We explore theoretically how the topological properties of 2D materials can be manipulated by cavity quantum electromagnetic fields for both resonant and off-resonant electron-photon coupling, with a focus on van der Waals moiré superlattices. We investigate an electron-photon topological Chern number for the cavity-dressed energy minibands that is well defined for any degree of hybridization of the electron and photon states. While an off-resonant cavity mode can renormalize electronic topological phases that exist without cavity coupling, we show that when the cavity mode is resonant to electronic miniband transitions, new and higher electron-photon Chern numbers can emerge.
The Chern insulator displays a quantized Hall effect without Landau levels. In a landmark paper in 1988, Haldane showed that a Chern insulator could be realized through complex next-nearest-neighbor hopping in a honeycomb lattice. Despite its profound impact on the field of topological physics and recent implementation in cold-atom experiments, the Haldane model has remained elusive in solid-state materials. Here, we report the experimental realization of a Haldane Chern insulator in AB-stacked MoTe2/WSe2 moiré bilayers, which form a honeycomb moiré lattice with two sublattices residing in dif…
We theoretically study the effect of magnetic moiré superlattice on the topological surface states by introducing a continuum model of Dirac electrons with a single Dirac cone moving in the time-reversal symmetry breaking periodic pontential. The Zeeman-type moiré potentials generically gap out the moiré surface Dirac cones and give rise to isolated flat Chern minibands with Chern number $\pm1$. This result provides a promising platform for realizing the time-reversal breaking correlated topological phases. In a $C_6$ periodic potential, when the scalar $U_0$ and Zeeman $Δ_1$ moiré potential s…
We study the edge spectrum of twisted sheets of single layer and bilayer graphene in cases where the continuum model predicts a valley Chern insulator -- an insulating state in which the occupied moiré mini-bands from each valley have a net Chern number, but both valleys together have no net Chern number, as required by time reversal symmetry. In a simple picture, such a state might be expected to have chiral valley polarized counter-propagating edge states. We present results from exact diagonalization of the tight-binding model of commensurate structures in the ribbon geometry. We find that …
Moir{é} superlattice realized in two-dimensional heterostructures offers an exciting platform to access strongly-correlated electronic states. In this work, we study transition metal dichalcogenides (TMD) Moir{é} superlattices with time-reversal-symmetry and nontrivial spin{/valley}-Chern numbers. Utilizing realistic material parameters and the method of exact diagonalization, we find that at a certain twisting angle and fractional filling, gapped fractional topological states, i.e., fractional Chern insulators, are naturally {stabilized} by simply introducing the Coulomb repulsion. In contras…
Studies on two-dimensional electron systems in a strong magnetic field first revealed the quantum Hall (QH) effect, a topological state of matter featuring a finite Chern number (C) and chiral edge states. Haldane later theorized that Chern insulators with integer QH effects could appear in lattice models with complex hopping parameters even at zero magnetic field. The ABC-trilayer graphene/hexagonal boron nitride (TLG/hBN) moiré superlattice provides an attractive platform to explore Chern insulators because it features nearly flat moiré minibands with a valley-dependent electrically tunable …
Moiré Fractional Chern Insulators III: Hartree-Fock Phase Diagram, Magic Angle Regime for Chern Insulator States, the Role of the Moiré Potential and Goldstone Gaps in Rhombohedral Graphene Superlattices
Electrons in moiré flat band systems can spontaneously break time reversal symmetry, giving rise to a quantized anomalous Hall effect. Here we use a superconducting quantum interference device to image stray magnetic fields in one such system composed of twisted bilayer graphene aligned to hexagonal boron nitride. We find a magnetization of several Bohr magnetons per charge carrier, demonstrating that the magnetism is primarily orbital in nature. Our measurements reveal a large change in the magnetization as the chemical potential is swept across the quantum anomalous Hall gap consistent with …
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 "Moiré Capacitor Effect" and Stabilization of Fractional Chern Insulators in Rhombohedral Graphene Superlattices
Center for Computational Quantum Physics, Flatiron Institute（Flatiron研究所计算量子物理中心）；Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité（巴黎高等师范学院物理实验室，ENS，PSL大学，CNRS，索邦大学，巴黎第七大学，索邦巴黎城）；Department of Physics, Princeton University（普林斯顿大学物理系）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；Princeton Center for Theoretical Science, Princeton University（普林斯顿大学理论科学中心）；Department of Physics, University of Texas at Dallas（德克萨斯大学达拉斯分校物理系）；IKERBASQUE, Basque Foundation for Science（伊卡巴斯基克，巴斯克科学基金会）；Department of Physics, Massachusetts Institute of Technology（麻省理工学院物理系）
Twisted double- and mono-bilayer graphene are graphene-based moiré materials hosting strongly correlated fermions in a gate-tunable conduction band with a topologically non-trivial character. Using unbiased exact diagonalization complemented by unrestricted Hartree-Fock calculations, we find that the strong electron-electron interactions lead to a non-coplanar magnetic state, which has the same symmetries as the tetrahedral antiferromagnet on the triangular lattice and can be thought of as a skyrmion lattice commensurate with the moiré scale, competing with a set of ferromagnetic, topological …
We explore the moiré magnon bands in twisted bilayer magnets with next-nearest neighboring Dzyaloshinskii-Moriya interactions, assuming that the out-of-plane collinear magnetic order is preserved under weak interlayer coupling. By calculating the magnonic band structures and the topological Chern numbers for four representative cases, we find that (i) the valley moiré bands are extremely flat over a wide range of continuous twist angles; (ii) the topological Chern numbers of the lowest few flat bands vary significantly with the twist angle; and (iii) the lowest few topological flat bands in bi…
While Fabry-Pérot resonances and Moiré superlattices are intensively studied in graphene on hexagonal boron nitride (hBN), the two effects have not been discussed in their coexistence. Here we investigate the FP oscillations in a ballistic pnp-junctions in the presence and absence of a Moiré superlattice. First, we address the effect of the smoothness of the confining potential on the visibility of the FP resonances and carefully map the evolution of the FP cavity size as a function of densities in and outside the cavity in the absence of a superlattice, when the cavity is bound by regular pn-…
Moiré flatbands, occurring, e.g., in twisted bilayer graphene at magic angles, have attracted ample interest due to their high degree of experimental tunability and the intriguing possibility of generating novel strongly interacting phases. Here we consider the core problem of Coulomb interactions within fractionally filled spin and valley polarized Moiré flatbands and demonstrate that the dual description in terms of holes, which acquire a nontrivial hole dispersion, provides key physical intuition and enables the use of standard perturbative techniques for this strongly correlated problem. I…
Moiré systems have emerged in recent years as a rich platform to study strong correlations. Here, we will discuss a simple, experimentally feasible setup based on periodically strained graphene that reproduces several key aspects of twisted moiré heterostructures -- but without introducing a twist. We consider a monolayer graphene sheet subject to a $C_2$-breaking periodic strain-induced psuedomagnetic field (PMF) with period $L_M \gg a$, along with a scalar potential of the same period. This system has {\it almost ideal} flat bands with valley-resolved Chern number $\pm 1$, where the deviatio…
Moiré interlayer exciton in transition metal dichalcogenide heterobilayer features a permanent electric dipole that enables the electrostatic control of its flow, and optical dipole that is spatially varying in the moiré landscape. We show the hybridization of moiré interlayer exciton with photons in a planar 2D cavity leads to two types of moiré polaritons that exhibit distinct forms of topological transport phenomena including the spin/valley Hall and polarization Hall effects, which feature remarkable electrical tunability through the control of exciton-cavity detuning by the interlayer bia…
The interplay of topological characteristics in real space and reciprocal space can lead to the emergence of unconventional topological phases. In this Letter, we implement a novel mechanism for generating higher-Chern flat bands on the basis of twisted bilayer graphene (TBG) coupled to topological magnetic structures in the form of the skyrmion lattice. In particular, we discover a scenario for generating $|C|=2$ dispersionless electronic bands when the skyrmion periodicity and the moiré periodicity are matched. Following the Wilczek argument, the statistics of the charge-carrying excitations…
Rhombohedral $N = 3$ trilayer graphene on hexagonal boron nitride (TLG/BN) hosts gate-tunable, valley-contrasting, nearly flat topological bands that can trigger spontaneous quantum Hall phases under appropriate conditions of the valley and spin polarization. Recent experiments have shown signatures of C = 2 valley Chern bands at 1/4 hole filling, in contrast to the predicted value of C = 3. We discuss the low-energy model for rhombohedral N-layer graphene (N = 1, 2, 3) aligned with hexagonal boron nitride (hBN) subject to off-diagonal moire vector potential terms that can alter the valley Che…
Interaction-driven spontaneous symmetry breaking lies at the heart of many quantum phases of matter. In moiré systems, broken spin/valley 'flavour' symmetry in flat bands underlies the parent state out of which ultimately correlated and topological ground states emerge. However, the microscopic mechanism of such flavour symmetry breaking and its connection to the low-temperature many-body phases remain to be understood. Here, we investigate the symmetry-broken many-body ground state of magic angle twisted bilayer graphene (MATBG) and its nontrivial topology using simultaneous thermodynamic and…
We study the edge states of twisted bilayer graphene and their topological origin. We show that the twisted bilayer graphene has special edge states associated with the moiré pattern, and the emergence of these moiré edge states is linked with the sliding Chern number, which describes topological charge pumping caused by relative interlayer sliding. When one layer of the twisted bilayer is relatively slid with respect to the other layer, the edge states are transferred from a single band to another across the band gap, and the number of the edge states pumped in a sliding cycle is shown to be …
Competing Chern states revealed by quasiparticle charging in moiré rhombohedral graphene
Cornell University（康奈尔大学）；Max Planck Institute for the Structure and Dynamics of Matter（马克斯·普朗克物质结构与动力学研究所）；Massachusetts Institute of Technology（麻省理工学院）；Florida State University（佛罗里达州立大学）；National Institute for Materials Science（国立材料研究所）
We study the adiabatic topological charge pumping driven by interlayer sliding in the moiré superlattices. We show that, when we slide a single layer of the twisted bilayer system relatively to the other, a moiré pattern flow and a quantized transport of electrons occurs. When the Fermi energy is in a spectral gap, the number of pumped charges in the interlayer sliding process is quantized to a sliding Chern number, which obeys a Diophantine equation analogous to the quantum Hall effect. We apply the argument to the twisted bilayer graphene, and find that energy gaps above and below the nearly…
We theoretically study the piezoelectric effects in moirè graphene systems. Since the strain couples to the electrons in the system as a pseudo vector potential, which has opposite signs for the $K$ and $K'$ valleys of graphene, its effects on the two valleys with opposite Chern numbers do not cancel out, but adds up. As a result, some components of the piezoelectric tensor in these systems, which typically have non-trivial topology in their flat bands, are nearly quantized in terms of the valley Chern numbers. Such a conclusion is verified by numerical calculations of the in-plane piezoelectr…
The flat bands resulting from moiré superlattices in magic-angle twisted bilayer graphene (MATBG) and ABC-trilayer graphene aligned with hexagonal boron nitride (ABC-TLG/hBN) have been shown to give rise to fascinating correlated electron phenomena such as correlated insulators and superconductivity. More recently, orbital magnetism associated with correlated Chern insulators was found in this class of layered structures centered at integer multiples of n0, the density corresponding to one electron per moiré superlattice unit cell. Here we report the experimental observation of ferromagnetism …
