Optical Detection of Long Electron Spin Transport Lengths in a Monolayer Semiconductor.

Using a spatially resolved optical pump-probe experiment, we measure the lateral transport of spin-valley polarized electrons over very long distances (tens of micrometers) in a single WSe_{2} monolayer. By locally pumping the Fermi sea of 2D electrons to a high degree of spin-valley polarization (up to 75%) using circularly polarized light, the lateral diffusion of the electron polarization can be mapped out via the photoluminescence induced by a spatially separated and linearly polarized probe laser. Up to 25% spin-valley polarization is observed at pump-probe separations up to 20 µm. Characteristic spin-valley diffusion lengths of 18±3 µm are revealed at low temperatures. The dependence on temperature, pump helicity, pump intensity, and electron density highlight the key roles played by spin relaxation time and pumping efficiency on polarized electron transport in monolayer semiconductors possessing spin-valley locking.

Measurement of Conduction and Valence Bands g-Factors in a Transition Metal Dichalcogenide Monolayer.

The electron valley and spin degree of freedom in monolayer transition-metal dichalcogenides can be manipulated in optical and transport measurements performed in magnetic fields. The key parameter for determining the Zeeman splitting, namely, the separate contribution of the electron and hole g factor, is inaccessible in most measurements. Here we present an original method that gives access to the respective contribution of the conduction and valence band to the measured Zeeman splitting. It exploits the optical selection rules of exciton complexes, in particular the ones involving intervalley phonons, avoiding strong renormalization effects that compromise single particle g-factor determination in transport experiments. These studies yield a direct determination of single band g factors. We measure g_{c1}=0.86±0.1, g_{c2}=3.84±0.1 for the bottom (top) conduction bands and g_{v}=6.1±0.1 for the valence band of monolayer WSe_{2}. These measurements are helpful for quantitative interpretation of optical and transport measurements performed in magnetic fields. In addition, the measured g factors are valuable input parameters for optimizing band structure calculations of these 2D materials.

Measurement of the spin-forbidden dark excitons in MoS2 and MoSe2 monolayers.

Excitons with binding energies of a few hundreds of meV control the optical properties of transition metal dichalcogenide monolayers. Knowledge of the fine structure of these excitons is therefore essential to understand the optoelectronic properties of these 2D materials. Here we measure the exciton fine structure of MoS2 and MoSe2 monolayers encapsulated in boron nitride by magneto-photoluminescence spectroscopy in magnetic fields up to 30 T. The experiments performed in transverse magnetic field reveal a brightening of the spin-forbidden dark excitons in MoS2 monolayer: we find that the dark excitons appear at 14 meV below the bright ones. Measurements performed in tilted magnetic field provide a conceivable description of the neutral exciton fine structure. The experimental results are in agreement with a model taking into account the effect of the exchange interaction on both the bright and dark exciton states as well as the interaction with the magnetic field.

Revealing exciton masses and dielectric properties of monolayer semiconductors with high magnetic fields.

In semiconductor physics, many essential optoelectronic material parameters can be experimentally revealed via optical spectroscopy in sufficiently large magnetic fields. For monolayer transition-metal dichalcogenide semiconductors, this field scale is substantial-tens of teslas or more-due to heavy carrier masses and huge exciton binding energies. Here we report absorption spectroscopy of monolayer [Formula: see text], and [Formula: see text] in very high magnetic fields to 91 T. We follow the diamagnetic shifts and valley Zeeman splittings of not only the exciton's [Formula: see text] ground state but also its excited [Formula: see text] Rydberg states. This provides a direct experimental measure of the effective (reduced) exciton masses and dielectric properties. Exciton binding energies, exciton radii, and free-particle bandgaps are also determined. The measured exciton masses are heavier than theoretically predicted, especially for Mo-based monolayers. These results provide essential and quantitative parameters for the rational design of opto-electronic van der Waals heterostructures incorporating 2D semiconductors.

Control of the Exciton Radiative Lifetime in van der Waals Heterostructures.

Optical properties of atomically thin transition metal dichalcogenides are controlled by robust excitons characterized by a very large oscillator strengths. Encapsulation of monolayers such as MoSe_{2} in hexagonal boron nitride (hBN) yields narrow optical transitions approaching the homogenous exciton linewidth. We demonstrate that the exciton radiative rate in these van der Waals heterostructures can be tailored by a simple change of the hBN encapsulation layer thickness as a consequence of the Purcell effect. The time-resolved photoluminescence measurements show that the neutral exciton spontaneous emission time can be tuned by one order of magnitude depending on the thickness of the surrounding hBN layers. The inhibition of the radiative recombination can yield spontaneous emission time up to 10 ps. These results are in very good agreement with the calculated recombination rate in the weak exciton-photon coupling regime. The analysis shows that we are also able to observe a sizable enhancement of the exciton radiative decay rate. Understanding the role of these electrodynamical effects allows us to elucidate the complex dynamics of relaxation and recombination for both neutral and charged excitons.

Enabling valley selective exciton scattering in monolayer WSe2 through upconversion.

Excitons, Coulomb bound electron-hole pairs, are composite bosons and their interactions in traditional semiconductors lead to condensation and light amplification. The much stronger Coulomb interaction in transition metal dichalcogenides such as WSe2 monolayers combined with the presence of the valley degree of freedom is expected to provide new opportunities for controlling excitonic effects. But so far the bosonic character of exciton scattering processes remains largely unexplored in these two-dimensional materials. Here we show that scattering between B-excitons and A-excitons preferably happens within the same valley in momentum space. This leads to power dependent, negative polarization of the hot B-exciton emission. We use a selective upconversion technique for efficient generation of B-excitons in the presence of resonantly excited A-excitons at lower energy; we also observe the excited A-excitons state 2s. Detuning of the continuous wave, low-power laser excitation outside the A-exciton resonance (with a full width at half maximum of 4 meV) results in vanishing upconversion signal.

Gate-Controlled Spin-Valley Locking of Resident Carriers in WSe_{2} Monolayers.

Using time-resolved Kerr rotation, we measure the spin-valley dynamics of resident electrons and holes in single charge-tunable monolayers of the archetypal transition-metal dichalcogenide (TMD) semiconductor WSe_{2}. In the n-type regime, we observe long (∼130 ns) polarization relaxation of electrons that is sensitive to in-plane magnetic fields B_{y}, indicating spin relaxation. In marked contrast, extraordinarily long (∼2 µs) polarization relaxation of holes is revealed in the p-type regime, which is unaffected by B_{y}, directly confirming long-standing expectations of strong spin-valley locking of holes in the valence band of monolayer TMDs. Supported by continuous-wave Kerr spectroscopy and Hanle measurements, these studies provide a unified picture of carrier polarization dynamics in monolayer TMDs, which can guide design principles for future valleytronic devices.

In-Plane Propagation of Light in Transition Metal Dichalcogenide Monolayers: Optical Selection Rules.

The optical selection rules for interband transitions in WSe_{2}, WS_{2}, and MoSe_{2} transition metal dichalcogenide monolayers are investigated by polarization-resolved photoluminescence experiments with a signal collection from the sample edge. These measurements reveal a strong polarization dependence of the emission lines. We see clear signatures of the emitted light with the electric field oriented perpendicular to the monolayer plane, corresponding to an interband optical transition forbidden at normal incidence used in standard optical spectroscopy measurements. The experimental results are in agreement with the optical selection rules deduced from group theory analysis, highlighting the key role played by the different symmetries of the conduction and valence bands split by the spin-orbit interaction. These studies yield a direct determination of the bright-dark exciton splitting, for which we measure 40±1 meV and 55±2 meV in WSe_{2} and WS_{2} monolayer, respectively.

Control of Exciton Valley Coherence in Transition Metal Dichalcogenide Monolayers.

The direct gap interband transitions in transition metal dichalcogenide monolayers are governed by chiral optical selection rules. Determined by laser helicity, optical transitions in either the K^{+} or K^{-} valley in momentum space are induced. Linearly polarized laser excitation prepares a coherent superposition of valley states. Here, we demonstrate the control of the exciton valley coherence in monolayer WSe_{2} by tuning the applied magnetic field perpendicular to the monolayer plane. We show rotation of this coherent superposition of valley states by angles as large as 30° in applied fields up to 9 T. This exciton valley coherence control on the ps time scale could be an important step towards complete control of qubits based on the valley degree of freedom.

Double resonant Raman scattering and valley coherence generation in monolayer WSe_{2}.

The electronic states at the direct band gap of monolayer transition metal dichalcogenides such as WSe_{2} at the K^{+} and K^{-} valleys are related by time reversal and may be viewed as pseudospins. The corresponding optical interband transitions are governed by robust excitons. Excitation with linearly polarized light yields the coherent superposition of exciton pseudospin states, referred to as coherent valley states. Here, we uncover how and why valley coherence can be generated efficiently. In double resonant Raman spectroscopy, we show that the optically generated 2s exciton state differs from the 1s state by exactly the energy of the combination of several prominent phonons. Superimposed on the exciton photoluminescence (PL), we observe the double resonant Raman signal. This spectrally narrow peak shifts with the excitation laser energy as incoming photons match the 2s and outgoing photons the 1s exciton transition. The multiphonon resonance has important consequences: following linearly polarized excitation of the 2s exciton, a superposition of valley states is efficiently transferred from the 2s to 1s state. This explains the high degree of valley coherence measured for the 1s exciton PL.

Giant enhancement of the optical second-harmonic emission of WSe(2) monolayers by laser excitation at exciton resonances.

We show that the light-matter interaction in monolayer WSe_{2} is strongly enhanced when the incoming electromagnetic wave is in resonance with the energy of the exciton states of strongly Coulomb bound electron-hole pairs below the electronic band gap. We perform second harmonic generation (SHG) spectroscopy as a function of laser energy and polarization at T=4 K. At the exciton resonance energies we record an enhancement by up to 3 orders of magnitude of the SHG efficiency, due to the unusual combination of electric dipole and magnetic dipole transitions. The energy and parity of the exciton states showing the strong resonance effects are identified in 1- and 2-photon photoluminescence excitation experiments, corroborated by first principles calculations. Targeting the identified exciton states in resonant 2-photon excitation allows us to maximize k-valley coherence and polarization.

Carrier and polarization dynamics in monolayer MoS2.

In monolayer MoS2, optical transitions across the direct band gap are governed by chiral selection rules, allowing optical valley initialization. In time-resolved photoluminescence (PL) experiments, we find that both the polarization and emission dynamics do not change from 4 to 300 K within our time resolution. We measure a high polarization and show that under pulsed excitation the emission polarization significantly decreases with increasing laser power. We find a fast exciton emission decay time on the order of 4 ps. The absence of a clear PL polarization decay within our time resolution suggests that the initially injected polarization dominates the steady-state PL polarization. The observed decrease of the initial polarization with increasing pump photon energy hints at a possible ultrafast intervalley relaxation beyond the experimental ps time resolution. By compensating the temperature-induced change in band gap energy with the excitation laser energy, an emission polarization of 40% is recovered at 300 K, close to the maximum emission polarization for this sample at 4 K.

Nuclear magnetization in gallium arsenide quantum dots at zero magnetic field.

Optical and electrical control of the nuclear spin system allows enhancing the sensitivity of NMR applications and spin-based information storage and processing. Dynamic nuclear polarization in semiconductors is commonly achieved in the presence of a stabilizing external magnetic field. Here we report efficient optical pumping of nuclear spins at zero magnetic field in strain-free GaAs quantum dots. The strong interaction of a single, optically injected electron spin with the nuclear spins acts as a stabilizing, effective magnetic field (Knight field) on the nuclei. We optically tune the Knight field amplitude and direction. In combination with a small transverse magnetic field, we are able to control the longitudinal and transverse components of the nuclear spin polarization in the absence of lattice strain--that is, in dots with strongly reduced static nuclear quadrupole effects, as reproduced by our model calculations.

Dark-bright mixing of interband transitions in symmetric semiconductor quantum dots.

In photoluminescence spectra of symmetric [111] grown GaAs/AlGaAs quantum dots in longitudinal magnetic fields applied along the growth axis, we observe in addition to the expected bright states also nominally dark transitions for both charged and neutral excitons. We uncover a strongly nonmonotonic, sign-changing field dependence of the bright neutral exciton splitting resulting from the interplay between exchange and Zeeman effects. Our theory shows quantitatively that these surprising experimental results are due to magnetic-field-induced ±3/2 heavy-hole mixing, an inherent property of systems with C(3v) point-group symmetry.

Robust quantum dot exciton generation via adiabatic passage with frequency-swept optical pulses.

The energy states in semiconductor quantum dots are discrete as in atoms, and quantum states can be coherently controlled with resonant laser pulses. Long coherence times allow the observation of Rabi flopping of a single dipole transition in a solid state device, for which occupancy of the upper state depends sensitively on the dipole moment and the excitation laser power. We report on the robust population inversion in a single quantum dot using an optical technique that exploits rapid adiabatic passage from the ground to an excited state through excitation with laser pulses whose frequency is swept through the resonance. This observation in photoluminescence experiments is made possible by introducing a novel optical detection scheme for the resonant electron hole pair (exciton) generation.

Controlling the interaction of electron and nuclear spins in a tunnel-coupled quantum dot.

We present a technique for manipulating the nuclear spins and the emission polarization from a single optically active quantum dot. When the quantum dot is tunnel coupled to a Fermi sea, we have discovered a natural cycle in which an electron spin is repeatedly created with resonant optical excitation. The spontaneous emission polarization and the nuclear spin polarization exhibit a bistability. For a σ(+) pump, the emission switches from σ(+) to σ(-) at a particular detuning of the laser. Simultaneously, the nuclear spin polarization switches from positive to negative. Away from the bistability, the nuclear spin polarization can be changed continuously from negative to positive, allowing precise control via the laser wavelength.

Anomalous Hanle effect due to optically created transverse overhauser field in single InAs/GaAs quantum dots.

We report on experimental observations of an anomalous Hanle effect in individual self-assembled InAs/GaAs quantum dots. A sizable electron spin polarization photocreated under constant illumination is maintained in transverse magnetic fields as high as approximately 1 T, up to a critical field where it abruptly collapses. These striking anomalies of the Hanle curve point to a novel mechanism of dynamic nuclear spin polarization giving rise to an effective magnetic field generated perpendicular to the optically injected electron spin polarization. This transverse Overhauser field, confirmed by the cancellation of electron Zeeman splitting below the critical field, is likely to be a consequence of the strong inhomogeneous quadrupolar interactions typical for strained quantum dots.

Direct observation of the electron spin relaxation induced by nuclei in quantum dots.

We have studied the electron spin relaxation in semiconductor InAs/GaAs quantum dots by time-resolved optical spectroscopy. The average spin polarization of the electrons in an ensemble of p-doped quantum dots decays down to 1/3 of its initial value with a characteristic time T(Delta) approximately 500 ps, which is attributed to the hyperfine interaction with randomly oriented nuclear spins. We show that this efficient electron spin relaxation mechanism can be suppressed by an external magnetic field as small as 100 mT.

Electrical control of hole spin relaxation in charge tunable InAs/GaAs quantum dots.

We report on optical orientation of singly charged excitons (trions) in charge-tunable self-assembled InAs/GaAs quantum dots. When the charge varies from 0 to -2, the trion photoluminescence of a single quantum dot shows up and under quasiresonant excitation gets progressively polarized from zero to approximately 100%. This behavior is interpreted as the electric control of the trion thermalization process, which subsequently acts on the hole-spin relaxation driven in nanosecond time scale by the anisotropic electron-hole exchange. This is supported by the excitation spectroscopy and time-resolved measurements of a quantum dot ensemble.

Fine structure of highly charged excitons in semiconductor quantum dots.

An exciton in a symmetric semiconductor quantum dot has two possible states, one dark and one bright, split in energy by the electron-hole exchange interaction. We demonstrate that for a doubly charged exciton, there are also two states split by the electron-hole exchange, but both states are now bright. We also uncover a fine structure in the emission from the triply charged exciton. By measuring these splittings, and also those from the singly charged and doubly charged biexcitons, all on the same quantum dot, we show how the various electron-hole exchange energies can be measured without having to break the symmetry of the dot.