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Evidence is presented for a first-order magnetic phase transition in a gated two-dimensional semiconductor, monolayer-MoS$_2$. The phase boundary separates a spin-polarised (ferromagnetic) phase at low electron density and a paramagnetic phase at high electron density. Abrupt changes in the optical response signal an abrupt change in the magnetism. The magnetic order is thereby controlled via the voltage applied to the gate electrode of the device. Accompanying the change in magnetism is a large change in the electron effective mass.

Atomically thin semiconductors made from transition metal dichalcogenides (TMDs) are model systems for investigations of strong light-matter interactions and applications in nanophotonics, opto-electronics and valley-tronics. However, the photoluminescence spectra of TMD monolayers display a large number of features that are particularly challenging to decipher. On a practical level, monochromatic TMD-based emitters would be beneficial for low-dimensional devices but this challenge is yet to be resolved. Here, we show that graphene, directly stacked onto TMD monolayers enables single and narrow-line photoluminescence arising solely from TMD neutral excitons. This filtering effect stems from complete neutralization of the TMD by graphene combined with selective non-radiative transfer of long-lived excitonic species to graphene. Our approach is applied to four tungsten and molybdenum-based TMDs and establishes TMD/graphene heterostructures as a unique set of opto-electronic building blocks, suitable for electroluminescent systems emitting visible and near-infrared photons at near THz rate with linewidths approaching the lifetime limit., Comment: Main manuscript with 5 figures plus supplementary information file (including 9 supplementary sections and 14 supplementary figures)

We report the observation of optical second harmonic generation (SHG) in single-layer indium selenide (InSe). We measure a second harmonic signal of $>10^3$ $\textrm{cts/s}$ under nonresonant excitation using a home-built confocal microscope and a standard pulsed pico-second laser. We demonstrate that polarization-resolved SHG serves as a fast, non-invasive tool to determine the crystal axes in single-layer InSe and to relate the sharp edges of the flake to the armchair and zigzag edges of the crystal structure. Our experiment determines these angles to an accuracy better than $\pm$ $0.2^{\circ}$. Treating the two-dimensional material as a nonlinear polarizable sheet, we determine a second-order nonlinear sheet polarizability $| \chi_{\textrm{sheet}}^{(2)}|=(17.9 \pm 11.0)\times 10^{-20}$ $\textrm{m}^2 \textrm{V}^{-1}$ for single-layer InSe, corresponding to an effective nonlinear susceptibility value of $| \chi_\textrm{eff}^{(2)}| \approx (223 \pm 138) \times 10^{-12}$ $\textrm{m} \textrm{V}^{-1}$ accounting for the sheet thickness ($\textrm{d} \approx 0.8$ $\textrm{nm}$). We demonstrate that the SHG technique can also be applied to encapsulated samples to probe their crystal orientations. The method is therefore suitable for creating high quality van der Waals heterostructures with control over the crystal directions.

The optical susceptibility is a local, minimally-invasive and spin-selective probe of the ground state of a two-dimensional electron gas. We apply this probe to a gated monolayer of MoS$_2$. We demonstrate that the electrons are spin polarized. Of the four available bands, only two are occupied. These two bands have the same spin but different valley quantum numbers. We argue that strong Coulomb interactions are a key aspect of this spontaneous symmetry breaking. The Bohr radius is so small that even electrons located far apart in phase space interact, facilitating exchange couplings to align the spins.

The optics of dangling-bond-free van der Waals heterostructures containing transition metal dichalcogenides are dominated by excitons. A crucial property of a confined exciton is the quantum confined Stark effect (QCSE). Here, such a heterostructure is used to probe the QCSE by applying a uniform vertical electric field across a molybdenum disulfide (MoS$_2$) monolayer. The photoluminescence emission energies of the neutral and charged excitons shift quadratically with the applied electric field provided the electron density remains constant, demonstrating that the exciton can be polarized. Stark shifts corresponding to about half the homogeneous linewidth were achieved. Neutral and charged exciton polarizabilities of $(7.8~\pm~1.0)\times 10^{-10}~\tr{D~m~V}^{-1}$ and $(6.4~\pm~0.9)\times 10^{-10}~\tr{D~m~V}^{-1}$ at relatively low electron density ($8 \times 10^{11}~\tr{cm}^{-2}$) have been extracted, respectively. These values are one order of magnitude lower than the previously reported values, but in line with theoretical calculations. The methodology presented here is versatile and can be applied to other semiconducting layered materials as well.

We report a comparative study of rigid layer Raman-active modes in $N$-layer transition metal dichalcogenides. Trigonal prismatic (2Hc, such as MoSe$_2$, MoTe$_2$, WS$_2$, WSe$_2$) and distorted octahedral (1T', such as ReS$_2$ and ReSe$_2$) phases are considered. The Raman-active in-plane interlayer shear modes and out-of-plane interlayer breathing modes appear as well-defined features with wavenumbers in the range 0-40~cm$^{-1}$. These rigid layer modes are well-described by an elementary linear chain model from which the interlayer force constants are readily extracted. Remarkably, these force constants are all found to be of the same order of magnitude. Finally, we show that the prominent interlayer shear and breathing mode features allow high-precision hyperspectral Raman imaging of $N-$layer domains within a given transition metal dichalcogenide flake.

Van der Waals heterostuctures, made from stacks of two-dimensional materials, exhibit unique light-matter interactions and are promising for novel optoelectronic devices. The performance of such devices is governed by near-field coupling through, e.g., interlayer charge and/or energy transfer. New concepts and experimental methodologies are needed to properly describe two-dimensional heterointerfaces. Here, we report on interlayer charge and energy transfer in atomically thin metal (graphene)/semiconductor (transition metal dichalcogenide (TMD, here MoSe$_2$)) heterostructures using a combination of photoluminescence and Raman scattering spectroscopies. The photoluminescence intensity in graphene/MoSe$_2$ is quenched by more than two orders of magnitude and rises linearly with the photon flux, demonstrating a drastically shortened ($\sim 1~\tr{ps}$) room temperature MoSe$_2$ exciton lifetime. Key complementary insights are provided from analysis of the graphene and MoSe$_2$ Raman modes, which reveals net photoinduced electron transfer from MoSe$_2$ to graphene and hole accumulation in MoSe$_2$. Remarkably, the steady state Fermi energy of graphene saturates at $290\pm 15~\tr{meV}$ above the Dirac point. This behavior is observed both in ambient air and in vacuum and is discussed in terms of band offsets and environmental effects. In this saturation regime, balanced photoinduced flows of electrons and holes may transfer to graphene, a mechanism that effectively leads to energy transfer. Using a broad range of photon fluxes and diverse environmental conditions, we find that the presence of net photoinduced charge transfer has no measurable impact on the near-unity photoluminescence quenching efficiency in graphene/MoSe$_2$. This absence of correlation strongly suggests that energy transfer to graphene is the dominant interlayer coupling mechanism between atomically-thin TMDs and graphene., Comment: Physical Review X, in press. 14 pages, 7 figures, with supplemental material

Large assemblies of self-organized aluminum nanoclusters embedded in an oxide layer are formed on graphene templates and used to build tunnel-junction devices. Unexpectedly, single-electron-transport behavior with well-defined Coulomb oscillations is observed for a record junction area containing millions of metal islands. Such hybrid materials offer new prospects for single-electron electronics.

We present a combined experimental and theoretical study of resonant Raman spectroscopy in single- and triple-layer MoTe$_2$. Raman intensities are computed entirely from first principles by calculating finite differences of the dielectric susceptibility. In our analysis, we investigate the role of quantum interference effects and the electron-phonon coupling. With this method, we explain the experimentally observed intensity inversion of the $A^\prime_1$ vibrational modes in triple-layer MoTe2 with increasing laser photon energy. Finally, we show that a quantitative comparison with experimental data requires the proper inclusion of excitonic effects., Comment: Main Text (5 Figures, 1 Tables) + Supporting Information (6 Figures)

We study the effects of vertical sinusoidal vibrations on a liquid droplet with a low surface tension (ethanol) deposited on a solid substrate. In a precise range of amplitudes and frequencies, the drop exhibits a dramatic worm-like shape instability with a strong symmetry breaking, comparable to the one observed by Pucci et al. (Phys. Rev. Lett., 106 (2011) 024503) on a vibrated floating lens. However, the geometry of our system is much simpler since it does not involve the oscillation and deformation of a liquid-liquid-air contact line. We show that the Faraday waves appearing on the surface of the droplet control its shape and we draw a systematic phase diagram of the instability. A simple theoretical model allows us to derive a relation between the elongation of the droplet and the amplitude of the Faraday wave, in good agreement with measurements of both quantities., Comment: 7 pages, 4 figures

Electrostatic gating offers elegant ways to simultaneously strain and dope atomically thin membranes. Here, we report on a detailed \textit{in situ} Raman scattering study on graphene, suspended over a Si/SiO$_2$ substrate. In such a layered structure, the intensity of the Raman G- and 2D-mode features of graphene are strongly modulated by optical interference effects and allow an accurate determination of the electrostatically-induced membrane deflection, up to irreversible collapse. The membrane deflection is successfully described by an electromechanical model, which we also use to provide useful guidelines for device engineering. In addition, electrostatically-induced tensile strain is determined by examining the softening of the Raman features. Due to a small residual charge inhomogeneity $\sim 5\times 10^{10}~\rm cm^{-2}$, we find that non-adiabatic anomalous phonon softening is negligible compared to strain-induced phonon softening. These results open perspectives for innovative Raman scattering-based readout schemes in two-dimensional nanoreso

We probe the room temperature photoluminescence of $N$-layer molybdenum ditelluride (MoTe$_2$) in the continuous wave (cw) regime. The photoluminescence quantum yield of monolayer MoTe$_2$ is three times larger than in bilayer MoTe$_2$ and forty times greater than in the bulk limit. Mono- and bilayer MoTe$_2$ display almost symmetric emission lines at $1.10~\rm eV$ and $1.07~\rm eV$, respectively, which predominantly arise from direct radiative recombination of the A exciton. In contrast, $N\geq3-$layer MoTe$_2$ exhibits a much reduced photoluminescence quantum yield and a broader, redshifted and seemingly bimodal photoluminescence spectrum. The low- and high-energy contributions are attributed to emission from the indirect and direct optical band gaps, respectively. Bulk MoTe$_2$ displays a broad emission line with a dominant contribution at 0.94~eV that is assigned to emission from the indirect optical band gap. As compared to related systems (such as MoS$_2$, MoSe$_2$, WS$_2$ and WSe$_2$), the smaller energy difference between the monolayer direct optical band gap and the bulk indirect optical band gap leads to a smoother increase of the photoluminescence quantum yield as $N$ decreases. In addition, we study the evolution of the photoluminescence intensity in monolayer MoTe$_2$ as a function of the exciton formation rate $W_\mathrm{abs}$ up to $3.6\times 10^{22}~\rm{cm}^{-2} s^{-1}$. The lineshape of the photoluminescence spectrum remains largely independent of $W_\mathrm{abs}$, whereas the photoluminescence intensity grows sub-linearly above $W_\mathrm{abs}\sim 10^{21}~\rm cm^{-2} s^{-1}$. This behavior is assigned to exciton-exciton annihilation and is well-captured by an elementary rate equation model.

We investigate the interlayer phonon modes in $N$-layer rhenium diselenide (ReSe$_2$) and rhenium disulfide (ReS$_2$) by means of ultralow-frequency micro-Raman spectroscopy. These transition metal dichalcogenides exhibit a stable distorted octahedral (1T') phase with significant in-plane anisotropy, leading to sizable splitting of the (in-plane) layer shear modes. The fan-diagrams associated with the measured frequencies of the interlayer shear modes and the (out-of-plane) interlayer breathing modes are perfectly described by a finite linear chain model and allow the determination of the interlayer force constants. Nearly identical values are found for ReSe$_2$ and ReS$_2$. The latter are appreciably smaller than but on the same order of magnitude as the interlayer force constants reported in graphite and in trigonal prismatic (2Hc) transition metal dichalcogenides (such as MoS$_2$, MoSe$_2$, MoTe$_2$, WS$_2$, WSe$_2$), demonstrating the importance of van der Waals interactions in $N$-layer ReSe$_2$ and ReS$_2$. In-plane anisotropy results in a complex angular dependence of the intensity of all Raman modes, which can be empirically utilized to determine the crystal orientation. However, we also demonstrate that the angular dependence of the Raman response drastically depends on the incoming photon energy, shedding light on the importance of resonant exciton-phonon coupling in ReSe$_2$ and ReS$_2$.

$N$-layer transition metal dichalcogenides provide a unique platform to investigate the evolution of the physical properties between the bulk (three dimensional) and monolayer (quasi two-dimensional) limits. Here, using high-resolution micro-Raman spectroscopy, we report a unified experimental description of the $\Gamma$-point optical phonons in $N$-layer $2H$-molybdenum ditelluride (MoTe$_2$). We observe a series of $N$-dependent low-frequency interlayer shear and breathing modes (below $40~\rm cm^{-1}$, denoted LSM and LBM) and well-defined Davydov splittings of the mid-frequency modes (in the range $100-200~\rm cm^{-1}$, denoted iX and oX), which solely involve displacements of the chalcogen atoms. In contrast, the high-frequency modes (in the range $200-300~\rm cm^{-1}$, denoted iMX and oMX), arising from displacements of both the metal and chalcogen atoms, exhibit considerably reduced splittings. The manifold of phonon modes associated with the in-plane and out-of-plane displacements are quantitatively described by a force constant model, including interactions up to the second nearest neighbor and surface effects as fitting parameters. The splittings for the iX and oX modes observed in $N$-layer crystals are directly correlated to the corresponding bulk Davydov splittings between the $E_{2u}/E_{1g}$ and $B_{1u}/A_{1g}$ modes, respectively, and provide a measurement of the frequencies of the bulk silent $E_{2u}$ and $B_{1u}$ optical phonon modes. Our analysis could readily be generalized to other layered crystals., Comment: Main Text (5 Figures, 2 Tables) + Supporting Information (12 Figures)

We report a comprehensive micro-Raman scattering study of electrochemically-gated graphene field-effect transistors. The geometrical capacitance of the electrochemical top-gates is accurately determined from dual-gated Raman measurements, allowing a quantitative analysis of the frequency, linewidth and integrated intensity of the main Raman features of graphene. The anomalous behavior observed for the G-mode phonon is in very good agreement with theoretical predictions and provides a measurement of the electron-phonon coupling constant for zone-center ($\Gamma$ point) optical phonons. In addition, the decrease of the integrated intensity of the 2D-mode feature with increasing doping, makes it possible to determine the electron-phonon coupling constant for near zone-edge (K and K' points) optical phonons. We find that the electron-phonon coupling strength at $\Gamma$ is five times weaker than at K (K'), in very good agreement with a direct measurement of the ratio of the integrated intensities of the resonant intra- (2D') and inter-valley (2D) Raman features. We also show that electrochemical reactions, occurring at large gate biases, can be harnessed to efficiently create defects in graphene, with concentrations up to approximately $1.4\times 10^{12}~\rm cm^{-2}$. At such defect concentrations, we estimate that the electron-defect scattering rate remains much smaller than the electron-phonon scattering rate. The evolution of the G- and 2D-mode features upon doping remain unaffected by the presence of defects and the doping dependence of the D mode closely follows that of its two-phonon (2D mode) overtone. Finally, the linewidth and frequency of the G-mode phonon as well as the frequencies of the G- and 2D-mode phonons in doped graphene follow sample-independent correlations that can be utilized for accurate estimations of the charge carrier density., Comment: 18 pages, 14 figures, 1 table

The near-field Coulomb interaction between a nano-emitter and a graphene monolayer results in strong F\"orster-type resonant energy transfer and subsequent fluorescence quenching. Here, we investigate the distance dependence of the energy transfer rate from individual, i) zero-dimensional CdSe/CdS nanocrystals and ii) two-dimensional CdSe/CdS/ZnS nanoplatelets to a graphene monolayer. For increasing distances $d$, the energy transfer rate from individual nanocrystals to graphene decays as $1/d^4$. In contrast, the distance dependence of the energy transfer rate from a two-dimensional nanoplatelet to graphene deviates from a simple power law, but is well described by a theoretical model, which considers a thermal distribution of free excitons in a two-dimensional quantum well. Our results show that accurate distance measurements can be performed at the single particle level using graphene-based molecular rulers and that energy transfer allows probing dimensionality effects at the nanoscale., Comment: Main text (+ 5 figures) and Supporting Information (+ 7 figures)

Lubrication theory is broadly applicable to the flow characterization of thin fluid films and the motion of particles near surfaces. We offer an extension to lubrication theory by starting with Stokes equations and considering higher-order terms in a systematic perturbation expansion to describe the fluid flow in a channel with features of a modest aspect ratio. Experimental results qualitatively confirm the higher-order analytical solutions while numerical results are in very good agreement with the higher-order analytical results. We show that the extended lubrication theory is a robust tool for an accurate estimate of pressure drop in channels with shape changes on the order of the channel height, accounting for both smooth and sharp changes in geometry., Comment: 15 pages, 6 figures