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Chiral superconductors are unconventional superconducting states that break time reversal symmetry spontaneously and typically feature Cooper pairing at non-zero angular momentum. Such states may host Majorana fermions and provide an important platform for topological physics research and fault-tolerant quantum computing. Despite of intensive search and prolonged studies of several candidate systems, chiral superconductivity has remained elusive so far. Here we report the discovery of unconventional superconductivity in rhombohedral tetra-layer graphene. We observed two superconducting states in the gate-induced flat conduction bands with Tc up to 300 mK and charge density ne as low as 2.4*1011 cm-2, appearing robustly in three different devices, where electrons reside close to a proximate WSe2 layer, far away from WSe2, and in the absence of WSe2 respectively. Spontaneous time-reversal-symmetry-breaking (TRSB) due to electron's orbital motion is found, and several observations indicate the chiral nature of these superconducting states, including 1. In the superconducting state, Rxx shows fluctuations at zero magnetic field and magnetic hysteresis versus an out-of-plane magnetic field B, which are absent from all other superconductors; 2. one superconducting state develops within a spin- and valley-polarized quarter-metal phase, and is robust against the neighboring spin-valley-polarized quarter-metal state under B; 3. the normal states show anomalous Hall signals at zero magnetic field and magnetic hysteresis. We also observed a critical B > 0.9 Tesla, higher than any graphene superconductivity reported so far and indicates a strong-coupling superconductivity close the BCS-BEC crossover. Our observations establish a pure carbon material for the study of topological superconductivity, and pave the way to explore Majorana modes and topological quantum computing.

Rhombohedral multilayer graphene, with its flat electronic bands and concentrated Berry curvature, is a promising material for the realization of correlated topological phases of matter. When aligned to an adjacent hexagonal boron nitride (hBN) layer, the graphene develops narrow minibands with non-trivial topology. By tuning an externally-applied electric displacement field, the conduction electrons can either be pushed towards or away from the moir\'e superlattice. Motivated by the recent observation of the fractional quantum anomalous Hall effect (FQAHE) in the moir\'e-distant case, we study the opposite moir\'e-proximal case, where the superlattice potential is considerably stronger. We explore the physics within the moir\'e conduction bands through capacitance measurements that allow us to determine the inverse electronic compressibility and extract energy gaps of incompressible states. We observe integer and fractional Chern insulator states at superlattice filling factors v = 1, 2/3, and 1/3 with Streda slopes of -1, -2/3, and -1/3, respectively. Remarkably, the v = 1/3 state persists down to a magnetic field of 0.2 T. In addition, we also observe numerous trivial and topological charge density waves. We map out a phase diagram that is highly sensitive to both displacement and magnetic fields, which tune the system between various ground states by modifying the band dispersion and the structure of the electronic wavefunctions. This work demonstrates displacement field control of topological phase transitions in the moir\'e-proximal limit of rhombohedral pentalayer graphene, creating a highly-tunable platform for studying the interplay between intrinsic band topology and strong lattice effects.

Electrons in topological flat bands can form novel topological states driven by the correlation effects. The penta-layer rhombohedral graphene/hBN moire superlattice has been shown to host fractional quantum anomalous Hall effect (FQAHE) at ~400 mK, triggering discussions around the underlying mechanism and the role of moire effects. In particular, novel electron crystal states with non-trivial topology have been proposed. Here we report DC electrical transport measurement in rhombohedral penta- and tetra-layer graphene/hBN moire superlattices at electronic temperatures down to ~40 mK. We observed two more FQAH states in the penta-layer devices than previously reported. In a new tetra-layer device, we observed FQAHE at filling factors v = 3/5 and 2/3 at 300 mK. With a small bias current and the lowest temperature, we observed a new extended quantum anomalous Hall (EQAH) state and magnetic hysteresis, where Rxy = h/e2 and vanishing Rxx span a wide range of moire filling factor v from 0.5 to up to 1.3. By increasing the temperature or current, FQAHE can be recovered -- suggesting the break-down of the EQAH states and a phase transition into the fractional quantum Hall liquid. Furthermore, we observed displacement field-induced quantum phase transitions from the EQAH states to Fermi liquid, FQAH liquid and the likely composite Fermi liquid. Our observation establishes a new topological phase of electrons with quantized Hall resistance at zero magnetic field, and enriches the emergent quantum phenomena in materials with topological flat bands.

Engineering non-Abelian quasiparticles by combining superconductivity and topological states have been proposed as a route to realize topological quantum computation. Rhombohedral multilayer graphene with layer number N>=3 has been shown as a promising platform, as it hosts integer and fractional quantum anomalous Hall effects when proximitized by transition metal dichalcogenide (TMD) and a moire potential. However, superconductivity in similar devices have remained largely unexplored, although proximitized spin-orbit-coupling (SOC) effect has been shown to strengthen or induce superconductivity in both crystalline and twisted graphene. Here we report electron transport measurements of TMD-proximitized rhombohedral trilayer graphene (RTG) at temperatures down to 40 mK. We observed a new hole-doped superconducting state SC4 with a transition temperature Tc of 230 mK. On the electron-doped side, we identified a new isospin-symmetry breaking three-quarter-metal (TQM) phase. Near this three-quarter-metal state, the state SC3, very weak in bare RTG, is fully developed into a superconducting state at 110 mK. By performing fermiology analysis based on the quantum oscillation measurement, we showed that the SC3 and SC4 states reside at the phase boundaries between different isospin-symmetry-breaking states. These observations are aligned with the existing understanding that SOC enhances graphene superconductivity. Surprisingly, the original superconducting state SC1 in bare RTG is strongly suppressed in the presence of TMD, and we cannot find it down to the base temperature of our measurement. Our observations form the basis of exploring superconductivity and non-Abelian quasiparticles in rhombohedral graphene devices, and provide experimental evidence that challenges the understanding of the impacts of SOC on graphene superconductivity., Comment: 35 pages; 4 figures, 1 table, 13 extended data figures

The quantum anomalous Hall effect (QAHE) is a robust topological phenomenon featuring quantized Hall resistance at zero magnetic field. We report the QAHE in a rhombohedral pentalayer graphene/monolayer WS2 heterostructure. Distinct from other experimentally confirmed QAHE systems, this system has neither magnetic element nor moir\'e superlattice effect. The QAH states emerge at charge neutrality and feature Chern numbers C = +-5 at temperatures up to about 1.5 K. 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., Comment: to be published in Science

The fractional quantum anomalous Hall effect (FQAHE), the analog of the fractional quantum Hall effect1 at zero magnetic field, is predicted to exist in topological flat bands under spontaneous time-reversal-symmetry breaking. The demonstration of FQAHE could lead to non-Abelian anyons which form the basis of topological quantum computation. So far, FQAHE has been observed only in twisted MoTe2 (t-MoTe2) at moire filling factor v > 1/2. Graphene-based moire 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 moire superlattice. At zero magnetic field, we observed plateaus of quantized Hall resistance Rxy = h/(ve^2) at filling factors v = 1, 2/3, 3/5, 4/7, 4/9, 3/7 and 2/5 of the moire superlattice respectively. These features are accompanied by clear dips in the longitudinal resistance Rxx. In addition, at zero magnetic field, Rxy equals 2h/e^2 at v = 1/2 and varies linearly with the filling factor-similar to the composite Fermi liquid (CFL) in the half-filled lowest Landau level at high magnetic fields. By tuning the gate displacement field D and v, we observed phase transitions from CFL and FQAH states to other correlated electron states. Our graphene system provides an ideal platform for exploring charge fractionalization and (non-Abelian) anyonic braiding at zero magnetic field, especially considering a lateral junction between FQAHE and superconducting regions in the same device., Comment: Nature, in press

Ferroic orders describe spontaneous polarization of spin, charge, and lattice degrees of freedom in materials. Materials featuring multiple ferroic orders, known as multiferroics, play important roles in multi-functional electrical and magnetic device applications. 2D materials with honeycomb lattices offer exciting opportunities to engineer unconventional multiferroicity, where the ferroic orders are driven purely by the orbital degrees of freedom but not electron spin. These include ferro-valleytricity corresponding to the electron valley and ferro-orbital-magnetism supported by quantum geometric effects. Such 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 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 (tan{\Theta}H > 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\cdot B, but not the individual fields. Tuning E would switch each ferroic order independently, and achieve non-volatile switching of them together. Our observations demonstrate a new type of multiferroics and point to electrically tunable ultra-low power valleytronic and magnetic devices.

Rhombohedral stacked multilayer graphene is an ideal platform to search for correlated electron phenomena, due to its pair of flat bands touching at zero energy and further tunability by an electric field. Furthermore, its valley-dependent Berry phase at zero energy points to possible topological states when the pseudospin symmetry is broken by electron correlation. However, experimental explorations of these opportunities are very limited so far, due to a lack of devices with optimized layer numbers and configurations. Here we present electron transport measurements of hBN-encapsulated pentalayer graphene at down to 100 milli-Kelvin. We observed a correlated insulating state with >MOhm resistance at zero charge density and zero displacement field, where the tight-binding calculation predicts a metallic ground state. By increasing the displacement field, we observed a Chern insulator state with C = -5 and two other states with C = -3 at a low magnetic field of ~1 Tesla. At high displacement fields and charge densities, we observed isospin-polarized quarter- and half-metals. Therefore, rhombohedral-stacked pentalayer graphene is the first graphene system to exhibit two different types of Fermi-surface instabilities: driven by a pair of flat bands touching at zero energy, and by the Stoner mechanism in a single flat band. Our results demonstrate a new direction to explore intertwined electron correlation and topology phenomena in natural graphitic materials without the need of moir\'e superlattice engineering.

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 gamma-InSe on epsilon-GaSe, whose pronounced emission is adjustable just by varying their thicknesses given their number of layers dependent direct bandgaps. 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 \pm 0.1) {\AA} with d being very close to dSe = 3.4 {\AA} 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 moir\'e 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., Comment: ACS Nano, in press 42 pages plus, 4 figures, plus supplementary information file, containing 21 supplementary figures

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.

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 limit - the field required to reach the lowest LL - of 0.8 Tesla - unprecedentedly low for Weyl Fermions. LL spectroscopy allows us to isolate these Weyl Fermions from all other carriers in TaAs and our result provides a new way for directly exploring the more exotic quantum phenomena in Weyl semimetals, such as the chiral anomaly.

Low temperature optical spectroscopy in applied magnetic fields provides clear evidence of magnetoelastic coupling in the spin ice material Ho$_2$Ti$_2$O$_7$. In far-IR reflectometry measurements, we observe field dependent features around 30, 61, 72 and 78~meV, energies corresponding to crystal electronic field (CEF) doublets. The calculations of the crystal-field Hamiltonian model confirm that the observed features in IR spectra are consistent with magnetic-dipole-allowed excitations from the ground state to higher $^5$I$_8$ CEF levels. We present the CEF parameters that best describe our field-dependent IR reflectivity measurements. Additionally, we identify a weak field-dependent shoulder near one of the CEF doublets. This indicates that this level is split even in zero-field, which we associate with a vibronic bound state. Modeling of the observed splitting shows that the phonon resides at slightly lower energy compared to the CEF level that it couples to, which is in contrast with previously published inelastic neutron measurements. The magnetic field dependence of the vibronic state shows a gradual decoupling of the phonon with the CEF level as it shifts. This approach should work in pyrochlores and other systems that have magnetic dipole transitions in the IR spectroscopic range, which can elucidate the presence and the ability to tune the nature of vibronic states in a wide variety of materials.

Excitons are composite bosons that can feature spin singlet and triplet states. In usual semiconductors, without an additional spin-flip mechanism, triplet excitons are extremely inefficient optical emitters. Transition metal dichalcogenides (TMDs), with their large spin-orbit coupling, have been of special interest for valleytronic applications for their coupling of circularly polarized light to excitons with selective valley and spin$^{1-4}$. In atomically thin MoSe$_2$/WSe$_2$ TMD van der Waals (vdW) heterostructures, the unique atomic registry of vdW layers provides a quasi-angular momentum to interlayer excitons$^{5,6}$, enabling emission from otherwise dark spin triplet excitons. Here, we report electrically tunable spin singlet and triplet exciton emission from atomically aligned TMD heterostructures. We confirm the spin configurations of the light-emitting excitons employing magnetic fields to measure effective exciton g-factors. The interlayer tunneling current across the TMD vdW heterostructure enables the electrical generation of singlet and triplet exciton emission in this atomically thin PN junction. We demonstrate electrically tunability between the singlet and triplet excitons that are generated by charge injection. Atomically thin TMD heterostructure light emitting diodes thus enables a route for optoelectronic devices that can configure spin and valley quantum states independently by controlling the atomic stacking registry., Comment: Extended work of previous study: arXiv:1912.07678

We used a combination of polarized Raman spectroscopy and spin wave calculations to study magnetic excitations in the strong spin-orbit-coupled (SOC) bilayer perovskite antiferromagnet $Sr_3Ir_2O_7$. We observed two broad Raman features at ~ 800 $cm^{-1}$ 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 $\Gamma$ 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 RIXS magnetic excitation spectra of $Sr_3Ir_2O_7$.

Antiferromagnets display enormous potential in spintronics owing to its intrinsic nature, including terahertz resonance, multilevel states, and absence of stray fields. Combining with the layered nature, van der Waals (vdW) antiferromagnets hold the promise in providing new insights and new designs in two-dimensional (2D) spintronics. The zero net magnetic moments of vdW antiferromagnets strengthens the spin stability, however, impedes the correlation between spin and other excitation elements, like excitons. Such coupling is urgently anticipated for fundamental magneto-optical studies and potential opto-spintronic devices. Here, we report an ultra-sharp excitonic emission with excellent monochromaticity in antiferromagnetic nickel phosphorus trisulfides (NiPS3) from bulk to atomically thin flakes. We prove that the linear polarization of the excitonic luminescence is perpendicular to the ordered spin orientation in NiPS3. By applying an in-plane magnetic field to alter the spin orientation, we further manipulate the excitonic emission polarization. Such strong correlation between exciton and spins provides new insights for the study of magneto-optics in 2D materials, and hence opens a path for developing opto-spintronic devices and antiferromagnet-based quantum information technologies.

The electronic exciton polaron is a hypothetical many-body quasiparticle formed by an exciton dressed with a polarized electron-hole cloud in the Fermi sea (FS). It is predicted to display rich many-body physics and unusual roton-like dispersion. Exciton polarons were recently evoked to explain the excitonic spectra of doped monolayer transition metal dichalcogenides (TMDs), but these studies are limited to the ground state. Excited-state exciton polarons can exhibit richer many-body physics due to their larger spatial extent, but detection is challenging due to their inherently weak signals. Here we observe gate-tunable exciton polarons for the 1s - 3s excitonic Rydberg series in ultraclean monolayer MoSe$_2$ devices by optical spectroscopy. When the FS expands, we observe increasingly severe suppression and steep energy shift from low to high Rydberg states. Their gate-dependent energy shifts go beyond the trion description but match our exciton-polaron theory. Notably, the exciton-polaron absorption and emission bands are separated with an energy gap, which increases from ground to excited state. Such peculiar characteristics are attributed to the roton-like exciton-polaron dispersion, where energy minima occur at finite momenta. The roton effect increases from ground to excited state. Such exciton-polaron Rydberg series with progressively significant many-body and roton effect shall provide a new platform to explore complex many-body phenomena.

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 Moire potential modulation of the interlayer exciton. In this work, we unambiguously identify the spin-singlet and spin-triplet interlayer excitons in the WSe2/MoSe2 hetero-bilayer with a 60-degree 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 Lande g-factor of the singlet interlayer exciton and triplet interlayer exciton, which are experimentally determined to be ~ 10.7 and ~ 15.2, respectively, in good agreement with theoretical expectation. The 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 approaches 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.

Excitons are composite bosons that can feature spin singlet and triplet states. In usual semiconductors, without an additional spin-flip mechanism, triplet excitons are extremely inefficient optical emitters. Large spin-orbit coupling in transition metal dichalcogenides (TMDs) couples circularly polarized light to excitons with selective valley and spin. Here, we demonstrate electrically controlled brightening of spin-triplet interlayer excitons in a MoSe$_2$/WSe$_2$ TMD van der Waals (vdW) heterostructure. The atomic registry of vdW layers in TMD heterostructures provides a quasi-angular momentum to interlayer excitons, enabling emission from otherwise dark spin-triplet excitons. Employing magnetic field, we show that photons emitted by triplet and singlet excitons in the same valley have opposite chirality. We also measure effective exciton g-factors, presenting direct and quantitative evidence of triplet interlayer excitons. We further demonstrate gate tuning of the relative photoluminescence intensity between singlet and triplet charged excitons. Electrically controlled emission between singlet and triplet excitons enables a route for optoelectronic devices that can configure excitonic chiral, spin, and valley quantum states.

Inversion symmetry breaking and three-fold rotation symmetry grant the valley degree of freedom to the robust exciton in monolayer transition metal dichalcogenides (TMDCs), which can be exploited for valleytronics applications. However, the short lifetime of the exciton significantly constrains the possible applications. In contrast, 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 (PL) 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 (PAM) 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.

Scanning tunneling spectroscopy (STS) has yielded significant insight on the electronic structure of graphene and other two-dimensional (2D) materials. STS directly measures a fundamental and directly calculable quantity: the single particle density of states (SPDOS). Due to experimental setup limitations, however, STS has been unable to explore 2D materials in ultra-high magnetic fields where electron-electron interactions can drastically change the SPDOS. Recent developments in the assembly of heterostructures composed of graphene and hexagonal boron nitride have enabled a device-based alternative to potentially overcome these roadblocks. Thus far, however, these nascent efforts are incomplete in analyzing and understanding tunneling spectra and have yet to explore graphene at high magnetic fields. Here we report an experiment at magnetic fields up to 18 T that uses graphene tunneling field effect transistors (TFETs) to establish a clear benchmark for measurement and analysis of graphene planar tunneling spectroscopy. We acquire gate tunable tunneling spectra of graphene and then use these data and electrostatic arguments to develop a systematic analysis scheme. This analysis reveals that TFET devices directly probe electronic structure features near and far from the Fermi level. In particular, our study yields identification of the Dirac point and numerous Landau levels as they fill and empty with charge via application of a gate voltage. Our work demonstrates that TFET devices are a viable platform for directly probing the electronic structure of graphene and other 2D materials in high magnetic fields, where novel electronic states emerge.

Spin-forbidden intravalley dark exciton in tungsten-based transition metal dichalcogenides (TMDCs), owing to its unique spin texture and long lifetime, has attracted intense research interest. Here, we show that we can control the dark exciton electrostatically by dressing it with one free electron or free hole, forming the dark trions. The existence of the dark trions is suggested by the unique magneto-photoluminescence spectroscopy pattern of the boron nitride (BN) encapsulated monolayer WSe2 device at low temperature. The unambiguous evidence of the dark trions is further obtained by directly resolving the radiation pattern of the dark trions through back focal plane imaging. The dark trions possess binding energy of ~ 15 meV, and it inherits the long lifetime and large g-factor from the dark exciton. Interestingly, under the out-of-plane magnetic field, dressing the dark exciton with one free electron or hole results in distinctively different valley polarization of the emitted phonon, a result of the different intervalley scattering mechanism for the electron and hole. Finally, the lifetime of the positive dark trion can be further tuned from ~ 50 to ~ 215 ps by controlling the gate voltage. The gate tunable dark trions ushers in new opportunities for excitonic optoelectronics and valleytronics.

The valley degree of freedom is a sought-after quantum number in monolayer transition-metal dichalcogenides. Similar to optical spin orientation in semiconductors, the helicity of absorbed photons can be relayed to the valley (pseudospin) quantum number of photoexcited electrons and holes. Also similar to the quantum-mechanical spin, the valley quantum number is not a conserved quantity. Valley depolarization of excitons in monolayer transition-metal dichalcogenides due to long-range electron-hole exchange typically takes a few ps at low temperatures. Exceptions to this behavior are monolayers MoSe$_2$ and MoTe$_2$ wherein the depolarization is much faster. We elucidate the enigmatic anomaly of these materials, finding that it originates from Rashba-induced coupling of the dark and bright exciton branches next to their degeneracy point. When photoexcited excitons scatter during their energy relaxation between states next to the degeneracy region, they reach the light cone after losing the initial helicity. The valley depolarization is not as fast in monolayers WSe$_2$, WS$_2$ and likely MoS$_2$ wherein the Rashba-induced coupling is negligible., Comment: We would appreciate any feedback

Strong electronic interactions can drive a system into a state with a symmetry breaking. Lattice frustration or competing interactions tend to prevent a symmetry breaking, leading to quantum disordered phases. In spin systems frustration can produce a spin liquid state. Frustration of a charge degree of freedom also can result in various exotic states, however, experimental data on these effects is scarce. In this work we demonstrate how a charge ordered ferroelectric looses the order on cooling to low temperatures using an example of a Mott insulator on a weakly anisotropic triangular lattice $\kappa$-(BEDT-TTF)$_2$Hg(SCN)$_2$Cl. Typically, a low temperature ordered state is a ground state of a system, and the demonstrated re-entrant behavior is unique. Raman scattering spectroscopy finds that this material enters an insulating ferroelectric `dipole solid' state at $T=30~K$, but below $T=15~K$ the order melts, while preserving the insulating energy gap. The resulting phase diagram is relevant to other quantum paraelectric materials.

Monolayers of semiconducting transition metal dichalcogenides (TMDCs) with unique spin-valley contrasting properties and remarkably strong excitonic effects continue to be a subject of intense research interests. These model 2D semiconductors feature two fundamental intravalley excitons species - optically accessible ' bright' excitons with anti-parallel spins and optically inactive 'dark' excitons with parallel spins. For applications exploiting radiative recombination of bright excitons or long lifetime dark excitons, it is essential to understand the radiative character of the exciton ground state and establish the energy separation between the lowest energy bright and dark excitons. Here, we report a direct spectroscopic measure of dark excitons in monolayer MoSe$_2$ encapsulated in hexagonal boron nitride. By applying strong in-plane magnetic field, we induce mixing and splitting of bright and dark exciton branches, which enables an accurate spectroscopic determination of their energies. We confirm the bright character of the exciton ground state separated by a 1.5~meV gap from the higher energy dark exciton state, much smaller compared to the previous theoretical expectations. These findings provide critical information for further improvement of the accurate theoretical description of TMDCs electronic structure., Comment: 11 pages, 5 figures

Tungsten-based monolayer transition metal dichalcogenides host a long-lived dark exciton, an electron-hole pair in a spin-triplet configuration. The long lifetime and unique spin properties of the dark exciton provide exciting opportunities to explore light-matter interactions beyond electric dipole transitions. Here we demonstrate that the coupling of the dark exciton and an optically silent chiral phonon enables the intrinsic photoluminescence of the dark-exciton replica in monolayer WSe2. Gate and magnetic-field dependent PL measurements unveil a circularly-polarized replica peak located below the dark exciton by 21.6 meV, equal to E" phonon energy from Se vibrations. First-principles calculations show that the exciton-phonon interaction selectively couples the spin-forbidden dark exciton to the intravalley spin-allowed bright exciton, permitting the simultaneous emission of a chiral phonon and a circularly-polarized photon. Our discovery and understanding of the phonon replica reveals a chirality dictated emission channel of the phonons and photons, unveiling a new route of manipulating valley-spin.

Two-dimensional lateral heterojunctions are basic components for low-power and flexible optoelectronics. In contrast to monolayers, devices based on few-layer lateral heterostructures could offer superior performance due to their lower susceptibility to environmental conditions. Here, we report the controlled synthesis of multi-junction bilayer lateral heterostructures based on MoS2-WS2 and MoSe2-WSe2, where the hetero-junctions are created via sequential lateral edge-epitaxy that happens simultaneously in both the first and the second layer. With respect to their monolayer counterparts, bilayer lateral heterostructures yield nearly one order of magnitude higher rectification currents. They also display a clear photovoltaic response, with short circuit currents ~103 times larger than those extracted from the monolayers, in addition to room-temperature electroluminescence. The superior performance of bilayer heterostructures significantly expands the functionalities of 2D crystals.

We report the experimental observation of radiative recombination from Rydberg excitons in a two-dimensional semiconductor, monolayer WSe2, encapsulated in hexagonal boron nitride. Excitonic emission up to the 4s excited state is directly observed in photoluminescence spectroscopy in an out-of-plane magnetic field up to 31 Tesla. We confirm the progressively larger exciton size for higher energy excited states through diamagnetic shift measurements. This also enables us to estimate the 1s exciton binding energy to be about 170 meV, which is significantly smaller than most previous reports. The Zeeman shift of the 1s to 3s states, from both luminescence and absorption measurements, exhibits a monotonic increase of g-factor, reflecting nontrivial magnetic-dipole-moment differences between ground and excited exciton states. This systematic evolution of magnetic dipole moments is theoretically explained from the spreading of the Rydberg states in momentum space.

We report the observation and gate manipulation of intrinsic dark trions in monolayer WSe$_2$. By using ultraclean WSe$_2$ devices encapsulated by boron nitride, we directly resolve the weak photoluminescence of dark trions. The dark trions can be tuned continuously between negative and positive charged trions with electrostatic gating. We also reveal their spin triplet configuration and distinct valley optical emission by their characteristic Zeeman splitting under magnetic field. The dark trions exhibit large binding energy (14-16 meV). Their lifetime (~1.3 ns) is two orders of magnitude longer than the bright trion lifetime (~10 ps) and can be tuned between 0.4 to 1.3 ns by electrostatic gating. Such robust, optically detectable, and gate tunable dark trions provide a new path to realize electrically controllable trion transport in two-dimensional materials., Comment: 26 pages, 16 figures

Strong Coulomb interactions in single-layer transition metal dichalcogenides (TMDs) result in the emergence of strongly bound excitons, trions and biexcitons. These excitonic complexes possess the valley degree of freedom, which can be exploited for quantum optoelectronics. However, in contrast to the good understanding of the exciton and trion properties, the binding energy of the biexciton remains elusive, with theoretical calculations and experimental studies reporting discrepant results. In this work, we resolve the conflict by employing low-temperature photoluminescence spectroscopy to identify the biexciton state in BN encapsulated single-layer WSe2. The biexciton state only exists in charge neutral WSe2, which is realized through the control of efficient electrostatic gating. In the lightly electron-doped WSe2, one free electron binds to a biexciton and forms the trion-exciton complex. Improved understanding of the biexciton and trion-exciton complexes paves the way for exploiting the many-body physics in TMDs for novel optoelectronics applications.

Monolayer transition metal dichalcogenide (TMDC) crystals, as direct-gap materials with unusually strong light-matter interaction, have attracted much recent attention. In contrast to the initial understanding, the minima of the conduction band are predicted to be spin split. Because of this splitting and the spin-polarized character of the valence bands, the lowest-lying excitonic states in WX2 (X=S, Se) are expected to be spin-forbidden and optically dark. To date, however, there has been no direct experimental probe of these dark band-edge excitons, which strongly influence the light emission properties of the material. Here we show how an in-plane magnetic field can brighten the dark excitonic states and allow their properties to be revealed experimentally in monolayer WSe2. In particular, precise energy levels for both the neutral and charged dark excitons were obtained and compared with ab-initio calculations using the GW-BSE approach. Greatly increased emission and valley lifetimes were observed for the brightened dark states as a result of their spin configuration. These studies directly probe the excitonic spin manifold and provide a new route to tune the optical and valley properties of these prototypical two-dimensional semiconductors., Comment: 10 pages, 4 figures

In ReS$_2$ a layer-independent direct band-gap of 1.5 eV implies a potential for its use in optoelectronic applications. ReS$_2$ crystallizes in the 1T$^{\prime}$-structure which leads to anisotropic physical properties and whose concomitant electronic structure might host a non-trivial topology. Here, we report an overall evaluation of the anisotropic Raman response and the transport properties of few-layered ReS$_2$ field-effect transistors. We find that ReS$_2$ exfoliated on SiO$_2$ behaves as an $n$-type semiconductor with an intrinsic carrier mobility surpassing $\mu_i$ ~30 cm$^2$/Vs at $T = 300$ K which increases up to ~350 cm$^2$/Vs at 2 K. Semiconducting behavior is observed at low electron densities $n$, but at high values of n the resistivity decreases by a factor > 7 upon cooling to 2 K and displays a metallic $T^2$-dependence. This indicates that the band structure of 1T$^{\prime}$-ReS$_2$ is quite susceptible to an electric field applied perpendicularly to the layers. The electric-field induced metallic state observed in transition metal dichalcogenides was recently claimed to result from a percolation type of transition. Instead, through a scaling analysis of the conductivity as a function of $T$ and $n$, we find that the metallic state of ReS$_2$ results from a second-order metal to insulator transition driven by electronic correlations. This gate-induced metallic state offers an alternative to phase engineering for producing ohmic contacts and metallic interconnects in devices based on transition metal dichalcogenides., Comment: 25 pages, 5 figures

Here, we report the observation of a hitherto unreported optoelectronic effect, namely a light-induced diode-like response in multi-layered MoSe$_2$ field-effect transistors whose sense of current rectification is controllable through a gate voltage. We argue, through numerical simulations, that this behavior results from the difference in the size of the Schottky barriers between drain and source metal contacts. Each barrier can be modeled as a Schottky diode but with opposite senses of current rectification between them, with the diode response resulting from the light induced promotion of photo-generated carriers across the smaller barrier. The back gate voltage controls the sense of current rectification by modulating the relative amplitude between them. This effect, which gives rise to a novel type of optoelectronic switch, also yields a photovoltaic response. Hence, it could provide an alternative to PN-junctions when harvesting photovoltaic currents from transition metal dichalcogenides. We argue that the photovoltaic efficiency associated to this effect could be increased by just increasing the relative asymmetry between both Schottky barriers. We also suggest that this new electro-optical effect has potential for technological applications., Comment: 46 pages, including Supporting Information. 6 main figures, plus 7 supporting figures. Advanced Electronic Materials (in press)

Here, we report the photoconducting response of field-effect transistors based on three atomic layers of chemical vapor transport grown WSe$_2$ crystals mechanically exfoliated onto SiO$_2$. We find that tri-layered WSe$_2$ field-effect transistors, built with the simplest possible architecture, can display high hole mobilities ranging from 350 cm$^2$/Vs at room temperature (saturating at a value of ~500 cm$^2$/Vs below 50 K) displaying a strong photocurrent response which leads to exceptionally high photo responsivities up to 7 A/W under white light illumination of the entire channel for power densities p < 10$^2$ W/m$^2$. Under a fixed wavelength of $\lambda$ = 532 nm and a laser spot size smaller than the conducting channel area we extract photo responsitivities approaching 100 mA/W with concomitantly high external quantum efficiencies up to ~ 40 % at room temperature. These values surpass values recently reported from more complex architectures, such as graphene and transition metal dichalcogenides based heterostructures. Also, tri-layered WSe$_2$ photo-transistors display photo response times in the order of 10 microseconds. Our results indicate that the addition of a few atomic layers considerably decreases the photo response times, probably by minimizing the interaction with the substrates, while maintaining a very high photo-responsivity., Comment: 39 pages, 6 figures, and supplemental information including 5 supplemental figures. To appear in ACS Applied Materials and Interfaces

Transition metal dichalcogenides (TMDs) are layered semiconductors with indirect band gaps comparable to Si. These compounds can be grown in large area, while their gap(s) can be tuned by changing their chemical composition or by applying a gate voltage. The experimental evidence collected so far, points towards a strong interaction with light, which contrasts with the small photovoltaic efficiencies $\eta \geq 1$ % extracted from bulk crystals or exfoliated monolayers. Here, we evaluate the potential of these compounds by studying the photovoltaic response of electrostatically generated PN-junctions composed of approximately ten atomic-layers of MoSe$_2$ stacked onto the dielectric $h$-BN. In addition to ideal diode-like response, we find that these junctions can yield, under AM-1.5 illumination, photovoltaic efficiencies $\eta$ exceeding 14 %, with fill-factors of ~ 70 %. Given the available strategies for increasing $\eta$ such as gap tuning, improving the quality of the electrical contacts, or the fabrication of tandem cells, our study suggests a remarkable potential for photovoltaic applications based on TMDs., Comment: Over 25 pages with the inclusion of the supplementary information (Nano Letters, in press)