Large quantum anomalous Hall effect in spin-orbit proximitized rhombohedral graphene.

The quantum anomalous Hall effect (QAHE) is a robust topological phenomenon that features quantized Hall resistance at zero magnetic field. We report the QAHE in a rhombohedral pentalayer graphene-monolayer tungsten disulfide (WS2) heterostructure. Distinct from other experimentally confirmed QAHE systems, this system has neither magnetic element nor moiré superlattice effect. The QAH states emerge at charge neutrality and feature Chern numbers C = ±5 at temperatures of up to about 1.5 kelvin. This large QAHE arises from the synergy of the electron correlation in intrinsic flat bands of pentalayer graphene, the gate-tuning effect, and the proximity-induced Ising spin-orbit coupling. Our experiment demonstrates the potential of crystalline two-dimensional materials for intertwined electron correlation and band topology physics and may enable a route for engineering chiral Majorana edge states.

Fractional quantum anomalous Hall effect in multilayer graphene.

The fractional quantum anomalous Hall effect (FQAHE), the analogue of the fractional quantum Hall effect1 at zero magnetic field, is predicted to exist in topological flat bands under spontaneous time-reversal-symmetry breaking2-6. The demonstration of FQAHE could lead to non-Abelian anyons that form the basis of topological quantum computation7-9. So far, FQAHE has been observed only in twisted MoTe2 at a moiré filling factor v > 1/2 (refs. 10-13). Graphene-based moiré superlattices are believed to host FQAHE with the potential advantage of superior material quality and higher electron mobility. Here we report the observation of integer and fractional QAH effects in a rhombohedral pentalayer graphene-hBN moiré superlattice. At zero magnetic field, we observed plateaus of quantized Hall resistance [Formula: see text] at v = 1, 2/3, 3/5, 4/7, 4/9, 3/7 and 2/5 of the moiré superlattice, respectively, accompanied by clear dips in the longitudinal resistance Rxx. Rxy equals [Formula: see text] at v = 1/2 and varies linearly with v, similar to the composite Fermi liquid in the half-filled lowest Landau level at high magnetic fields14-16. By tuning the gate-displacement field D and v, we observed phase transitions from composite Fermi liquid and FQAH states to other correlated electron states. Our system provides an ideal platform for exploring charge fractionalization and (non-Abelian) anyonic braiding at zero magnetic field7-9,17-19, especially considering a lateral junction between FQAHE and superconducting regions in the same device20-22.

Correlated insulator and Chern insulators in pentalayer rhombohedral-stacked graphene.

Rhombohedral-stacked multilayer graphene hosts a pair of flat bands touching at zero energy, which should give rise to correlated electron phenomena that can be tuned further by an electric field. Moreover, when electron correlation breaks the isospin symmetry, the valley-dependent Berry phase at zero energy may give rise to topologically non-trivial states. Here we measure electron transport through hexagonal boron nitride-encapsulated pentalayer graphene down to 100 mK. We observed a correlated insulating state with resistance at the megaohm level or greater at charge density n = 0 and displacement field D = 0. Tight-binding calculations predict a metallic ground state under these conditions. By increasing D, we observed a Chern insulator state with C = -5 and two other states with C = -3 at a magnetic field of around 1 T. At high D and n, we observed isospin-polarized quarter- and half-metals. Hence, rhombohedral pentalayer graphene exhibits two different types of Fermi-surface instability, one driven by a pair of flat bands touching at zero energy, and one induced by the Stoner mechanism in a single flat band. Our results establish rhombohedral multilayer graphene as a suitable system for exploring intertwined electron correlation and topology phenomena in natural graphitic materials without the need for moiré superlattice engineering.

Orbital multiferroicity in pentalayer rhombohedral graphene.

Ferroic orders describe spontaneous polarization of spin, charge and lattice degrees of freedom in materials. Materials exhibiting multiple ferroic orders, known as multiferroics, have important parts in multifunctional electrical and magnetic device applications1-4. Two-dimensional materials with honeycomb lattices offer opportunities to engineer unconventional multiferroicity, in which the ferroic orders are driven purely by the orbital degrees of freedom and not by electron spin. These include ferro-valleytricity corresponding to the electron valley5 and ferro-orbital-magnetism6 supported by quantum geometric effects. These orbital multiferroics could offer strong valley-magnetic couplings and large responses to external fields-enabling device applications such as multiple-state memory elements and electric control of the valley and magnetic states. Here we report orbital multiferroicity in pentalayer rhombohedral graphene using low-temperature magneto-transport measurements. We observed anomalous Hall signals Rxy with an exceptionally large Hall angle (tanΘH > 0.6) and orbital magnetic hysteresis at hole doping. There are four such states with different valley polarizations and orbital magnetizations, forming a valley-magnetic quartet. By sweeping the gate electric field E, we observed a butterfly-shaped hysteresis of Rxy connecting the quartet. This hysteresis indicates a ferro-valleytronic order that couples to the composite field E · B (where B is the magnetic field), but not to the individual fields. Tuning E would switch each ferroic order independently and achieve non-volatile switching of them together. Our observations demonstrate a previously unknown type of multiferroics and point to electrically tunable ultralow-power valleytronic and magnetic devices.

Comprehensive Studies of Magnetic Transitions and Spin-Phonon Couplings in the Tetrahedral Cobalt Complex Co(AsPh3)2I2.

A combination of inelastic neutron scattering (INS), far-IR magneto-spectroscopy (FIRMS), and Raman magneto-spectroscopy (RaMS) has been used to comprehensively probe magnetic excitations in Co(AsPh3)2I2 (1), a reported single-molecule magnet (SMM). With applied field, the magnetic zero-field splitting (ZFS) peak (2D') shifts to higher energies in each spectroscopy. INS placed the ZFS peak at 54 cm-1, as revealed by both variable-temperature (VT) and variable-magnetic-field data, giving results that agree well with those from both far-IR and Raman studies. Both FIRMS and RaMS also reveal the presence of multiple spin-phonon couplings as avoided crossings with neighboring phonons. Here, phonons refer to both intramolecular and lattice vibrations. The results constitute a rare case in which the spin-phonon couplings are observed with both Raman-active (g modes) and far-IR-active phonons (u modes; space group P21/c, no. 14, Z = 4 for 1). These couplings are fit using a simple avoided crossing model with coupling constants of ca. 1-2 cm-1. The combined spectroscopies accurately determine the magnetic excited level and the interaction of the magnetic excitation with phonon modes. Density functional theory (DFT) phonon calculations compare well with INS, allowing for the assignment of the modes and their symmetries. Electronic calculations elucidate the nature of ZFS in the complex. Features of different techniques to determine ZFS and other spin-Hamiltonian parameters in transition-metal complexes are summarized.

Thickness- and Twist-Angle-Dependent Interlayer Excitons in Metal Monochalcogenide Heterostructures.

Interlayer excitons, or bound electron-hole pairs whose constituent quasiparticles are located in distinct stacked semiconducting layers, are being intensively studied in heterobilayers of two-dimensional semiconductors. They owe their existence to an intrinsic type-II band alignment between both layers that convert these into p-n junctions. Here, we unveil a pronounced interlayer exciton (IX) in heterobilayers of metal monochalcogenides, namely, γ-InSe on ε-GaSe, whose pronounced emission is adjustable just by varying their thicknesses given their number of layers dependent direct band gaps. Time-dependent photoluminescense spectroscopy unveils considerably longer interlayer exciton lifetimes with respect to intralayer ones, thus confirming their nature. The linear Stark effect yields a bound electron-hole pair whose separation d is just (3.6 ± 0.1) Å with d being very close to dSe = 3.4 Å which is the calculated interfacial Se separation. The envelope of IX is twist-angle-dependent and describable by superimposed emissions that are nearly equally spaced in energy, as if quantized due to localization induced by the small moiré periodicity. These heterostacks are characterized by extremely flat interfacial valence bands making them prime candidates for the observation of magnetism or other correlated electronic phases upon carrier doping.

Light sources with bias tunable spectrum based on van der Waals interface transistors.

Light-emitting electronic devices are ubiquitous in key areas of current technology, such as data communications, solid-state lighting, displays, and optical interconnects. Controlling the spectrum of the emitted light electrically, by simply acting on the device bias conditions, is an important goal with potential technological repercussions. However, identifying a material platform enabling broad electrical tuning of the spectrum of electroluminescent devices remains challenging. Here, we propose light-emitting field-effect transistors based on van der Waals interfaces of atomically thin semiconductors as a promising class of devices to achieve this goal. We demonstrate that large spectral changes in room-temperature electroluminescence can be controlled both at the device assembly stage -by suitably selecting the material forming the interfaces- and on-chip, by changing the bias to modify the device operation point. Even though the precise relation between device bias and kinetics of the radiative transitions remains to be understood, our experiments show that the physical mechanism responsible for light emission is robust, making these devices compatible with simple large areas device production methods.

Weyl Fermion magneto-electrodynamics and ultralow field quantum limit in TaAs.

Topological semimetals are predicted to exhibit unconventional electrodynamics, but a central experimental challenge is singling out the contributions from the topological bands. TaAs is the prototypical example, where 24 Weyl points and 8 trivial Fermi surfaces make the interpretation of any experiment in terms of band topology ambiguous. We report magneto-infrared reflection spectroscopy measurements on TaAs. We observed sharp inter-Landau level transitions from a single pocket of Weyl Fermions in magnetic fields as low as 0.4 tesla. We determine the W2 Weyl point to be 8.3 meV below the Fermi energy, corresponding to a quantum limit­the field required to reach the lowest LL­of 0.8 tesla­unprecedentedly low for Weyl Fermions. LL spectroscopy allows us to isolate these Weyl Fermions from all other carriers in TaAs, and our result provides a way for directly exploring the more exotic quantum phenomena in Weyl semimetals, such as the chiral anomaly.

Electronic Raman scattering in the 2D antiferromagnet NiPS3.

Correlated-electron systems have long been an important platform for various interesting phenomena and fundamental questions in condensed matter physics. As a pivotal process in these systems, d-d transitions have been suggested as a key factor toward realizing optical spin control in two-dimensional (2D) magnets. However, it remains unclear how d-d excitations behave in quasi-2D systems with strong electronic correlation and spin-charge coupling. Here, we present a systematic electronic Raman spectroscopy investigation on d-d transitions in a 2D antiferromagnet­NiPS3, from bulk to atomically thin samples. Two electronic Raman modes originating from the scattering of incident photons with d electrons in Ni2+ ions are observed at ~1.0 eV. This electronic process persists down to trilayer flakes and exhibits insensitivity to the spin ordering of NiPS3. Our study demonstrates the utility of electronic Raman scattering in investigating the unique electronic structure and its coupling to magnetism in correlated 2D magnets.

Exciton-polaron Rydberg states in monolayer MoSe2 and WSe2.

Exciton polaron is a hypothetical many-body quasiparticle that involves an exciton dressed with a polarized electron-hole cloud in the Fermi sea. It has been evoked to explain the excitonic spectra of charged monolayer transition metal dichalcogenides, but the studies were limited to the ground state. Here we measure the reflection and photoluminescence of monolayer MoSe2 and WSe2 gating devices encapsulated by boron nitride. We observe gate-tunable exciton polarons associated with the 1 s-3 s exciton Rydberg states. The ground and excited exciton polarons exhibit comparable energy redshift (15~30 meV) from their respective bare excitons. The robust excited states contradict the trion picture because the trions are expected to dissociate in the excited states. When the Fermi sea expands, we observe increasingly severe suppression and steep energy shift from low to high exciton-polaron Rydberg states. Their gate-dependent energy shifts go beyond the trion description but match our exciton-polaron theory. Our experiment and theory demonstrate the exciton-polaron nature of both the ground and excited excitonic states in charged monolayer MoSe2 and WSe2.

Applying Unconventional Spectroscopies to the Single-Molecule Magnets, Co(PPh3 )2 X2 (X=Cl, Br, I): Unveiling Magnetic Transitions and Spin-Phonon Coupling.

Large separation of magnetic levels and slow relaxation in metal complexes are desirable properties of single-molecule magnets (SMMs). Spin-phonon coupling (interactions of magnetic levels with phonons) is ubiquitous, leading to magnetic relaxation and loss of memory in SMMs and quantum coherence in qubits. Direct observation of magnetic transitions and spin-phonon coupling in molecules is challenging. We have found that far-IR magnetic spectra (FIRMS) of Co(PPh3 )2 X2 (Co-X; X=Cl, Br, I) reveal rarely observed spin-phonon coupling as avoided crossings between magnetic and u-symmetry phonon transitions. Inelastic neutron scattering (INS) gives phonon spectra. Calculations using VASP and phonopy programs gave phonon symmetries and movies. Magnetic transitions among zero-field split (ZFS) levels of the S=3/2 electronic ground state were probed by INS, high-frequency and -field EPR (HFEPR), FIRMS, and frequency-domain FT terahertz EPR (FD-FT THz-EPR), giving magnetic excitation spectra and determining ZFS parameters (D, E) and g values. Ligand-field theory (LFT) was used to analyze earlier electronic absorption spectra and give calculated ZFS parameters matching those from the experiments. DFT calculations also gave spin densities in Co-X, showing that the larger Co(II) spin density in a molecule, the larger its ZFS magnitude. The current work reveals dynamics of magnetic and phonon excitations in SMMs. Studies of such couplings in the future would help to understand how spin-phonon coupling may lead to magnetic relaxation and develop guidance to control such coupling.

Spin-induced linear polarization of photoluminescence in antiferromagnetic van der Waals crystals.

Antiferromagnets are promising components for spintronics due to their terahertz resonance, multilevel states and absence of stray fields. However, the zero net magnetic moment of antiferromagnets makes the detection of the antiferromagnetic order and the investigation of fundamental spin properties notoriously difficult. Here, we report an optical detection of Néel vector orientation through an ultra-sharp photoluminescence in the van der Waals antiferromagnet NiPS3 from bulk to atomically thin flakes. The strong correlation between spin flipping and electric dipole oscillator results in a linear polarization of the sharp emission, which aligns perpendicular to the spin orientation in the crystal. By applying an in-plane magnetic field, we achieve manipulation of the photoluminescence polarization. This correlation between emitted photons and spins in layered magnets provides routes for investigating magneto-optics in two-dimensional materials, and hence opens a path for developing opto-spintronic devices and antiferromagnet-based quantum information technologies.

Giant Valley-Polarized Rydberg Excitons in Monolayer WSe2 Revealed by Magneto-photocurrent Spectroscopy.

A strong Coulomb interaction could lead to a strongly bound exciton with high-order excited states, similar to the Rydberg atom. The interaction of giant Rydberg excitons can be engineered for a correlated ordered exciton array with a Rydberg blockade, which is promising for realizing quantum simulation. Monolayer transition metal dichalcogenides, with their greatly enhanced Coulomb interaction, are an ideal platform to host the Rydberg excitons in two dimensions. Here, we employ helicity-resolved magneto-photocurrent spectroscopy to identify Rydberg exciton states up to 11s in monolayer WSe2. Notably, the radius of the Rydberg exciton at 11s can be as large as 214 nm, orders of magnitude larger than the 1s exciton. The giant valley-polarized Rydberg exciton not only provides an exciting platform to study the strong exciton-exciton interaction and nonlinear exciton response but also allows the investigation of the different interplay between the Coulomb interaction and Landau quantization, tunable from a low- to high-magnetic-field limit.

Symmetry-Resolved Two-Magnon Excitations in a Strong Spin-Orbit-Coupled Bilayer Antiferromagnet.

We used a combination of polarized Raman spectroscopy and spin wave calculations to study magnetic excitations in the strong spin-orbit-coupled bilayer perovskite antiferromagnet Sr_{3}Ir_{2}O_{7}. We observed two broad Raman features at ∼800 and ∼1400 cm^{-1} arising from magnetic excitations. Unconventionally, the ∼800 cm^{-1} feature is fully symmetric (A_{1g}) with respect to the underlying tetragonal (D_{4h}) crystal lattice which, together with its broad line shape, definitively rules out the possibility of a single magnon excitation as its origin. In contrast, the ∼1400 cm^{-1} feature shows up in both the A_{1g} and B_{2g} channels. From spin wave and two-magnon scattering cross-section calculations of a tetragonal bilayer antiferromagnet, we identified the ∼800 cm^{-1} (1400 cm^{-1}) feature as two-magnon excitations with pairs of magnons from the zone-center Γ point (zone-boundary van Hove singularity X point). We further found that this zone-center two-magnon scattering is unique to bilayer perovskite magnets which host an optical branch in addition to the acoustic branch, as compared to their single layer counterparts. This zone-center two-magnon mode is distinct in symmetry from the time-reversal symmetry broken "spin wave gap" and "phase mode" proposed to explain the ∼92 meV (742 cm^{-1}) gap in resonant inelastic x-ray spectroscopy magnetic excitation spectra of Sr_{3}Ir_{2}O_{7}.

Author Correction: Unconventional valley-dependent optical selection rules and landau level mixing in bilayer graphene.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Unconventional valley-dependent optical selection rules and landau level mixing in bilayer graphene.

Selection rules are of vital importance in determining the basic optical properties of atoms, molecules and semiconductors. They provide general insights into the symmetry of the system and the nature of relevant electronic states. A two-dimensional electron gas in a magnetic field is a model system where optical transitions between Landau levels (LLs) are described by simple selection rules associated with the LL index N. Here we examine the inter-LL optical transitions of high-quality bilayer graphene by photocurrent spectroscopy measurement. We observed valley-dependent optical transitions that violate the conventional selection rules Δ|N| = ± 1. Moreover, we can tune the relative oscillator strength by tuning the bilayer graphene bandgap. Our findings provide insights into the interplay between magnetic field, band structure and many-body interactions in tunable semiconductor systems, and the experimental technique can be generalized to study symmetry-broken states and low energy magneto-optical properties of other nano and quantum materials.

Giant Valley-Zeeman Splitting from Spin-Singlet and Spin-Triplet Interlayer Excitons in WSe2/MoSe2 Heterostructure.

Transition metal dichalcogenides (TMDCs) heterostructure with a type II alignment hosts unique interlayer excitons with the possibility of spin-triplet and spin-singlet states. However, the associated spectroscopy signatures remain elusive, strongly hindering the understanding of the Moiré potential modulation of the interlayer exciton. In this work, we unambiguously identify the spin-singlet and spin-triplet interlayer excitons in the WSe2/MoSe2 heterobilayer with a 60° twist angle through the gate- and magnetic field-dependent photoluminescence spectroscopy. Both the singlet and triplet interlayer excitons show giant valley-Zeeman splitting between the K and K' valleys, a result of the large Landé g-factor of the singlet interlayer exciton and triplet interlayer exciton, which are experimentally determined to be ∼10.7 and ∼15.2, respectively, which is in good agreement with theoretical expectation. The photoluminescence (PL) from the singlet and triplet interlayer excitons show opposite helicities, determined by the atomic registry. Helicity-resolved photoluminescence excitation (PLE) spectroscopy study shows that both singlet and triplet interlayer excitons are highly valley-polarized at the resonant excitation with the valley polarization of the singlet interlayer exciton approaching unity at ∼20 K. The highly valley-polarized singlet and triplet interlayer excitons with giant valley-Zeeman splitting inspire future applications in spintronics and valleytronics.

Momentum-Dark Intervalley Exciton in Monolayer Tungsten Diselenide Brightened via Chiral Phonon.

Inversion symmetry breaking and 3-fold rotation symmetry grant the valley degree of freedom to the robust exciton in monolayer transition-metal dichalcogenides, which can be exploited for valleytronics applications. However, the short lifetime of the exciton significantly constrains the possible applications. In contrast, the dark exciton could be long-lived but does not necessarily possess the valley degree of freedom. In this work, we report the identification of the momentum-dark, intervalley exciton in monolayer WSe2 through low-temperature magneto-photoluminescence spectra. Interestingly, the intervalley exciton is brightened through the emission of a chiral phonon at the corners of the Brillouin zone (K point), and the pseudoangular momentum of the phonon is transferred to the emitted photon to preserve the valley information. The chiral phonon energy is determined to be ∼23 meV, based on the experimentally extracted exchange interaction (∼7 meV), in excellent agreement with the theoretical expectation of 24.6 meV. The long-lived intervalley exciton with valley degree of freedom adds an exciting quasiparticle for valleytronics, and the coupling between the chiral phonon and intervalley exciton furnishes a venue for valley spin manipulation.

Author Correction: Emerging photoluminescence from the dark-exciton phonon replica in monolayer WSe2.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.