The last few years have witnessed a surge in interest and research efforts in the field of twistronics, especially in low-angle twisted bilayers of transition metal dichalocogenides. These novel material platforms have been demonstrated to host periodic arrays of excitonic quantum emitters, interlayer excitons with long lifetimes, and exotic many-body states. While much remains to be known and understood about these heterostructures, the field of large-angle, incommensurate bilayers is even less explored. At twist angles larger than a few degrees, the presence of periodicity in these bilayers becomes chaotic, making the systems essentially aperiodic and incommensurate in nature due to the limitations of fabrication techniques. In this work, we demonstrate the emergence of a brightened dark intralayer exciton in twisted n-doped molybdenum diselenide homobilayer. We show that this dark exciton diffuses across the excitation spot more efficiently as compared to bright trions or excitons, reaching diffusion lengths greater than 4 microns. Temperature-dependent spectra provide corroborative evidence and reveal a brightened dark trion. Almost inexplicably, this dark exciton showcases a robust valley coherence, which we attribute to a small mixing of the spin-resolved conduction bands due to an absence of out-of-plane reflection symmetry arising from a strong dielectric contrast. Our results reveal some of the richness of the physics of these large-angle systems while uncovering new opportunities for valleytronic devices that may utilize these more valley-robust "mixed" dark excitons.
In long-wavelength moiré patterns of homobilayer semiconductors, the layer pseudospin of electrons is subject to a sizable Zeeman field that is spatially modulated from the interlayer coupling in moiré. By interference of this spatial modulation with a homogeneous but dynamically tunable component from out-of-plane electric field, we show that the spatial-temporal profile of the overall Zeeman field therefore features a topological texture that can be controlled in an ultrafast timescale by a terahertz field or an interlayer bias. Such dynamical modulation leads to the emergence of an in-plane…
In twisted homobilayer transition metal dichalcogenides, intra- and inter-layer valley excitons hybridize with the layer configurations spatially varying in the moiré. The ground state valley excitons are trapped at two high-symmetry points with opposite electric dipoles in a moiré supercell, forming a honeycomb superlattice of nearest-neighbor dipolar attraction. We find that the spatial texture of layer configuration results in a luminescence anomaly of the moiré trapped excitons, where a tiny displacement by interactions dramatically increases the brightness and changes polarization from ci…
The spatial texture of internal degree of freedom of electrons has profound effects on the properties of materials. Such texture in real space can manifest as an emergent magnetic field (or Berry curvature), which is expected to induce interesting valley/spin-related transport phenomena. Moiré pattern, which emerges as a spatial variation at the interface of 2D atomic crystals, provides a natural platform for investigating such real space Berry curvature effects. Here we study moiré structures formed in homobilayer transition metal dichalcogenides (TMDs) due to twisting, various uniform strain…
Moiré superlattices in twisted van der Waals materials constitute a promising platform for engineering electronic and optical properties. However, a major obstacle to fully understanding these systems and harnessing their potential is the limited ability to correlate the local moiré structure with optical properties. By using a recently developed scanning electron microscopy technique to image twisted WSe$_2$/WSe$_2$ bilayers, we directly correlate increasing moiré periodicity with the emergence of two distinct exciton species. These can be tuned individually through electrostatic gating, and …
Optoelectronic properties of van der Waals homostructures can be selectively engineered by the relative twist angle between layers. Here, we study the twist-dependent moire coupling in MoSe2 homobilayers. For small angles, we find a pronounced redshift of the K-K and Γ-K excitons accompanied by a transition from K-K to Γ-K emission. Both effects can be traced back to the underlying moire pattern in the MoSe2 homobilayers, as confirmed by our low-energy continuum model for different moire excitons. We identify two distinct intralayer moire excitons for R-stacking, while H-stacking yields two de…
We show that moiré bands of twisted homobilayers can be topologically nontrivial, and illustrate the tendency by studying valence band states in $\pm K$ valleys of twisted bilayer transition metal dichalcogenides, in particular, bilayer MoTe$_2$. Because of the large spin-orbit splitting at the monolayer valence band maxima, the low energy valence states of the twisted bilayer MoTe$_2$ at $+K$ ($-K$) valley can be described using a two-band model with a layer-pseudospin magnetic field $\boldsymbolΔ(\boldsymbol{r})$ that has the moiré period. We show that $\boldsymbolΔ(\boldsymbol{r})$ has a to…
We predict that in a twisted homobilayer of transition-metal dichalcogenide MoS$_2$, spin-orbit coupling in the conduction band states from $\pm K$ valleys can give rise to moiré flat bands with nonzero Chern numbers in each valley. The nontrivial band topology originates from a unique combination of angular twist and local mirror symmetry breaking in each individual layer, which results in unusual skyrmionic spin textures in momentum space with skyrmion number $\mathcal{S} = \pm 2$. Our Hartree-Fock analysis further suggests that density-density interactions generically drive the system at $1…
The incommensurate stacking of multi-layered two-dimensional materials is a challenging problem from a theoretical perspective and an intriguing avenue for manipulating their physical properties. Here we present a multi-scale model to obtain the mechanical relaxation pattern of twisted trilayer van der Waals (vdW) heterostructures with two independent twist angles, a generally incommensurate system without a supercell description. We adopt the configuration space as a natural description of such incommensurate layered materials, based on the local environment of atomic positions, bypassing the…
Cylindrical multishell structure is one of the prevalent atomic arrangements in nanowires. Being multishell, the well-defined atomic periodicity is hardly realized in it because the periodic units of individual shells therein generally do not match except for very few cases, posing a challenge to understand its physical properties. Here we show that moiré patterns generated by superimposing atomic lattices of individual shells are decisive in determining its electronic structures. Double- walled carbon nanotubes, as an example, are shown to have spectacular variations in their electronic prope…
Recent experiments have observed correlated insulating and possible superconducting phases in twisted homobilayer transition metal dichalcogenides (TMDs). Besides the spin-valley locked moire bands due to the intrinsic Ising spin-orbit coupling, homobilayer moire TMDs also possess either logarithmic or power-law divergent Van Hove singularities (VHS) near the Fermi surface, controllable by an external displacement field. The former and the latter are dubbed conventional and higher-order VHS, respectively. Here, we perform a perturbative renormalization group (RG) analysis to unbiasedly study t…
Twisted graphene multi-layers have been recently demonstrated to share several correlation-driven behaviours with twisted bilayer graphene. In general, the van Hove singularities (VHSs) can be used as a proxy of the tendency for correlated behaviours. In this paper, we adopt an atomistic method by combining tight-binding method with the semi-classical molecular dynamics to investigate the electronic structures of twisted trilayer graphene (TTG) with two independent twist angles. The two independent twist angles can lead to the interference of the moiré patterns forming a variety of commensurat…
We study untwisted heterobilayers of ferromagnetic and antiferromagnetic van der Waals materials, with in particular a Dzyaloshinskii-Moriya interaction in the ferromagnetic layer. A continuum low energy field theory is utilized to study such systems. We develop a phase diagram as a function of the strength of inter-layer exchange and Dzyaloshinskii-Moriya interactions, combining perturbative and strong coupling analyses with numerical simulations using Landau-Lifshitz-Gilbert equations. Various moiré-periodic commensurate phases are found, and the commensurate-incommensurate transition is dis…
Periodicity of long wavelength moiré patterns is very often destroyed by the inhomogeneous strain introduced in fabrications of van der Waals layered structures. We present a framework to describe massive Dirac fermions in such distorted moiré pattern of transition metal dichalcogenides homobilayers, accounting for the dynamics of layer pseudospin. In decoupled bilayers, we show two causes of in-plane layer pseudospin precession: By the coupling of layer antisymmetric strain to valley magnetic moment; and by the Aharonov-Bohm effect in the SU(2) gauge potential for the case of R-type bilayer u…
Recent advances in the field of vertically stacked 2D materials have revealed a rich exciton landscape. In particular, it has been demonstrated that out-of-plane electrical fields can be used to tune the spectral position of spatially separated interlayer excitons. Other studies have shown that there is a strong hybridization of exciton states, resulting from the mixing of electronic states in both layers. However, the connection between the twist-angle dependent hybridization and field-induced energy shifts has remained in the dark. Here, we investigate on a microscopic footing the interplay …
Twistronic assembly of 2D materials employs the twist angle between adjacent layers as a tuning parameter for designing the electronic and optical properties of van der Waals heterostructures. Here, we study how interlayer hybridization, weak ferroelectric charge transfer between layers, and piezoelectric response to deformations set the valence and conduction band edges across the moir{é} supercell in twistronic homobilayers of MoS$_2$, MoSe$_2$, WS$_2$ and WSe$_2$. We show that, due to the lack of inversion symmetry in the monolayer crystals, bilayers with parallel (P) and anti-parallel (AP)…
Lattice reconstruction in twisted transition-metal dichalcogenide (TMD) bilayers gives rise to piezo- and ferroelectric moiré potentials for electrons and holes, as well as a modulation of the hybridisation across the bilayer. Here, we develop hybrid $\mathbf{k}\cdot \mathbf{p}$ tight-binding models to describe electrons and holes in the relevant valleys of twisted TMD homobilayers with parallel (P) and anti-parallel (AP) orientations of the monolayer unit cells. We apply these models to describe moiré superlattice effects in twisted WSe${}_2$ bilayers, in conjunction with microscopic \emph{ab…
We show that a sliding motion between the two layers of a \moire superlattice induces an electric current and realizes a two-dimensional version of the topological Thouless pump when the Fermi energy lies in one of the minigaps. Interestingly, a chiral charge pump, namely, a transverse current induced by the sliding motion, is possible in twisted homobilayers. This result is confirmed by a concrete calculation of the adiabatic current in twisted bilayer graphene. Our work reveals an interesting link between mechanical motion and electricity unique to \moire superlattices, and may find applicat…
The valence band maxima of most group-VI transition metal dichalcogenide thin films remain at the $Γ$-point all the way from bulk to bilayer. In this paper we develop a continuum theory of the moirè minibands that are formed in the valence bands of $Γ$-valley homobilayers by a small relative twist. Our effective theory is benchmarked against large-scale ab initio electronic structure calculations that account for lattice relaxation. As a consequence of an emergent $D_6$ symmetry we find that low-energy $Γ$-valley moirè holes differ qualitatively from their K-valley counterparts addressed previ…
Experimental signature of layer skyrmions and implications for band topology in twisted WSe2 bilayers
University of Texas at Austin（德克萨斯大学奥斯汀分校）；The University of Hong Kong（香港大学）；National Yang Ming Chiao Tung University（阳明交通大学）；Pennsylvania State University（宾夕法尼亚州立大学）；National Institute for Materials Science（日本物质材料研究机构）
Geometrical moiré patterns, generic for almost aligned bilayers of two-dimensional (2D) crystals with similar lattice structure but slightly different lattice constants, lead to zone folding and miniband formation for electronic states. Here, we show that moiré superlattice (mSL) effects in $\mathrm{MoSe}_2/\mathrm{WS}_2$ and $\mathrm{MoTe}_2/\mathrm{MoSe}_2$ heterobilayers that feature alignment of the band edges are enhanced by resonant interlayer hybridization, and anticipate similar features in twisted homobilayers of TMDs, including examples of narrow minibands close to the actual band ed…
Moiré superlattices serve as a playground for emerging phenomena, such as localization of band states, superconductivity, and localization of excitons. These superlattices are large and are often modeled in the zero angle limit, which obscures the effect of finite twist angles. Here, by means of first-principles calculations we quantify the twist-angle dependence of the moiré potential in the MoS$_2$ homobilayer and identify the contributions from the constituent elements of the moiré potential. Furthermore, by considering the zero-angle limit configurations, we show that the moiré potential i…
We present a general theoretical formulation to describe the interlayer interaction in incommensurate bilayer systems with arbitrary crystal structures. By starting from the tight- binding model with the distance-dependent transfer integral, we show that the interlayer coupling, which is highly complex in the real space, can be simply written in terms of generalized Umklapp process in the reciprocal space. The formulation is useful to describe the interaction in the two-dimensional interface of different materials with arbitrary lattice structures and relative orientations. We apply the method…
While it is known that the double-layer Bi$_2$Sr$_2$CaCu$_2$O$_{8+y}$ (BSCCO) cuprate superconductor exhibits a one-dimensional (1D) incommensurate superlattice (IS), the effect of IS on the electronic structure remains elusive. Following the recent shift of the interest from underdoped to optimum and overdoped phase in BSCCO by increasing the hole doping $x$, controlled by the oxygen interstitials concentration $y$, here we focus on the multiple splitting of the density of states (DOS) peaks and emergence of higher order van Hove singularities (VHS) due to the 1D incommensurate superlattice. …
We present a comprehensive dynamical mean field study of the triangular lattice moiré Hubbard model, which is believed to represent the physics of moiré bilayer transition metal dichalcogenides. In these materials, important aspects of the band structure including the bandwidth and the order and location of van Hove singularities can be tuned by varying the interlayer potential. We present a magnetic and metal-insulator phase diagram and a detailed study of the dependence of the resistivity on temperature, band filling and interlayer potential. We find that transport displays Fermi liquid, str…
Twisted Van der Waals systems offer the unprecedented possibility to tune different states of correlated quantum matter with an external non-invasive electrostatic doping. The nature of the superconducting order presents a recurring open question in this context. In this work, we quantitatively assess the case of spin-fluctuation-mediated pairing for $Γ$-valley twisted transition metal dichalcogenide homobilayers. We self-consistently and dynamically calculate the doping dependent superconducting transition temperature $T_{\mathrm{c}}$ revealing a superconducting dome with a maximal $T_{\mathr…
Cascade of Spin Moiré Superlattices with In-Plane Field in Triangle Lattice Semimetal EuAg$_4$Sb$_2$
Massachusetts Institute of Technology（麻省理工学院）；California Institute of Technology（加州理工学院）；Institut Laue Langevin（朗之万研究所）；Hokkaido University（北海道大学）；PSI Center for Neutron and Muon Sciences（瑞士保罗谢勒研究所中子与μ子科学中心）
Lattice dynamics play a crucial role in the physics of Moiré systems. In twisted bilayer graphene (TBG), it was shown that, in addition to the graphene phonons, there is another set of gapless excitations termed Moiré Phonons [Phys. Rev. B, 075416, 2019] reflecting the lattice dynamics at the Moire superlattice level. These modes were later suggested to be phasons due to the incommensurate stacking of the two graphene layers [Phys. Rev. B, 155426, 2019]. In this work, we elucidate the equivalence of these two seemingly distinct perspectives by identifying an underlying symmetry, which we dub m…
In twisted bilayer graphene, long-wavelength lattice fluctuations on the scale of the moiré period are dominated by phason modes, i.e., acoustic branches of the incommensurate lattice resulting from coherent superpositions of optical phonons. In the limit of small twist angles, these modes describe the sliding motion of stacking domain walls separating regions of partial commensuration. The resulting soliton network is a soft elastic manifold, whose reduced rigidity arises from the competition between intralayer (elastic) and interlayer (adhesion) forces governing lattice relaxation. Shear def…
The long wavelength moiré superlattices in twisted 2D structures have emerged as a highly tunable platform for strongly correlated electron physics. We study the moiré bands in twisted transition metal dichalcogenide homobilayers, focusing on WSe$_2$, at small twist angles using a combination of first principles density functional theory, continuum modeling, and Hartree-Fock approximation. We reveal the rich physics at small twist angles $θ<4^\circ$, and identify a particular magic angle at which the top valence moiré band achieves almost perfect flatness. In the vicinity of this magic angle, …
