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We report magneto-absorption spectroscopy of gated WSe$_2$ monolayers in high magnetic fields up to 60~T. When doped with a 2D Fermi sea of mobile holes, well-resolved sequences of optical transitions are observed in both $\sigma^\pm$ circular polarizations, which unambiguously and separately indicate the number of filled Landau levels (LLs) in both $K$ and $K'$ valleys. This reveals the interaction-enhanced valley Zeeman energy, which is found to be highly tunable with hole density $p$. We exploit this tunability to align the LLs in $K$ and $K'$, and find that the 2D hole gas becomes unstable against small changes in LL filling and can spontaneously valley-polarize. These results cannot be understood within a single-particle picture, highlighting the importance of exchange interactions in determining the ground state of 2D carriers in monolayer semiconductors., Comment: 8 pages, 4 figures + 3 supplementary figures

The recent discovery of two-dimensional (2D) magnets offers unique opportunities for the experimental exploration of low-dimensional magnetism4 and the magnetic proximity effects, and for the development of novel magnetoelectric, magnetooptic and spintronic devices. These advancements call for 2D materials with diverse magnetic structures as well as effective probes for their magnetic symmetries, which is key to understanding intralayer magnetic order and interlayer magnetic coupling. Here we apply second harmonic generation (SHG), a technique acutely sensitive to symmetry breaking, to probe the magnetic structure of a new 2D magnetic semiconductor, CrSBr. We find that CrSBr monolayers are ferromagnetically ordered below 146 K, an observation enabled by the discovery of a giant magnetic dipole SHG effect in the centrosymmetric 2D structure. In multilayers, the ferromagnetic monolayers are coupled antiferromagnetically, with the N\'eel temperature notably increasing with decreasing layer number. The magnetic structure of CrSBr, comprising spins co-aligned in-plane with rectangular unit cell, differs markedly from the prototypical 2D hexagonal magnets CrI3 and Cr2Ge2Te6 with out-of-plane moments. Moreover, our SHG analysis suggests that the order parameters of the ferromagnetic monolayer and the antiferromagnetic bilayer are the magnetic dipole and the magnetic toroidal moments, respectively. These findings establish CrSBr as an exciting 2D magnetic semiconductor and SHG as a powerful tool to probe 2D magnetic symmetry, opening the door to the exploration of coupling between magnetic order and excitonic/electronic properties, as well as the magnetic toroidal moment, in a broad range of applications., Comment: 15 pages, 4 figures, +27 pages Supporting Information

Using bilayer CrI$_3$ as an example, we demonstrate that stacking domain walls in van der Waals magnets can host one dimensional (1D) magnon channels, which have lower energies than bulk magnons. Interestingly, some magnon channels are hidden in magnetically homogeneous background and can only be inferred with the knowledge of stacking domain walls. Compared to 1D magnons confined in magnetic domain walls, 1D magnons in stacking domain walls are more stable against external perturbations. We show that the relaxed moir\'e superlattices of small-angle twisted bilayer CrI$_3$ is a natural realization of stacking domain walls and host interconnected moir\'e magnon network. Our work reveals the importance of stacking domain walls in understanding magnetic properties of van der Waals magnets, and extends the scope of stacking engineering to magnetic dynamics., Comment: 6 pages, 3 figures with supplemental materials. Accepted for publication in PRL

We present a systematic study of the nematic fluctuations in the iron chalcogenide superconductor Fe$_{1+y}$Te$_{1-x}$Se$_{x}$ ($0 \leq x \leq 0.53$) using the elastoresistivity technique. Near $x = 0$, in proximity to the double-stripe magnetic order of Fe$_{1+y}$Te, a diverging $B_{1g}$ nematic susceptibility is observed. Upon increasing $x$, despite the absence of magnetic order, the $B_{2g}$ nematic susceptibility increases and becomes dominant, closely following the strength of the $(\pi, \pi)$ spin fluctuations. Over a wide range of compositions ($0.17 \leq x \leq 0.53$), while the $B_{2g}$ nematic susceptibility follows a Curie temperature dependence (with zero Weiss temperature) at low temperatures, it shows deviations from Curie-Weiss behavior for temperatures higher than $50K$. This is the opposite of what is observed in typical iron pnictides, where Curie-Weiss deviations are seen at low temperatures. We attribute this unusual temperature dependence to a loss of coherence of the $d_{xy}$ orbital, which is supported by our theoretical calculations. Our results highlight the importance of orbital differentiation on the nematic properties of iron-based materials.

We present a high-resolution resonance Raman study of hBN encapsulated MoSe$_2$ and WSe$_2$ monolayers at 4 K using excitation energies from 1.6 eV to 2.25 eV. We report resonances with the WSe$_2$ A2s and MoSe$_2$ A2s and B2s excited Rydberg states despite their low oscillator strength. When resonant with the 2s states we identify new Raman peaks which are associated with intravalley scattering between different Rydberg states via optical phonons. By calibrating the Raman scattering efficiency and separately constraining the electric dipole matrix elements, we reveal that the scattering rates for k=0 optical phonons are comparable for both 1s and 2s states despite differences in the envelope functions. We also observe multiple new dispersive Raman peaks including a peak at the WSe$_2$ A2s resonance that demonstrates non-linear dispersion and peak-splitting behavior that suggests that the dispersion relations for dark excitonic states at energies near the 2s state are extremely complex., Comment: Submitted to IOP 2D Materials 16/04/20. Accepted in IOP 2D Materials 02/06/20. This is the version of the article before peer review or editing, as submitted by the authors to 2D Materials. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it

The recent discovery of magnetism within the family of exfoliatable van der Waals (vdW) compounds has attracted considerable interest in these materials for both fundamental research and technological applications. However current vdW magnets are limited by their extreme sensitivity to air, low ordering temperatures, and poor charge transport properties. Here we report the magnetic and electronic properties of CrSBr, an air-stable vdW antiferromagnetic semiconductor that readily cleaves perpendicular to the stacking axis. Below its N\'{e}el temperature, $T_N = 132 \pm 1$ K, CrSBr adopts an A-type antiferromagnetic structure with each individual layer ferromagnetically ordered internally and the layers coupled antiferromagnetically along the stacking direction. Scanning tunneling spectroscopy and photoluminescence (PL) reveal that the electronic gap is $\Delta_E = 1.5 \pm 0.2$ eV with a corresponding PL peak centered at $1.25 \pm 0.07$ eV. Using magnetotransport measurements, we demonstrate strong coupling between magnetic order and transport properties in CrSBr, leading to a large negative magnetoresistance response that is unique amongst vdW materials. These findings establish CrSBr as a promising material platform for increasing the applicability of vdW magnets to the field of spin-based electronics.

Twisted van der Waals heterostructures with flat electronic bands have recently emerged as a platform for realizing correlated and topological states with an extraordinary degree of control and tunability. In graphene-based moir\'e heterostructures, the correlated phase diagram and band topology depend strongly on the number of graphene layers, their relative stacking arrangement, and details of the external environment from the encapsulating crystals. Here, we report that the system of twisted monolayer-bilayer graphene (tMBG) hosts a variety of correlated metallic and insulating states, as well as topological magnetic states. Because of its low symmetry, the phase diagram of tMBG approximates that of twisted bilayer graphene when an applied perpendicular electric field points from the bilayer towards the monolayer graphene, or twisted double bilayer graphene when the field is reversed. In the former case, we observe correlated states which undergo an orbitally driven insulating transition above a critical perpendicular magnetic field. In the latter case, we observe the emergence of electrically tunable ferromagnetism at one-quarter filling of the conduction band, with a large associated anomalous Hall effect. Uniquely, the magnetization direction can be switched purely with electrostatic doping at zero magnetic field. Our results establish tMBG as a highly tunable platform for investigating a wide array of tunable correlated and topological states., Comment: 21 Pages, 20 Figures

Auger recombination in semiconductors is a many-body phenomenon in which recombination of electrons and holes is accompanied by excitation of other charge carriers. Being nonradiative, it is detrimental to light emission. The excess energy of the excited carriers is normally rapidly converted to heat, making Auger processes difficult to probe directly. Here, we employ a technique in which the Auger-excited carriers are detected by their ability to tunnel out of the semiconductor through a thin barrier, generating a current. We employ vertical van der Waals (vdW) heterostructures with monolayer WSe2 as the semiconductor and the wide band gap hexagonal boron nitride (hBN) as the tunnel barrier to preferentially transmit high-energy Auger-excited carriers to a graphite electrode. The unambiguous signatures of Auger processes are a rise in the photocurrent when excitons are created by resonant excitation, and negative differential photoconductance resulting from the shifts of the exciton resonances with voltage. We detect holes Auger-excited by both neutral and charged excitons, and find that the Auger scattering is surprisingly strong under weak excitation. The selective extraction of Auger carriers at low, controlled carrier densities that is enabled by vdW heterostructures illustrates an important addition to the techniques available for probing relaxation processes in 2D materials.

Monolayer transition metal dichalcogenides (TMDs) are the first truly two-dimensional (2D) semiconductor, providing an excellent platform to investigate light-matter interaction in the 2D limit. Apart from fundamental scientific exploration, this material system has attracted active research interest in the nanophotonic devices community for its unique optoelectronic properties. The inherently strong excitonic response in monolayer TMDs can be further enhanced by exploiting the temporal confinement of light in nanophotonic structures. Dielectric metasurfaces are one such two-dimensional nanophotonic structures, which have recently demonstrated strong potential to not only miniaturize existing optical components, but also to create completely new class of designer optics. Going beyond passive optical elements, researchers are now exploring active metasurfaces using emerging materials and the utility of metasurfaces to enhance the light-matter interaction. Here, we demonstrate a 2D exciton-polariton system by strongly coupling atomically thin tungsten diselenide (WSe2) monolayer to a silicon nitride (SiN) metasurface. Via energy-momentum spectroscopy of the WSe2-metasurface system, we observed the characteristic anti-crossing of the polariton dispersion both in the reflection and photoluminescence spectrum. A Rabi splitting of 18 meV was observed which matched well with our numerical simulation. The diffraction effects of the nano-patterned metasurface also resulted in a highly directional polariton emission. Finally, we showed that the Rabi splitting, the polariton dispersion and the far-field emission pattern could be tailored with subwavelength-scale engineering of the optical meta-atoms. Our platform thus opens the door for the future development of novel, exotic exciton-polariton devices by advanced meta-optical engineering.

A variety of correlated phases have recently emerged in select twisted van der Waals (vdW) heterostructures owing to their flat electronic dispersions. In particular, heterostructures of twisted double bilayer graphene (tDBG) manifest electric field-tunable correlated insulating (CI) states at all quarter fillings of the conduction band, accompanied by nearby states featuring signatures suggestive of superconductivity. Here, we report electrical transport measurements of tDBG in which we elucidate the fundamental role of spontaneous symmetry breaking within its correlated phase diagram. We observe abrupt resistivity drops upon lowering the temperature in the correlated metallic phases neighboring the CI states, along with associated nonlinear $I$-$V$ characteristics. Despite qualitative similarities to superconductivity, concomitant reversals in the sign of the Hall coefficient instead point to spontaneous symmetry breaking as the origin of the abrupt resistivity drops, while Joule heating appears to underlie the nonlinear transport. Our results suggest that similar mechanisms are likely relevant across a broader class of semiconducting flat band vdW heterostructures., Comment: 15 Pages, 15 Figures

Magic-angle twisted bilayer graphene (TBG), with rotational misalignment close to 1.1$^\circ$, features isolated flat electronic bands that host a rich phase diagram of correlated insulating, superconducting, ferromagnetic, and topological phases. The origins of the correlated insulators and superconductivity, and the interplay between them, are particularly elusive. Both states have been previously observed only for angles within $\pm0.1^\circ$ from the magic-angle value and occur in adjacent or overlapping electron density ranges; nevertheless, it is still unclear how the two states are related. Beyond the twist angle and strain, the dependence of the TBG phase diagram on the alignment and thickness of insulating hexagonal boron nitride (hBN) used to encapsulate the graphene sheets indicates the importance of the microscopic dielectric environment. Here we show that adding an insulating tungsten-diselenide (WSe$_2$) monolayer between hBN and TBG stabilizes superconductivity at twist angles much smaller than the established magic-angle value. For the smallest angle of $\theta$ = 0.79$^\circ$, we still observe clear superconducting signatures, despite the complete absence of the correlated insulating states and vanishing gaps between the dispersive and flat bands. These observations demonstrate that, even though electron correlations may be important, superconductivity in TBG can exist even when TBG exhibits metallic behaviour across the whole range of electron density. Finite-magnetic-field measurements further reveal breaking of the four-fold spin-valley symmetry in the system, consistent with large spin-orbit coupling induced in TBG via proximity to WSe$_2$. Our results highlight the importance of symmetry breaking effects in stabilizing electronic states in TBG and open new avenues for engineering quantum phases in moir\'e systems., Comment: 12 pages, 4 figures; main text

Exfoliated chromium triiodide (CrI$_3$) is a layered van der Waals (vdW) magnetic insulator that consists of ferromagnetic layers coupled through antiferromagnetic interlayer exchange. The resulting permutations of magnetic configurations combined with the underlying crystal symmetry produces tunable magneto-optical phenomena that is unique to the two-dimensional (2D) limit. Here, we report the direct observation of 2D magnons through magneto-Raman spectroscopy with optical selection rules that are strictly determined by the honeycomb lattice and magnetic states of atomically thin CrI$_3$. In monolayers, we observe an acoustic magnon mode of ~0.3 meV with cross-circularly polarized selection rules locked to the magnetization direction. These unique selection rules arise from the discrete conservation of angular momentum of photons and magnons dictated by threefold rotational symmetry in a rotational analogue to Umklapp scattering. In bilayers, by tuning between the layered antiferromagnetic and ferromagnetic-like states, we observe the switching of two magnon modes. The bilayer structure also enables Raman activity from the optical magnon mode at ~17 meV (~4.2 THz) that is otherwise Raman-silent in the monolayer. From these measurements, we quantitatively extract the spin wave gap, magnetic anisotropy, intralayer and interlayer exchange constants, and establish 2D magnets as a new system for exploring magnon physics.

We have synthesized unique colloidal nanoplatelets of the ferromagnetic two-dimensional (2D) van der Waals material CrI3 and have characterized these nanoplatelets structurally, magnetically, and by magnetic circular dichroism spectroscopy. The isolated CrI3 nanoplatelets have lateral dimensions of ~25 nm and ensemble thicknesses of only ~4 nm, corresponding to just a few CrI3 monolayers. Magnetic and magneto-optical measurements demonstrate robust 2D ferromagnetic ordering in these nanoplatelets with Curie temperatures similar to those observed in bulk CrI3, despite the strong spatial confinement. These data also show magnetization steps akin to those observed in micron-sized few-layer 2D sheets and associated with concerted spin-reversal of individual CrI3 layers within few-layer van der Waals stacks. Similar data have also been obtained for CrBr3 and anion-alloyed Cr(I1-xBrx)3 nanoplatelets. These results represent the first example of laterally confined 2D van der Waals ferromagnets of any composition. The demonstration of robust ferromagnetism at nanometer lateral dimensions opens new doors for miniaturization in spintronics devices based on van der Waals ferromagnets., Comment: 20 pages, 6 figures, plus supporting information of 7 pages, 5 figures. Submitted

Magnetic proximity effects are crucial ingredients for engineering spintronic, superconducting, and topological phenomena in heterostructures. Such effects are highly sensitive to the interfacial electronic properties, such as electron wave function overlap and band alignment. The recent emergence of van der Waals (vdW) magnets enables the possibility of tuning proximity effects via designing heterostructures with atomically clean interfaces. In particular, atomically thin CrI3 exhibits layered antiferromagnetism, where adjacent ferromagnetic monolayers are antiferromagnetically coupled. Exploiting this magnetic structure, we uncovered a layer-resolved magnetic proximity effect in heterostructures formed by monolayer WSe2 and bi/trilayer CrI3. By controlling the individual layer magnetization in CrI3 with a magnetic field, we found that the spin-dependent charge transfer between WSe2 and CrI3 is dominated by the interfacial CrI3 layer, while the proximity exchange field is highly sensitive to the layered magnetic structure as a whole. These properties enabled us to use monolayer WSe2 as a spatially sensitive magnetic sensor to map out layered antiferromagnetic domain structures at zero magnetic field as well as antiferromagnetic/ferromagnetic domains near the spin-flip transition in bilayer CrI3. Our work reveals a new way to control proximity effects and probe interfacial magnetic order via vdW engineering., Comment: to appear in Nature Nanotechnology

The coupling between spin, charge, and lattice degrees of freedom plays an important role in a wide range of fundamental phenomena. Monolayer semiconducting transitional metal dichalcogenides have emerged as an outstanding platform for studying these coupling effects because they possess unique spin-valley locking physics for hosting rich excitonic species and the reduced screening for strong Coulomb interactions. Here, we report the observation of multiple valley phonons, phonons with momentum vectors pointing to the corners of the hexagonal Brillouin zone, and the resulting exciton complexes in the monolayer semiconductor WSe2. From Lande g-factor and polarization analyses of photoluminescence peaks, we find that these valley phonons lead to efficient intervalley scattering of quasi particles in both exciton formation and relaxation. This leads to a series of photoluminescence peaks as valley phonon replicas of dark trions. Using identified valley phonons, we also uncovered an intervalley exciton near charge neutrality, and extract its short-range electron-hole exchange interaction to be about 10 meV. Our work not only identifies a number of previously unknown 2D excitonic species, but also shows that monolayer WSe2 is a prime candidate for studying interactions between spin, pseudospin, and zone-edge phonons., Comment: to appear in Nature Communications

The integration of diverse electronic phenomena, such as magnetism and nontrivial topology, into a single system is normally studied either by seeking materials that contain both ingredients, or by layered growth of contrasting materials. The ability to simply stack very different two dimensional (2D) van der Waals materials in intimate contact permits a different approach. Here we use this approach to couple the helical edges states in a 2D topological insulator, monolayer WTe2, to a 2D layered antiferromagnet, CrI3. We find that the edge conductance is sensitive to the magnetization state of the CrI3, and the coupling can be understood in terms of an exchange field from the nearest and next-nearest CrI3 layers that produces a gap in the helical edge. We also find that the nonlinear edge conductance depends on the magnetization of the nearest CrI3 layer relative to the current direction. At low temperatures this produces an extraordinarily large nonreciprocal current that is switched by changing the antiferromagnetic state of the CrI3.

The formation of interfacial moir\'e patterns from angular and/or lattice mismatch has become a powerful approach to engineer a range of quantum phenomena in van der Waals heterostructures. For long-lived and valley-polarized interlayer excitons in transition-metal dichalcogenide (TMDC) heterobilayers, signatures of quantum confinement by the moir\'e landscape have been reported in recent experimental studies. Such moir\'e confinement has offered the exciting possibility to tailor new excitonic systems, such as ordered arrays of zero-dimensional (0D) quantum emitters and their coupling into topological superlattices. A remarkable nature of the moir\'e potential is its dramatic response to strain, where a small uniaxial strain can tune the array of quantum-dot-like 0D traps into parallel stripes of one-dimensional (1D) quantum wires. Here, we present direct evidence for the 1D moir\'e potentials from real space imaging and the corresponding 1D moir\'e excitons from photoluminescence (PL) emission in MoSe2/WSe2 heterobilayers. Whereas the 0D moir\'e excitons display quantum emitter-like sharp PL peaks with circular polarization, the PL emission from 1D moir\'e excitons has linear polarization and two orders of magnitude higher intensity. The results presented here establish strain engineering as a powerful new method to tailor moir\'e potentials as well as their optical and electronic responses on demand.

The coupling between spin and charge degrees of freedom in a crystal imparts strong optical signatures on scattered electromagnetic waves. This has led to magneto-optical effects with a host of applications, from the sensitive detection of local magnetic order to optical modulation and data storage technologies. Here, we demonstrate a new magneto-optical effect, namely, the tuning of inelastically scattered light through symmetry control in atomically thin chromium triiodide (CrI$_3$). In monolayers, we found an extraordinarily large magneto-optical Raman effect from an A$_{1g}$ phonon mode due to the emergence of ferromagnetic order. The linearly polarized, inelastically scattered light rotates by ~40$^o$, more than two orders of magnitude larger than the rotation from MOKE under the same experimental conditions. In CrI$_3$ bilayers, we show that the same A$_{1g}$ phonon mode becomes Davydov-split into two modes of opposite parity, exhibiting divergent selection rules that depend on inversion symmetry and the underlying magnetic order. By switching between the antiferromagnetic states and the fully spin-polarized states with applied magnetic and electric fields, we demonstrate the magnetoelectrical control over their selection rules. Our work underscores the unique opportunities provided by 2D magnets for controlling the combined time-reversal and inversion symmetries to manipulate Raman optical selection rules and for exploring emergent magneto-optical effects and spin-phonon coupled physics., Comment: To appear in Nature Nanotechnology

Controlling the crystal structure is a powerful approach for manipulating the fundamental properties of solids. Unique to two-dimensional (2D) van der Waals materials, the control can be achieved by modifying the stacking order through rotation and translation between the layers. Here, we report the first observation of stacking dependent interlayer magnetism in the 2D magnetic semiconductor, chromium tribromide (CrBr3), enabled by the successful growth of its monolayer and bilayer through molecular beam epitaxy. Using in situ spin-polarized scanning tunneling microscopy and spectroscopy, we directly correlated the atomic lattice structure with observed magnetic order. We demonstrated that while individual CrBr3 monolayer is ferromagnetic, the interlayer coupling in bilayer depends strongly on the stacking order and can be either ferromagnetic or antiferromagnetic. Our observations provide direct experimental evidence for exploring the stacking dependent layered magnetism, and pave the way for manipulating 2D magnetism with unique layer twist angle control., Comment: originally submitted version, 12 pages, 4 figures

The physical properties of two-dimensional van der Waals (2D vdW) crystals depend sensitively on the interlayer coupling, which is intimately connected to the stacking arrangement and the interlayer spacing. For example, simply changing the twist angle between graphene layers can induce a variety of correlated electronic phases, which can be controlled further in a continuous manner by applying hydrostatic pressure to decrease the interlayer spacing. In the recently discovered 2D magnets, theory suggests that the interlayer exchange coupling strongly depends on layer separation, while the stacking arrangement can even change the sign of the magnetic exchange, thus drastically modifying the ground state. Here, we demonstrate pressure tuning of magnetic order in the 2D magnet CrI3. We probe the magnetic states using tunneling and scanning magnetic circular dichroism microscopy measurements. We find that the interlayer magnetic coupling can be more than doubled by hydrostatic pressure. In bilayer CrI3, pressure induces a transition from layered antiferromagnetic to ferromagnetic phases. In trilayer CrI3, pressure can create coexisting domains of three phases, one ferromagnetic and two distinct antiferromagnetic. The observed changes in magnetic order can be explained by changes in the stacking arrangement. Such coupling between stacking order and magnetism provides ample opportunities for designer magnetic phases and functionalities.