronic phases, such as superconductivity, requires a precise control of the challenging fabrication process, involving the rotational alignment of two atomically thin layers with an angular precision below 0.1 degrees. Here we review the essential properties of moiré materials and discuss their fabrication and physics from a reproducibility perspective.

Atomic Insights into Fracture Characteristics of Twisted Tri-Layer Graphene

Graphene twistronics have recently gained significant attention due their superconductive behavior as a consequence of their tunable electronic properties. Although the electronic properties of twisted graphene have been extensively studied, the mechanical properties and integrity of twisted trilayer graphene (tTLG) under loading is still elusive. We investigated the fracture mechanics of tTLG with a twist angle of ±1.53° utilizing molecular dynamics simulation. This twist angle was chosen because it is known to exhibit highly superconductive behavior. The results indicate that tTLG does not preserve the excellent mechanical properties typically associated with graphene, with toughness and fracture strain values much lower in comparison. The Young’s modulus was an exception with values relatively close to pristine graphene, whereas the tensile strength was found to be roughly half of the intrinsic strength of graphene. The fracture toughness, fracture strain and strength converge as the crack length increases, reaching 0.26 J/m3, 0.0217 and 39.9 GPa at a crack length of 8 nm, respectively. The Griffth critical strain energy is 19.98 J/m2 and the critical stress intensity factor Kc is 4.47 MPa M1/2, in good agreement with that of monolayer graphene in the experiment. Our atomic insights might be helpful in the material design of twisted trilayer graphene-based electronics.

Lattice reconstruction induced multiple ultra-flat bands in twisted bilayer WSe2

Moiré superlattices in van der Waals heterostructures provide a tunable platform to study emergent properties that are absent in the natural crystal form. Twisted bilayer transition metal dichalcogenides (TB-TMDs) can host moiré flat bands over a wide range of twist angles. For twist angle close to 60°, it was predicted that TB-TMDs undergo a lattice reconstruction which causes the formation of ultra-flat bands. Here, by using scanning tunneling microscopy and spectroscopy, we show the emergence of multiple ultra-flat bands in twisted bilayer WSe₂ when the twist angle is within 3° of 60°. The ultra-flat bands are manifested as narrow tunneling conductance peaks with estimated bandwidth less than 10 meV, which is only a fraction of the estimated on-site Coulomb repulsion energy. The number of these ultra-flat bands and spatial distribution of the wavefunctions match well with the theoretical predictions, strongly evidencing that the observed ultra-flat bands are induced by lattice reconstruction. Our work provides a foundation for further study of the exotic correlated phases in TB-TMDs.

It was predicted that lattice reconstruction can lead to the emergence of multiple ultra-flat electronic bands in twisted bilayer transition metal dichalcogenides. Here, by using scanning tunneling microscopy and spectroscopy, the authors demonstrate such bands in twisted bilayer WSe₂.

Engineering Three-Dimensional Moiré Flat Bands

Twisting two adjacent layers of van der Waals materials with respect to each other can lead to flat two-dimensional electronic bands which enables a wealth of physical phenomena. Here, we generalize this concept of so-called moiré flat bands to engineer flat bands in all three spatial dimensions controlled by the twist angle. The basic concept is to stack the material such that the large spatial moiré interference patterns are spatially shifted from one twisted layer to the next. We exemplify the general concept by considering graphitic systems, boron nitride, and WSe2, but the approach is applicable to any two-dimensional van der Waals material. For hexagonal boron nitride, we develop an ab initio fitted tight binding model that captures the corresponding three-dimensional low-energy electronic structure. We outline that interesting three-dimensional correlated phases of matter can be induced and controlled following this route, including quantum magnets and unconventional superconducting states.

Layer-dependent interface reconstruction and strain modulation in twisted WSe2

Twistronics has emerged as one of the most attractive playgrounds for manipulating the interfacial structures and electronic properties of two-dimensional materials. However, the layer-dependent lattice reconstruction and resulted strain distribution in marginally twisted transition metal dichalcogenides still remain elusive. Here we report a systematic study by both electron diffraction quantification and atomic-resolution imaging on the interface reconstruction of twisted WSe₂, which shows a strong dependence on the constituent layer numbers and twist angles. The competition between the interlayer interaction, which varies with local atomic configurations, and the intralayer elastic deformation, related to the layer thickness, leads to rich superlattice motifs and strain modulation patterns, i.e. triangular for odd and kagome-like textures for even layer numbers, against the rigid stacking moiré model. The strain effects of small twist angles are further demonstrated by electrical transport measurements, manifesting intriguing conducting states at low temperatures beyond the flat band features of large twist angles. Our work not only provides a comprehensive understanding of layer-dependent twist structures, but also may shed light on the future design of twistronic devices.

Chirality-Induced Giant Unidirectional Magnetoresistance in Twisted Bilayer Graphene

Twisted bilayer graphene (TBG) exhibits fascinating correlation-driven phenomena like the superconductivity and Mott insulating state, with flat bands and a chiral lattice structure. We find by quantum-transport calculations that the chirality leads to a giant unidirectional magnetoresistance (UMR) in TBG, where the unidirectionality refers to the resistance change under the reversal of the direction of current or magnetic field. We point out that flat bands significantly enhance this effect. The UMR increases quickly upon reducing the twist angle, and reaches about 20% for an angle of 1.5° in a 10 T in-plane magnetic field. We propose the band structure topology (asymmetry), which leads to a direction-sensitive mean free path, as a useful way to anticipate the UMR effect. The UMR provides a probe for chirality and band flatness in the twisted bilayers.

In situ manipulation of van der Waals heterostructures for twistronics

In van der Waals heterostructures, electronic bands of two-dimensional (2D) materials, their nontrivial topology, and electron-electron interactions can be markedly changed by a moiré pattern induced by twist angles between different layers. This process is referred to as twistronics, where the tuning of twist angle can be realized through mechanical manipulation of 2D materials. Here, we demonstrate an experimental technique that can achieve in situ dynamical rotation and manipulation of 2D materials in van der Waals heterostructures. Using this technique, we fabricated heterostructures where graphene is perfectly aligned with both top and bottom encapsulating layers of hexagonal boron nitride. Our technique enables twisted 2D material systems in one single stack with dynamically tunable optical, mechanical, and electronic properties.