The quantum spin Hall (QSH) effect, characterized by topologically protected spin-polarized edge states, was recently demonstrated in monolayers of the transition metal dichalcogenide (TMD) WTe$_2$. However, the robustness of this topological protection remains largely unexplored in van der Waals heterostructures containing one or more layers of a QSH insulator. In this work, we use scanning tunneling microscopy and spectroscopy (STM/STS) to explore the topological nature of twisted bilayer (tBL) WTe$_2$ which is produce from folded monolayers, as well as, tear-and-stack fabrication. At the tBL bilayer edge, we observe the characteristic spectroscopic signature of the QSH edge state that is absent in topologically trivial as-grown bilayer. For small twist angles, a rectangular moiré pattern develops, which results in local modifications of the band structure. Using first principles calculations, we quantify the interactions in tBL WTe$_2$ and its topological edge states as function of interlayer distance and conclude that it is possible to tune the topology of WTe$_2$ bilayers via the twist angle as well as interlayer interactions.
Monolayer WTe2 stripes are quantum spin Hall (QSH) insulators. Density functional theory was used for investigating the electronic properties of the stripes and steps in bilayer Td-WTe2. For the stripes oriented along the dimer chains of W atoms (x direction), the hybridization between the two layers suppresses the QSH states. However, the QSH nature can be recovered by forming a step, depending on the atomic structure of the step. Conversely, the stripes and steps along the y direction maintain the QSH states. These findings can expand the application range of the QSH states in WTe2.
Unconventional responses upon breaking discrete or crystal symmetries open avenues for exploring emergent physical systems and materials. By breaking inversion symmetry, a nonlinear Hall signal can be observed, even in the presence of time-reversal symmetry, quite different from the conventional Hall effects. Low-symmetry two-dimensional materials are promising candidates for the nonlinear Hall effect, but it is less known when a strong nonlinear Hall signal can be measured, in particular, its connections with the band-structure properties. By using model analysis, we find prominent nonlinear …
Unlike the conventional (linear) anomalous Nernst effect, the non-linear anomalous Nernst effect (NLANE) can survive in an inversion symmetry broken system even in the presence of time-reversal symmetry. Using semiclassical Boltzmann transport theory, we derive the general expression of the non-linear anomalous Nernst coefficient as the second-order response function to the applied temperature gradient. We find that the non-linear Nernst current, which flows perpendicular to the temperature gradient even in the absence of a magnetic field, arises due to the Berry curvature of the states near t…
Umklapp-Enhanced Interlayer Valley Drag in Moiré Bilayers
Institute of Mathematical Sciences（数学科学研究所）；Tata Institute of Fundamental Research（塔塔基础研究所）；Indiana University（印第安纳大学）；Indian Institute of Technology - Kanpur（坎普尔印度理工学院）
Aiming to clarify the mechanisms governing the interlayer magnetic coupling, we have investigated the stacking energy and interlayer magnetism of bilayer CrBr$_3$ systemically. The magnetic ground states of bilayer CrBr$_3$ with different R-type and H-type stacking orders are established, which is found to be in good agreement with recent experiment (Science $\mathbf{366}$,983(2019)).Further analyses indicate that the stacking energy is mainly determined by the Coulomb interaction between the interlayer nearest-neighbor Br-Br atoms. While interlayer magnetism can be understood by a competition…
We address the interplay between stacking and interlayer exchange for ferromagnetically ordered CrI$_3$, both for bilayers and bulk. Whereas bulk CrI$_3$ is ferromagnetic, both magneto-optical and transport experiments show that interlayer exchange for CrI$_3$ bilayers is antiferromagnetic. Bulk CrI$_3$ is known to assume two crystal structures, rhombohedral and monoclinic, that differ mostly in the stacking between monolayers. Below 210-220 Kelvin, bulk CrI$_3$ orders in a rhombohedral phase. Our density functional theory calculations show a very strong dependence of interlayer exchange and s…
We demonstrate that the electronic, thermal, and optical properties of a graphene bilayer with boron and nitrogen dopant atoms can be controlled by the interlayer distance between the layers in which the interaction energy and the van der Waals interaction between the dopant atoms play an essential role. We find a conversion of an AA- to an AB-stacked bilayer graphene caused by the repulsive interaction between dopant atoms. At a short interlayer distance, a strong repulsive interaction inducing a strong electric dipole moment of the dopant atoms is found. This gives rise to a breaking of the …
One-Dimensional Electronic States in a Moiré Superlattice of Twisted Bilayer WTe2
Osaka University（大阪大学）；Kyushu University（九州大学）；The University of Tokyo（东京大学）；Stony Brook University（石溪大学）；Japan Advanced Institute of Science and Technology（日本科学技术高级学院）
The interlayer coupling is emerging as a new parameter for tuning the physical properties of two-dimensional (2D) van der Waals materials. When two identical semiconductor monolayers are stacked with a twist angle, the periodic interlayer coupling modulation due to the moiré superlattice may endow exotic physical phenomena, such as moiré excitons and correlated electronic phases. To gain insight into these new phenomena, it is crucial to unveil the underlying coupling between atomic layers. Recently, the rhombohedral-stacked transition metal dichalcogenide (TMD) bilayer has attracted significa…
We study the electronic structure of quasicrystals composed of incommensurate stacks of atomic layers. We consider two systems: a pair of square lattices with a relative twist angle of $θ=45^\circ$ and a pair of hexagonal lattices with a relative twist angle of $θ=30^\circ$, with various interlayer interaction strengths. This constitutes every two-dimensional bilayer quasicrystal system. We investigate the resonant coupling governing the quasicrystalline order in each quasicrystal symmetry, and calculate the quasi-band dispersion. The resonant interaction emerges in bilayer quasicrystals if al…
We show how the excitonic features of biaxial MoS2 flakes are very sensitive to biaxial strain. We find a lower bound for the gauge factors of the A exciton and B exciton of (-41 +- 2) meV/% and (-45 +- 2) meV/% respectively, which are larger than those found for single-layer MoS2. Interestingly, the interlayer exciton feature also shifts upon biaxial strain but with a gauge factor that is systematically larger than that found for the A exciton, (-48 +- 4) meV/%. We attribute this larger gauge factor for the interlayer exciton to the strain tunable van der Waals interaction due to the Poisson …
We investigate the magnetic structures in a bilayer magnetic system with the locally inverted interlayer coupling region using Monte Carlo simulation. Stabilization of multiple magnetic structures including the magnetic skyrmion is possible in the locally inverted interlayer coupling region. Various factors such as the region area, anisotropy, interlayer coupling strength, and exchange coupling strength affects the properties of the structures including its size and chirality. We obtain conditions for their stabilization and for the magnetic structural transitions. Dzyaloshinskii-Moriya intera…
We introduce a design of electrically isolated floating bilayer GaAs quantum wells (QW) in which application of a large gating voltage controllably and highly reproducibly induces charges that remain trapped in the bilayer after removal of the gating voltage. At smaller gate voltages, the bilayer is fully electrically isolated from external electrodes by thick insulating barriers. This design permits full control of the total and differential densities of two coupled 2D electron systems. The floating bilayer design provides a unique approach for studying systems inaccessible by simple transpor…
Stacking order has strong influence on the coupling between the two layers of twisted bilayer graphene (BLG), which in turn determines its physical properties. Here, we report the investigation of the interlayer coupling of the epitaxially grown single-crystal 30° twisted BLG on Cu(111) at the atomic scale. The stacking order and morphology of BLG is controlled by a rationally designed two-step growth process, that is, the thermodynamically controlled nucleation and kinetically controlled growth. The crystal structure of the 30°-twisted bilayer graphene (30°-tBLG) is determined to have the qua…
Exciton condensates (EC) are macroscopic coherent states arising from condensation of electron-hole pairs. Bilayer heterostructures, consisting of two-dimensional electron and hole layers separated by a tunnel barrier, provide a versatile platform to realize and study EC. The tunnel barrier suppresses recombination yielding long-lived excitons. However, this separation also reduces interlayer Coulomb interactions, limiting the exciton binding strength. Here, we report the observation of EC in naturally occurring 2H-stacked bilayer WSe$_2$. In this system, the intrinsic spin-valley structure su…
The chiral Hamiltonian for twisted graphene bilayers is analyzed in terms of its squared Hamiltonian which removes the particle-hole symmetry and thus one bipartite lattice, allowing to write the Hamiltonian in terms of a $2\times 2$ matrix. This brings to the front the three main physical actors of twisted systems: kinetic energy, confinement potential and an interlayer interaction operator which is divided in two parts: a non-Abelian interlayer operator and an operator which contains an interaction energy between layers. Here, each of these components is analyzed as a function of the angle o…
The interlayer magnetic interaction in bilayer CrI$_3$ plays a crucial role for its device applications. In this work, we studied the interlayer magnetic interaction in $π/3$-twisted bilayer CrI$_3$ using first-principles calculations. Our calculations show that the interlayer coupling can be ferromagnetic or antiferromagnetic depending crucially on lateral shift. The strongest antiferromagnetic interlayer interaction appears in the $\bar{A}A$-stacking. The magnetic force theory calculations demonstrate that such an antiferromagnetic interaction is dominanted by the $e_g$-$e_g$ channel. Partic…
We introduce a new 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…
In Bernal stacked bilayer graphene interlayer coupling significantly affects the electronic bandstructure compared to monolayer graphene. Here we present magnetotransport experiments on high-quality $n$-doped bilayer MoS$_{2}$. By measuring the evolution of the Landau levels as a function of electron density and applied magnetic field we are able to investigate the occupation of conduction band states, the interlayer coupling in pristine bilayer MoS$_{2}$, and how these effects are governed by electron-electron interactions. We find that the two layers of the bilayer MoS$_{2}$ behave as two in…
Interlayer valley excitons in bilayer MoS2 feature concurrently large oscillator strength and long lifetime, and hence represent an advantageous scenario for valleytronic applications. However, control of valley pseudospin of interlayer excitons in pristine bilayer MoS2, which lies at the heart of valleytronics, has remained elusive. Here we report the observation of highly circularly polarized photoluminescence from interlayer excitons of bilayer MoS2 with both optical and magnetic addressability. Under excitation of circularly polarized light near exciton resonance, interlayer excitons of bi…
We model bilayer graphene-like materials with Si$_2$C$_{14}$ and BC$_{14}$N stoichiometry, where the interlayer interactions play important roles shaping the physical properties of the systems. We find the interlayer interaction in Si$_2$C$_{14}$ to be repulsive due to the interaction of Si-Si atoms, and in BC$_{14}$N it is attractive due to B and N atoms for both the AA- and the AB-stacking. The repulsive interlayer interaction opens up a bandgap in Si$_2$C$_{14}$ while the attractive interlayer interaction in BC$_{14}$N induces a small indirect bandgap or overlaping of the valence conduction…
