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2D materials have intriguing quantum phenomena that are distinctively different from their bulk counterparts. Recently, epitaxially synthesized wafer-scale 2D metals, composed of elemental atoms, are attracting attention not only for their potential applications but also for exotic quantum effects such as superconductivity. By mapping momentum-resolved electronic states using time-resolved and angle-resolved photoemission spectroscopy (ARPES), we reveal that monolayer Ag confined between bilayer graphene and SiC is a large gap (> 1 eV) 2D semiconductor, consistent with GW-corrected density functional theory. The measured valence band dispersion matches the DFT-GW quasiparticle band. However, the conduction band dispersion shows an anomalously large effective mass of 2.4 m0. Possible mechanisms for this large enhancement in the apparent mass are discussed.

We provide a complete theoretical interpretation of the metallic broken spin/valley symmetry states recently discovered in ABC trilayer graphene (ABC) perturbed by a large transverse displacement field. Our conclusions combine insights from ABC trilayer graphene electronic structure models and mean field theory, and are guided by precise magneto-oscillation Fermi-surface-area measurements. We conclude that the physics of ABC trilayer graphene is shaped by the principle of momentum-space condensation, which favors Fermi surface reconstructions enabled by broken spin/valley flavor symmetries when the single-particle bands imply thin annular Fermi seas. We find one large outer Fermi surface enclosed majority-flavor states and one or more small inner hole-like Fermi surfaces enclosed minority-flavor states that are primarily responsible for nematic order. The smaller surfaces can rotate along a ring of van-Hove singularities or reconstruct into multiple Fermi surfaces with little cost in energy. We propose that the latter property is responsible for the quantum oscillation frequency fractionalization seen experimentally in some regions of the carrier-density/displacement-field phase diagram., Comment: 4+2 pages

The quantum Hall (QH) effect, quantized Hall resistance combined with zero longitudinal resistance, is the characteristic experimental fingerprint of Chern insulators - topologically non-trivial states of two-dimensional matter with broken time-reversal symmetry. In Chern insulators, non-trivial bulk band topology is expressed by chiral states that carry current along sample edges without dissipation. The quantum anomalous Hall (QAH) effect refers to QH effects that occur in the absence of external magnetic fields due to spontaneously broken time-reversal symmetry. The QAH effect has now been realized in four different classes of two-dimensional materials: (i) thin films of magnetically (Cr- and/or V-) doped topological insulators in the (Bi,Sb)2Te3 family, (ii) thin films of the intrinsic magnetic topological insulator MnBi2Te4, (iii) moir\'e materials formed from graphene, and (iv ) moir\'e materials formed from transition metal dichalcogenides. In this Article, we review the physical mechanisms responsible for each class of QAH insulator, highlighting both differences and commonalities, and comment on potential applications of the QAH effect., Comment: 39 pages, 18 figures, comments are welcome

We investigate the possibility and implications of interlayer coherence in electrically isolated superconducting bilayers. We find that in a mean-field approximation bilayers can have superconducting and excitonic order simultaneously if repulsive interactions between layers are sufficiently strong. The excitonic order implies interlayer phase coherence, and can be studied in a representation of symmetric and antisymmetric bilayer states. When both orders are present we find several solutions of the mean-field equations with different values of the the symmetric and antisymmetric state pair amplitudes. The mixed state necessarily has non-zero pair amplitudes for electrons in different layers in spite of the repulsive interlayer interactions, and these are responsible for spatially indirect Andreev reflection processes in which an incoming electron in one layer can be reflected as a hole in the opposite layer. We evaluate layer diagonal and off-diagonal current-voltage relationships that can be used to identify this state experimentally.

Tailoring interlayer coupling has emerged as a powerful tool to tune the electronic structure of van der Waals (vdW) bilayers. One example is the usage of the moire pattern to create controllable two-dimensional electronic superlattices through the configurational dependence of interlayer electronic couplings. This approach has led to some remarkable discoveries in twisted graphene bilayers, and transition metal dichalcogenide (TMD) homo- and hetero-bilayers. However, a largely unexplored factor is the interlayer distance, d, which can impact the interlayer coupling strength exponentially. In this letter, we quantitatively determine the coupling strengths as a function of interlayer spacing at various critical points of the Brillouin zone in bilayer MoS2. The exponential dependence of the coupling parameter on the gap distance is demonstrated. Most significantly, we achieved a 280% enhancement of K-valley coupling strength with an 8% reduction of the vdW gap, pointing to a new strategy in designing a novel electronic system in vdW bilayers.

The Bistritzer-MacDonald (BM) model, introduced in \cite{Bistritzer2011}, attempts to capture the electronic properties of twisted bilayer graphene (TBG), even at incommensurate twist angles, by an effective periodic model over the bilayer moir\'e pattern. Starting from a tight-binding model, we identify a regime where the BM model emerges as the effective dynamics for electrons modeled as wave-packets spectrally concentrated at the monolayer Dirac points, up to error that can be rigorously estimated. Using measured values of relevant physical constants, we argue that this regime is realized in TBG at the first "magic" angle., Comment: 50 pages, 9 figures. Fixed wave-packet scaling, bounded some higher-order terms in the residual, and added reference to Bal-Cazeaux-Massatt-Quinn. Bounding the higher-order terms required strengthening our assumption on the regularity of initial data

We propose a realization of Kondo-lattice physics in moir\'e superlattices at the interface between a WX$_2$ homobilayer and MoX$_2$ monolayer (where X=S,Se). Under appropriate gating conditions, the interface-WX$_2$-layer forms a triangular lattice of local moments that couple to itinerant electrons in the other WX$_2$-layer via a gate-tunable Kondo exchange interaction. Using a parton mean-field approach we identify a range of twist-angles which support a gate-tuned quantum phase transition between a heavy-fermion liquid with large anomalous Hall conductance and a fractionalized chiral spin-liquid coexisting with a light Fermi liquid, and describe experimental signatures to distinguish among competing theoretical scenarios., Comment: 4+7 pages, 2+5 figures

The optical properties of weakly-doped two-dimensional materials are dominated by strong exciton and trion absorption and luminescence features. In this article we examine the influence of moir\'e patterns in semiconductor heterobilayers on exciton and trion states in the limit of strong moir\'e modulation potentials, commenting on similarities and differences compared to the case of excitons and trions in semiconductor quantum dots. We discuss strategies for using optical properties as quantitative probes of moir\'e materials, and the prospects for exploiting moir\'e materials to design unique light emitters.

In moir\'e crystals formed by stacking van der Waals (vdW) materials, surprisingly diverse correlated electronic phases and optical properties can be realized by a subtle change in the twist angle. Here, we discover that phonon spectra are also renormalized in MoS$_2$ twisted bilayers, adding a new perspective to moir\'e physics. Over a range of small twist angles, the phonon spectra evolve rapidly due to ultra-strong coupling between different phonon modes and atomic reconstructions of the moir\'e pattern. We develop a new low-energy continuum model for phonons that overcomes the outstanding challenge of calculating properties of large moir\'e supercells and successfully captures essential experimental observations. Remarkably, simple optical spectroscopy experiments can provide information on strain and lattice distortions in moir\'e crystals with nanometer-size supercells. The newly developed theory promotes a comprehensive and unified understanding of structural, optical, and electronic properties of moir\'e superlattices., Comment: 21 pages, 4 figures

Moire systems formed by 2D atomic layers have widely tunable electrical and optical properties and host exotic, strongly correlated and topological phenomena, including superconductivity, correlated insulator states and orbital magnetism. In this Viewpoint, researchers studying different aspects of moire materials discuss the most exciting directions in this rapidly expanding field.

We predict that layer antiferromagnetic bilayers formed from van der Waals (vdW) materials with weak interlayer versus intralayer exchange coupling have strong magnetoelectric response that can be detected in dual-gated devices where internal displacement fields and carrier densities can be varied independently. We illustrate this strong temperature-dependent magnetoelectric response in bilayer CrI3 at charge neutrality by calculating the gate voltage-dependent total magnetization through Monte Carlo simulations and mean-field solutions of the anisotropic Heisenberg model informed from density functional theory and experimental data and present a simple model for electrical control of magnetism by electrostatic doping.

Spontaneous order of layer pseudospins in two-dimensional bilayers is common in quantum Hall systems, where it is responsible for hysteretic responses to gate fields in states with Ising order, and giant drag voltages in states with XY (spontaneous inter-layer phase coherence) order. In this article we predict that layer pseudospin order will also occur in double-moir\'e strongly correlated two-dimensional electron systems. We comment on similarities and differences in the competition between the two types of order in quantum Hall and double-moir\'e systems, and relate our findings to previous work on Falicov-Kimball models of electronic ferroelectrics., Comment: 13 pages, 4 figures

Magnetism typically arises from the joint effect of Fermi statistics and repulsive Coulomb interactions, which favors ground states with non-zero electron spin. As a result, controlling spin magnetism with electric fields---a longstanding technological goal in spintronics and multiferroics---can be achieved only indirectly. Here, we experimentally demonstrate direct electric field control of magnetic states in an orbital Chern insulator, a magnetic system in which non-trivial band topology favors long range order of orbital angular momentum but the spins are thought to remain disordered. We use van der Waals heterostructures consisting of a graphene monolayer rotationally faulted with respect to a Bernal-stacked bilayer to realize narrow and topologically nontrivial valley-projected moir\'e minibands. At fillings of one and three electrons per moir\'e unit cell within these bands, we observe quantized anomalous Hall effects with transverse resistance approximately equal to $h/2e^2$, which is indicative of spontaneous polarization of the system into a single-valley-projected band with a Chern number equal to two. At a filling of three electrons per moir\'e unit cell, we find that the sign of the quantum anomalous Hall effect can be reversed via field-effect control of the chemical potential; moreover, this transition is hysteretic, which we use to demonstrate nonvolatile electric field induced reversal of the magnetic state. A theoretical analysis indicates that the effect arises from the topological edge states, which drive a change in sign of the magnetization and thus a reversal in the favored magnetic state. Voltage control of magnetic states can be used to electrically pattern nonvolatile magnetic domain structures hosting chiral edge states, with applications ranging from reconfigurable microwave circuit elements to ultralow power magnetic memory., Comment: 21 pages, 17 figures

The Hubbard model, formulated by physicist John Hubbard in the 1960s1, is a simple theoretical model of interacting quantum particles in a lattice. The model is thought to capture the essential physics of high-temperature superconductors, magnetic insulators and other complex quantum many-body ground states2,3. Although the Hubbard model provides a greatly simplified representation of most real materials, it is nevertheless difficult to solve accurately except in the one-dimensional case2,3. Therefore, the physical realization of the Hubbard model in two or three dimensions, which can act as an analogue quantum simulator (that is, it can mimic the model and simulate its phase diagram and dynamics4,5), has a vital role in solving the strong-correlation puzzle, namely, revealing the physics of a large number of strongly interacting quantum particles. Here we obtain the phase diagram of the two-dimensional triangular-lattice Hubbard model by studying angle-aligned WSe2/WS2 bilayers, which form moire superlattices6 because of the difference between the lattice constants of the two materials. We probe the charge and magnetic properties of the system by measuring the dependence of its optical response on an out-of-plane magnetic field and on the gate-tuned carrier density. At half-filling of the first hole moire superlattice band, we observe a Mott insulating state with antiferromagnetic Curie-Weiss behaviour, as expected for a Hubbard model in the strong-interaction regime2,3,7-9. Above half-filling, our experiment suggests a possible quantum phase transition from an antiferromagnetic to a weak ferromagnetic state at filling factors near 0.6. Our results establish a new solid-state platform based on moire superlattices that can be used to simulate problems in strong-correlation physics that are described by triangular-lattice Hubbard models.

Strong coupling between light and elementary excitations is emerging as a powerful tool to engineer the properties of solid-state systems. Spin-correlated excitations that couple strongly to optical cavities promise control over collective quantum phenomena such as magnetic phase transitions, but their suitable electronic resonances have yet to be found. Here we report strong light-matter coupling in $\textrm{NiPS}_3$, a van der Waals antiferromagnet with highly correlated electronic degrees of freedom. A previously unobserved class of polaritonic quasiparticles emerges from the strong coupling between its spin-correlated excitons and the photons inside a microcavity. Detailed spectroscopic analysis in conjunction with a microscopic theory provides unique insights into the origin and interactions of these exotic magnetically coupled excitations. Our work introduces van der Waals magnets to the field of strong light-matter physics and provides a path towards the design and control of correlated electron systems via cavity quantum electrodynamics.

Strong coupling between light and elementary excitations is emerging as a powerful tool to engineer the properties of solid-state systems. Spin-correlated excitations that couple strongly to optical cavities promise control over collective quantum phenomena such as magnetic phase transitions, but their suitable electronic resonances are yet to be found. Here, we report strong light-matter coupling in NiPS

In intrinsic magnetic topological insulators, Dirac surface state gaps are prerequisites for quantum anomalous Hall and axion insulating states. Unambiguous experimental identification of these gaps has proved to be a challenge, however. Here we use molecular beam epitaxy to grow intrinsic MnBi2Te4 thin films. Using scanning tunneling microscopy/spectroscopy, we directly visualize the Dirac mass gap and its disappearance below and above the magnetic order temperature. We further reveal the interplay of Dirac mass gaps and local magnetic defects. We find that in high defect regions, the Dirac mass gap collapses. Ab initio and coupled Dirac cone model calculations provide insight into the microscopic origin of the correlation between defect density and spatial gap variations. This work provides unambiguous identification of the Dirac mass gap in MnBi2Te4, and by revealing the microscopic origin of its gap variation, establishes a material design principle for realizing exotic states in intrinsic magnetic topological insulators., Comment: Main and SI

A hitherto unobserved three-body coupled composite of excitons, photons and spins is created by strong light-matter coupling in a van der Waals magnetic insulator hosting spin-correlated excitonic excitations [1]. (c) 2022 The Authors(s)

We report enhanced interlayer tunneling with reduced linewidth at zero interlayer bias in a twist-controlled double monolayer graphene heterostructure in the quantum Hall regime, when the top ($\nu_{\mathrm{T}}$) and bottom ($\nu_{\mathrm{B}}$) layer filling factors are near $\nu_{\mathrm{T}}=\pm1/2, \pm3/2$ and $\nu_{\mathrm{B}}=\pm1/2, \pm3/2$, and the total filling factor $\nu = \pm1$ or $\pm3$. The zero-bias interlayer conductance peaks are stable against variations of layer filling factor, and signal the emergence of interlayer phase coherence. Our results highlight twist control as a key attribute in revealing interlayer coherence using tunneling., Comment: 5 pages, 4 figures, includes supplementary material

Spin-orbit torques (SOT) enable efficient electrical control of the magnetic state of ferromagnets, ferrimagnets and antiferromagnets. However, the conventional SOT has severe limitation that only in-plane spins accumulate near the surface, whether interpreted as a spin Hall effect (SHE) or as an Edelstein effect. Such a SOT is not suitable for controlling perpendicular magnetization, which would be more beneficial for realizing low-power-consumption memory devices. Here we report the observation of a giant magnetic-field-like SOT in a topological antiferromagnet Mn3Sn, whose direction and size can be tuned by changing the order parameter direction of the antiferromagnet. To understand the magnetic SHE (MSHE)- and the conventional SHE-induced SOTs on an equal footing, we formulate them as interface spin-electric-field responses and analyzed using a macroscopic symmetry analysis and a complementary microscopic quantum kinetic theory. In this framework, the large out-of-plane spin accumulation due to the MSHE has an inter-band origin and is likely to be caused by the large momentum-dependent spin splitting in Mn3Sn. Our work demonstrates the unique potential of antiferromagnetic Weyl semimetals in overcoming the limitations of conventional SOTs and in realizing low-power spintronics devices with new functionalities., Conventional spin-orbit torque (SOT) enables electrical control of in-plane spins, not suitable for perpendicular magnetization. Here, the authors observe a large magnetic-field-like SOT due to a large out-of-plane spin accumulation in topological antiferromagnet Mn3Sn.

The hybridization of magnetism and superconductivity has been an intriguing playground for correlated electron systems, hosting various novel physical phenomena. Usually, localized d- or f-electrons are central to magnetism. In this study, by placing a PTCDA (3,4,9,10-perylene tetracarboxylic dianhydride) molecular monolayer on ultra-thin Pb films, we built a hybrid magnetism/superconductivity (M/SC) system consisting of only sp electronic levels. The magnetic moments reside in the unpaired molecular orbital originating from interfacial charge-transfers. We reported distinctive tunneling spectroscopic features of such a Kondo screened pi-electron impurity lattice on a superconductor in the regime of TK>>delta suggesting the formation of a two-dimensional bound states band. Moreover, moir\'e superlattices with tunable twist angle and the quantum confinement in the ultra-thin Pb films provide easy and flexible implementations to tune the interplay between the Kondo physics and the superconductivity, which are rarely present in M/SC hybrid systems., Comment: 4 figures

We explain the strong interlayer drag resistance observed at low temperatures in bilayer electron-hole systems in terms of an interplay between local electron-hole-pair condensation and disorder-induced carrier density variations. Smooth disorder drives the condensate into a granulated phase where interlayer coherence is formed only in well separated and disconnected regions, or grains, and the densities of electrons and holes accidentally match. The drag resistance is then dominated by Andreev scattering of charge carries between layers at the grains that transfers momentum between layers. We show that this scenario can account for the observed dependence of the drag resistivity on temperature, and on the average charge imbalance between layers., 10 pages, 6 figures, published version

Moir\'e materials formed in two-dimensional semiconductor heterobilayers are quantum simulators of Hubbard-like physics with unprecedented electron-density and interaction-strength tunability. Compared to atomic scale Hubbard-like systems, electrons or holes in moir\'e materials are less strongly attracted to their effective lattice sites because these are defined by finite-depth potential extrema. As a consequence, non-local interaction terms like interaction-assisted hopping and intersite-exchange are more relevant. We theoretically demonstrate the possibility of tuning the strength of these coupling constants to favor unusual states of matter, including spin liquids, insulating ferromagnets, and superconductors., Comment: 10 pages, 7 figures

Small-twist-angle transition metal dichalcogenide (TMD) heterobilayers develop isolated flat moir\'e bands that are approximately described by triangular lattice generalized Hubbard models [PhysRevLett.121.026402]. In this article we explore the metallic and insulating states that appear under different control conditions at a density of one-electron per moir\'e period, and the transitions between them. By combining fully self-consistent Hartree-Fock theory calculations with strong-coupling expansions around the atomic limit, we identify four different magnetic states and one nonmagnetic state near the model phase diagram's metal-insulator phase-transition line. Ferromagnetic insulating states, stabilized by non-local direct exchange interactions, are surprisingly prominent., Comment: 12 pages, 7 figures

Moir\'e superlattices in two-dimensional (2D) van der Waals (vdW) heterostructures provide 20 an efficient way to engineer electron band properties. The recent discovery of exotic quantum phases and their interplay in twisted bilayer graphene (tBLG) has built this moir\'e system one of the most renowned condensed matter platforms (1-10). So far the studies of tBLG has been mostly focused on the lowest two flat moir\'e bands at the first magic angle {\theta}m1 ~ 1.1{\deg}, leaving high-order moir\'e bands and magic angles largely unexplored. Here we report 25 an observation of multiple well-isolated flat moir\'e bands in tBLG close to the second magic angle {\theta}m2 ~ 0.5{\deg}, which cannot be explained without considering electron-election interactions. With high magnetic field magneto-transport measurements, we further reveal a qualitatively new, energetically unbound Hofstadter butterfly spectrum in which continuously extended quantized Landau level gaps cross all trivial band-gaps. The 30 connected Hofstadter butterfly strongly evidences the topologically nontrivial textures of the multiple moir\'e bands. Overall, our work provides a new perspective for understanding the quantum phases in tBLG and the fractal Hofstadter spectra of multiple topological bands.

In van der Waals (vdW) heterostructures formed by stacking two monolayer semiconductors, lattice mismatch or rotational misalignment introduces an in-plane moire superlattice. While it is widely recognized that a moire superlattice can modulate the electronic band structure and lead to novel transport properties including unconventional superconductivity and insulating behavior driven by correlations, its influence on optical properties has not been investigated experimentally. We present spectroscopic evidence that interlayer excitons are confined by the moire potential in a high-quality MoSe2/WSe2 heterobilayer with small rotational twist. A series of interlayer exciton resonances with either positive or negative circularly polarized emission is observed in photoluminescence, consistent with multiple exciton states confined within the moire potential. The recombination dynamics and temperature dependence of these interlayer exciton resonances are consistent with this interpretation. These results demonstrate the feasibility of engineering artificial excitonic crystals using vdW heterostructures for nanophotonics and quantum information applications.

The spin Hall effect (SHE)1–5 achieves coupling between charge currents and collective spin dynamics in magnetically ordered systems and is a key element of modern spintronics6–9. However, previous research has focused mainly on non-magnetic materials, so the magnetic contribution to the SHE is not well understood. Here we show that antiferromagnets have richer spin Hall properties than do non-magnetic materials. We find that in the non-collinear antiferromagnet10 Mn3Sn, the SHE has an anomalous sign change when its triangularly ordered moments switch orientation. We observe contributions to the SHE (which we call the magnetic SHE) and the inverse SHE (the magnetic inverse SHE) that are absent in non-magnetic materials and that can be dominant in some magnetic materials, including antiferromagnets. We attribute the dominance of this magnetic mechanism in Mn3Sn to the momentum-dependent spin splitting that is produced by non-collinear magnetic order. This discovery expands the horizons of antiferromagnet spintronics and spin–charge coupling mechanisms. A magnetic contribution to the spin Hall effect is observed in the non-collinear antiferromagnet Mn3Sn, which is attributed to momentum-dependent spin splitting produced by non-collinear magnetic order.

Graphene-based moir\'e superlattices are now established as an interesting platform for strongly correlated many-electron physics, and they have so far been characterized mainly by transport and scanning tunneling microscopy (STM) measurements. Motivated by recent experimental progress, we present a theoretical model study whose aim is to assess the potential of angle-resolved photoemission spectroscopy (ARPES) to resolve some of the many open issues in these systems. The theory is developed specifically for graphene on hexagonal boron nitride (G/hBN) and twisted bilayer graphene (TBG) moir\'e superlattices, but it is readily generalized to any system with active degrees of freedom in graphene sheets.

The quantum anomalous Hall (QAH) effect has recently been realized in thin films of intrinsic magnetic topological insulators (IMTIs) like $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}$. Here we point out that the QAH gaps of these IMTIs can be optimized and that both axion insulator/semimetal and Chern insulator/semimetal transitions can be driven by electrical gate fields on the $\ensuremath{\sim}10$ meV/nm scale. This effect is described by combining a simplified coupled-Dirac-cone model of multilayer thin films with Schr\"odinger-Poisson self-consistent-field equations.

It has long been speculated that quasi-two-dimensional superconductivity can reappear above its semiclassical upper critical field due to Landau quantization, yet this reentrant property has never been observed. Here, we argue that twisted bilayer graphene at a magic angle (MATBG) is an ideal system in which to search for this phenomenon because its Landau levels are doubly degenerate, and its superconductivity appears already at carrier densities small enough to allow the quantum limit to be reached at relatively modest magnetic fields. We study this problem theoretically by combining a simplified continuum model for the electronic structure of MATBG with a phenomenological attractive pairing interaction, and discuss obstacles to the observation of quantum Hall superconductivity presented by disorder, thermal fluctuations, and competing phases., Comment: Published version