Emergent Correlated Phases in Rhombohedral Trilayer Graphene Induced by Proximity Spin-Orbit and Exchange Coupling.

The impact of proximity-induced spin-orbit and exchange coupling on the correlated phase diagram of rhombohedral trilayer graphene (RTG) is investigated theoretically. By employing ab initio-fitted effective models of RTG encapsulated by transition metal dichalcogenides (spin-orbit proximity effect) and ferromagnetic Cr_{2}Ge_{2}Te_{6} (exchange proximity effect), we incorporate the Coulomb interactions within the random-phase approximation to explore potential correlated phases at different displacement fields and doping. We find a rich spectrum of spin-valley resolved Stoner and intervalley coherence instabilities induced by the spin-orbit proximity effects, such as the emergence of a spin-valley-coherent phase due to the presence of valley-Zeeman coupling. Similarly, proximity exchange removes the phase degeneracies by biasing the spin direction, enabling a magnetocorrelation effect-strong sensitivity of the correlated phases to the relative magnetization orientations (parallel or antiparallel) of the encapsulating ferromagnetic layers.

Ultraviolet interlayer excitons in bilayer WSe2.

Interlayer excitons in van der Waals heterostructures are fascinating for applications like exciton condensation, excitonic devices and moiré-induced quantum emitters. The study of these charge-transfer states has almost exclusively focused on band edges, limiting the spectral region to the near-infrared regime. Here we explore the above-gap analogues of interlayer excitons in bilayer WSe2 and identify both neutral and charged species emitting in the ultraviolet. Even though the transitions occur far above the band edge, the states remain metastable, exhibiting linewidths as narrow as 1.8 meV. These interlayer high-lying excitations have switchable dipole orientations and hence show prominent Stark splitting. The positive and negative interlayer high-lying trions exhibit significant binding energies of 20-30 meV, allowing for a broad tunability of transitions via electric fields and electrostatic doping. The Stark splitting of these trions serves as a highly accurate, built-in sensor for measuring interlayer electric field strengths, which are exceedingly difficult to quantify otherwise. Such excitonic complexes are further sensitive to the interlayer twist angle and offer opportunities to explore emergent moiré physics under electrical control. Our findings more than double the accessible energy range for applications based on interlayer excitons.

Charge Transfer and Asymmetric Coupling of MoSe2 Valleys to the Magnetic Order of CrSBr.

van der Waals heterostructures composed of two-dimensional (2D) transition metal dichalcogenides and vdW magnetic materials offer an intriguing platform to functionalize valley and excitonic properties in nonmagnetic TMDs. Here, we report magneto photoluminescence (PL) investigations of monolayer (ML) MoSe2 on the layered A-type antiferromagnetic (AFM) semiconductor CrSBr under different magnetic field orientations. Our results reveal a clear influence of the CrSBr magnetic order on the optical properties of MoSe2, such as an anomalous linear-polarization dependence, changes of the exciton/trion energies, a magnetic-field dependence of the PL intensities, and a valley g-factor with signatures of an asymmetric magnetic proximity interaction. Furthermore, first-principles calculations suggest that MoSe2/CrSBr forms a broken-gap (type-III) band alignment, facilitating charge transfer processes. The work establishes that antiferromagnetic-nonmagnetic interfaces can be used to control the valley and excitonic properties of TMDs, relevant for the development of opto-spintronics devices.

Signatures of Electric Field and Layer Separation Effects on the Spin-Valley Physics of MoSe2/WSe2 Heterobilayers: From Energy Bands to Dipolar Excitons.

Multilayered van der Waals heterostructures based on transition metal dichalcogenides are suitable platforms on which to study interlayer (dipolar) excitons, in which electrons and holes are localized in different layers. Interestingly, these excitonic complexes exhibit pronounced valley Zeeman signatures, but how their spin-valley physics can be further altered due to external parameters-such as electric field and interlayer separation-remains largely unexplored. Here, we perform a systematic analysis of the spin-valley physics in MoSe2/WSe2 heterobilayers under the influence of an external electric field and changes of the interlayer separation. In particular, we analyze the spin (Sz) and orbital (Lz) degrees of freedom, and the symmetry properties of the relevant band edges (at K, Q, and Γ points) of high-symmetry stackings at 0° (R-type) and 60° (H-type) angles-the important building blocks present in moiré or atomically reconstructed structures. We reveal distinct hybridization signatures on the spin and the orbital degrees of freedom of low-energy bands, due to the wave function mixing between the layers, which are stacking-dependent, and can be further modified by electric field and interlayer distance variation. We find that H-type stackings favor large changes in the g-factors as a function of the electric field, e.g., from -5 to 3 in the valence bands of the Hhh stacking, because of the opposite orientation of Sz and Lz of the individual monolayers. For the low-energy dipolar excitons (direct and indirect in k-space), we quantify the electric dipole moments and polarizabilities, reflecting the layer delocalization of the constituent bands. Furthermore, our results show that direct dipolar excitons carry a robust valley Zeeman effect nearly independent of the electric field, but tunable by the interlayer distance, which can be rendered experimentally accessible via applied external pressure. For the momentum-indirect dipolar excitons, our symmetry analysis indicates that phonon-mediated optical processes can easily take place. In particular, for the indirect excitons with conduction bands at the Q point for H-type stackings, we find marked variations of the valley Zeeman (∼4) as a function of the electric field, which notably stands out from the other dipolar exciton species. Our analysis suggests that stronger signatures of the coupled spin-valley physics are favored in H-type stackings, which can be experimentally investigated in samples with twist angle close to 60°. In summary, our study provides fundamental microscopic insights into the spin-valley physics of van der Waals heterostructures, which are relevant to understanding the valley Zeeman splitting of dipolar excitonic complexes, and also intralayer excitons.

Strain-Induced Exciton Hybridization in WS_{2} Monolayers Unveiled by Zeeman-Splitting Measurements.

Mechanical deformations and ensuing strain are routinely exploited to tune the band gap energy and to enhance the functionalities of two-dimensional crystals. In this Letter, we show that strain leads also to a strong modification of the exciton magnetic moment in WS_{2} monolayers. Zeeman-splitting measurements under magnetic fields up to 28.5 T were performed on single, one-layer-thick WS_{2} microbubbles. The strain of the bubbles causes a hybridization of k-space direct and indirect excitons resulting in a sizable decrease in the modulus of the g factor of the ground-state exciton. These findings indicate that strain may have major effects on the way the valley number of excitons can be used to process binary information in two-dimensional crystals.

Ultrafast pseudospin quantum beats in multilayer WSe2 and MoSe2.

Layered van-der-Waals materials with hexagonal symmetry offer an extra degree of freedom to their electrons, the so-called valley index or valley pseudospin, which behaves conceptually like the electron spin. Here, we present investigations of excitonic transitions in mono- and multilayer WSe2 and MoSe2 materials by time-resolved Faraday ellipticity (TRFE) with in-plane magnetic fields, B∥, of up to 9 T. In monolayer samples, the measured TRFE time traces are almost independent of B∥, which confirms a close to zero in-plane exciton g factor g∥, consistent with first-principles calculations. In contrast, we observe pronounced temporal oscillations in multilayer samples for B∥ > 0. Our first-principles calculations confirm the presence of a non-zero g∥ for the multilayer samples. We propose that the oscillatory TRFE signal in the multilayer samples is caused by pseudospin quantum beats of excitons, which is a manifestation of spin- and pseudospin layer locking in the multilayer samples.

Strong Substrate Strain Effects in Multilayered WS2 Revealed by High-Pressure Optical Measurements.

The optical properties of two-dimensional materials can be effectively tuned by strain induced from a deformable substrate. In the present work we combine first-principles calculations based on density functional theory and the effective Bethe-Salpeter equation with high-pressure optical measurements to thoroughly describe the effect of strain and dielectric environment onto the electronic band structure and optical properties of a few-layered transition-metal dichalcogenide. Our results show that WS2 remains fully adhered to the substrate at least up to a -0.6% in-plane compressive strain for a wide range of substrate materials. We provide a useful model to describe effect of strain on the optical gap energy. The corresponding experimentally determined out-of-plane and in-plane stress gauge factors for WS2 monolayers are -8 and 24 meV/GPa, respectively. The exceptionally large in-plane gauge factor confirms transition metal dichalcogenides as very promising candidates for flexible functionalities. Finally, we discuss the pressure evolution of an optical transition closely lying to the A exciton for bulk WS2 as well as the direct-to-indirect transition of the monolayer upon compression.

Engineering Proximity Exchange by Twisting: Reversal of Ferromagnetic and Emergence of Antiferromagnetic Dirac Bands in Graphene/Cr_{2}Ge_{2}Te_{6}.

We investigate the twist-angle and gate dependence of the proximity exchange coupling in twisted graphene on monolayer Cr_{2}Ge_{2}Te_{6} from first principles. The proximitized Dirac band dispersions of graphene are fitted to a model Hamiltonian, yielding effective sublattice-resolved proximity-induced exchange parameters (λ_{ex}^{A} and λ_{ex}^{B}) for a series of twist angles between 0° and 30°. For aligned layers (0° twist angle), the exchange coupling of graphene is the same on both sublattices, λ_{ex}^{A}≈λ_{ex}^{B}≈4 meV, while the coupling is reversed at 30° (with λ_{ex}^{A}≈λ_{ex}^{B}≈-4 meV). Remarkably, at 19.1° the induced exchange coupling becomes antiferromagnetic: λ_{ex}^{A}<0, λ_{ex}^{B}>0. Further tuning is provided by a transverse electric field and the interlayer distance. The predicted proximity magnetization reversal and emergence of an antiferromagnetic Dirac dispersion make twisted graphene/Cr_{2}Ge_{2}Te_{6} bilayers a versatile platform for realizing topological phases and for spintronics applications.

Supercurrent rectification and magnetochiral effects in symmetric Josephson junctions.

Transport is non-reciprocal when not only the sign, but also the absolute value of the current depends on the polarity of the applied voltage. It requires simultaneously broken inversion and time-reversal symmetries, for example, by an interplay of spin-orbit coupling and magnetic field. Hitherto, observation of nonreciprocity was tied to resistivity, and dissipationless non-reciprocal circuit elements were elusive. Here we engineer fully superconducting non-reciprocal devices based on highly transparent Josephson junctions fabricated on InAs quantum wells. We demonstrate supercurrent rectification far below the transition temperature. By measuring Josephson inductance, we can link the non-reciprocal supercurrent to an asymmetry of the current-phase relation, and directly derive the supercurrent magnetochiral anisotropy coefficient. A semiquantitative model explains well the main features of our experimental data. Non-reciprocal Josephson junctions have the potential to become for superconducting circuits what pn junctions are for traditional electronics, enabling new non-dissipative circuit elements.

Quasi-1D exciton channels in strain-engineered 2D materials.

Strain engineering is a powerful tool in designing artificial platforms for high-temperature excitonic quantum devices. Combining strong light-matter interaction with robust and mobile exciton quasiparticles, two-dimensional transition metal dichalcogenides (2D TMDCs) hold great promise in this endeavor. However, realizing complex excitonic architectures based on strain-induced electronic potentials alone has proven to be exceptionally difficult so far. Here, we demonstrate deterministic strain engineering of both single-particle electronic bandstructure and excitonic many-particle interactions. We create quasi-1D transport channels to confine excitons and simultaneously enhance their mobility through locally suppressed exciton-phonon scattering. Using ultrafast, all-optical injection and time-resolved readout, we realize highly directional exciton flow with up to 100% anisotropy both at cryogenic and room temperatures. The demonstrated fundamental modification of the exciton transport properties in a deterministically strained 2D material with effectively tunable dimensionality has broad implications for both basic solid-state science and emerging technologies.

Narrow-band high-lying excitons with negative-mass electrons in monolayer WSe2.

Monolayer transition-metal dichalcogenides (TMDCs) show a wealth of exciton physics. Here, we report the existence of a new excitonic species, the high-lying exciton (HX), in single-layer WSe2 with an energy of ~3.4 eV, almost twice the band-edge A-exciton energy, with a linewidth as narrow as 5.8 meV. The HX is populated through momentum-selective optical excitation in the K-valleys and is identified in upconverted photoluminescence (UPL) in the UV spectral region. Strong electron-phonon coupling results in a cascaded phonon progression with equidistant peaks in the luminescence spectrum, resolvable to ninth order. Ab initio GW-BSE calculations with full electron-hole correlations explain HX formation and unmask the admixture of upper conduction-band states to this complex many-body excitation. These calculations suggest that the HX is comprised of electrons of negative mass. The coincidence of such high-lying excitonic species at around twice the energy of band-edge excitons rationalizes the excitonic quantum-interference phenomenon recently discovered in optical second-harmonic generation (SHG) and explains the efficient Auger-like annihilation of band-edge excitons.

Electrical Control of Valley-Zeeman Spin-Orbit-Coupling-Induced Spin Precession at Room Temperature.

The ultimate goal of spintronics is achieving electrically controlled coherent manipulation of the electron spin at room temperature to enable devices such as spin field-effect transistors. With conventional materials, coherent spin precession has been observed in the ballistic regime and at low temperatures only. However, the strong spin anisotropy and the valley character of the electronic states in 2D materials provide unique control knobs to manipulate spin precession. Here, by manipulating the anisotropic spin-orbit coupling in bilayer graphene by the proximity effect to WSe_{2}, we achieve coherent spin precession in the absence of an external magnetic field, even in the diffusive regime. Remarkably, the sign of the precessing spin polarization can be tuned by a back gate voltage and by a drift current. Our realization of a spin field-effect transistor at room temperature is a cornerstone for the implementation of energy efficient spin-based logic.

Van der Waals heterostructures for spintronics and opto-spintronics.

The large variety of 2D materials and their co-integration in van der Waals heterostructures enable innovative device engineering. In addition, their atomically thin nature promotes the design of artificial materials by proximity effects that originate from short-range interactions. Such a designer approach is particularly compelling for spintronics, which typically harnesses functionalities from thin layers of magnetic and non-magnetic materials and the interfaces between them. Here we provide an overview of recent progress in 2D spintronics and opto-spintronics using van der Waals heterostructures. After an introduction to the forefront of spin transport research, we highlight the unique spin-related phenomena arising from spin-orbit and magnetic proximity effects. We further describe the ability to create multifunctional hybrid heterostructures based on van der Waals materials, combining spin, valley and excitonic degrees of freedom. We end with an outlook on perspectives and challenges for the design and production of ultracompact all-2D spin devices and their potential applications in conventional and quantum technologies.

Twist-angle engineering of excitonic quantum interference and optical nonlinearities in stacked 2D semiconductors.

Twist-engineering of the electronic structure in van-der-Waals layered materials relies predominantly on band hybridization between layers. Band-edge states in transition-metal-dichalcogenide semiconductors are localized around the metal atoms at the center of the three-atom layer and are therefore not particularly susceptible to twisting. Here, we report that high-lying excitons in bilayer WSe2 can be tuned over 235 meV by twisting, with a twist-angle susceptibility of 8.1 meV/°, an order of magnitude larger than that of the band-edge A-exciton. This tunability arises because the electronic states associated with upper conduction bands delocalize into the chalcogenide atoms. The effect gives control over excitonic quantum interference, revealed in selective activation and deactivation of electromagnetically induced transparency (EIT) in second-harmonic generation. Such a degree of freedom does not exist in conventional dilute atomic-gas systems, where EIT was originally established, and allows us to shape the frequency dependence, i.e., the dispersion, of the optical nonlinearity.

Swapping Exchange and Spin-Orbit Coupling in 2D van der Waals Heterostructures.

The concept of swapping the two most important spin interactions-exchange and spin-orbit coupling-is proposed based on two-dimensional multilayer van der Waals heterostructures. Specifically, we show by performing realistic ab initio simulations, that a single device consisting of a bilayer graphene sandwiched by a 2D ferromagnet Cr_{2}Ge_{2}Te_{6} (CGT) and a monolayer WS_{2}, is able not only to generate, but also to swap the two interactions. The highly efficient swapping is enabled by the interplay of gate-dependent layer polarization in bilayer graphene and short-range spin-orbit and exchange proximity effects affecting only the layers in contact with the sandwiching materials. We call these structures ex-so-tic, for supplying either exchange (ex) or spin-orbit (so) coupling in a single device, by gating. Such bifunctional devices demonstrate the potential of van der Waals spintronics engineering using 2D crystal multilayers.

Spin Relaxation in s-Wave Superconductors in the Presence of Resonant Spin-Flip Scatterers.

Employing analytical methods and quantum transport simulations we investigate the relaxation of quasiparticle spins in graphene proximitized by an s-wave superconductor in the presence of resonant magnetic and spin-orbit active impurities. Off resonance, the relaxation increases with decreasing temperature when electrons scatter off magnetic impurities-the Hebel-Slichter effect-and decreases when impurities have spin-orbit coupling. This distinct temperature dependence (not present in the normal state) uniquely discriminates between the two scattering mechanisms. However, we show that the Hebel-Slichter picture breaks down at resonances. The emergence of Yu-Shiba-Rusinov bound states within the superconducting gap redistributes the spectral weight away from magnetic resonances. The result is opposite to the Hebel-Slichter expectation: the spin relaxation decreases with decreasing temperature. Our findings hold for generic s-wave superconductors with resonant magnetic impurities, but also, as we show, for resonant magnetic Josephson junctions.

Quantum Anomalous Hall Effects in Graphene from Proximity-Induced Uniform and Staggered Spin-Orbit and Exchange Coupling.

We investigate an effective model of proximity modified graphene (or symmetrylike materials) with broken time-reversal symmetry. We predict the appearance of quantum anomalous Hall phases by computing bulk band gap and Chern numbers for benchmark combinations of system parameters. Allowing for staggered exchange field enables quantum anomalous Hall effect in flat graphene with Chern number C=1. We explicitly show edge states in zigzag and armchair nanoribbons and explore their localization behavior. Remarkably, the combination of staggered intrinsic spin-orbit and uniform exchange coupling gives topologically protected (unlike in time-reversal systems) pseudohelical states, whose spin is opposite in opposite zigzag edges. Rotating the magnetization from out of plane to in plane makes the system trivial, allowing us to control topological phase transitions. We also propose, using density functional theory, a material platform-graphene on Ising antiferromagnet MnPSe_{3}-to realize staggered exchange (pseudospin Zeeman) coupling.

Proximity Spin-Orbit Torque on a Two-Dimensional Magnet within van der Waals Heterostructure: Current-Driven Antiferromagnet-to-Ferromagnet Reversible Nonequilibrium Phase Transition in Bilayer CrI3.

The recently discovered two-dimensional magnetic insulator CrI3 is an intriguing case for basic research and spintronic applications since it is a ferromagnet in the bulk but an antiferromagnet in bilayer form, with its magnetic ordering amenable to external manipulations. Using the first-principles quantum transport approach, we predict that injecting unpolarized charge current parallel to the interface of the bilayer-CrI3/monolayer-TaSe2 van der Waals (vdW) heterostructure will induce spin-orbit torque and thereby drive the dynamics of magnetization on the first monolayer of CrI3 in direct contact with TaSe2. By combining the calculated complex angular dependence of spin-orbit torque with the Landau-Lifshitz-Gilbert equation for classical dynamics of magnetization, we demonstrate that current pulses can switch the direction of magnetization on the first monolayer to become parallel to that of the second monolayer, thereby converting CrI3 from antiferromagnet to ferromagnet while not requiring any external magnetic field. We explain the mechanism of this reversible current-driven nonequilibrium phase transition by showing that first monolayer of CrI3 carries current due to evanescent wave functions injected by metallic transition metal dichalcogenide TaSe2, while concurrently acquiring strong spin-orbit coupling via such a proximity effect, whereas the second monolayer of CrI3 remains insulating. The transition can be detected by passing vertical read current through the vdW heterostructure, encapsulated by a bilayer of hexagonal boron nitride and sandwiched between graphite electrodes, where we find a tunneling magnetoresistance of ≃240%.

Observation of Spin-Valley-Coupling-Induced Large Spin-Lifetime Anisotropy in Bilayer Graphene.

We report the first observation of a large spin-lifetime anisotropy in bilayer graphene (BLG) fully encapsulated between hexagonal boron nitride. We characterize the out-of-plane (τ_{⊥}) and in-plane (τ_{∥}) spin lifetimes by oblique Hanle spin precession. At 75 K and the charge neutrality point (CNP), we observe a strong anisotropy of τ_{⊥}/τ_{∥}=8±2. This value is comparable to graphene-transition-metal-dichalcogenide heterostructures, whereas our high-quality BLG provides with τ_{⊥} up to 9 ns, a spin lifetime more than 2 orders of magnitude larger. The anisotropy decreases to 3.5±1 at a carrier density of n=6×10^{11} cm^{-2}. Temperature-dependent measurements show above 75 K a decrease of τ_{⊥}/τ_{∥} with increasing temperature, reaching the isotropic case close to room temperature. We explain our findings with electric-field-induced spin-valley coupling arising from the small intrinsic spin-orbit fields in BLG of 12 µeV at the CNP.

Transport Spectroscopy of Sublattice-Resolved Resonant Scattering in Hydrogen-Doped Bilayer Graphene.

We report the experimental observation of sublattice-resolved resonant scattering in bilayer graphene by performing simultaneous cryogenic atomic hydrogen doping and electron transport measurements in an ultrahigh vacuum. This allows us to monitor the hydrogen adsorption on the different sublattices of bilayer graphene without atomic-scale microscopy. Specifically, we detect two distinct resonant scattering peaks in the gate-dependent resistance, which evolve as a function of the atomic hydrogen dosage. Theoretical calculations show that one of the peaks originates from resonant scattering by hydrogen adatoms on the α sublattice (dimer site) while the other originates from hydrogen adatoms on the ß sublattice (nondimer site), thereby enabling a method for characterizing the relative sublattice occupancy via transport measurements. Utilizing this new capability, we investigate the adsorption and thermal desorption of hydrogen adatoms via controlled annealing and conclude that hydrogen adsorption on the ß sublattice is energetically favored. Through site-selective desorption from the α sublattice, we realize hydrogen doping with adatoms primarily on a single sublattice, which is highly desired for generating ferromagnetism.