Valley Excitons Research Articles

Observation of Exciton-Exciton Interaction Mediated Valley Depolarization in Monolayer MoSe2.

The valley pseudospin in monolayer transition metal dichalcogenides (TMDs) has been proposed as a new way to manipulate information in various optoelectronic devices. This relies on a large valley polarization that remains stable over long time scales (hundreds of nanoseconds). However, time-resolved measurements report valley lifetimes of only a few picoseconds. This has been attributed to mechanisms such as phonon-mediated intervalley scattering and a precession of the valley pseudospin through electron-hole exchange. Here we use transient spin grating to directly measure the valley depolarization lifetime in monolayer MoSe2. We find a fast valley decay rate that scales linearly with the excitation density at different temperatures. This establishes the presence of strong exciton-exciton Coulomb exchange interactions enhancing the valley depolarization. Our work highlights the microscopic processes inhibiting the efficient use of the exciton valley pseudospin in monolayer TMDs.

Tunable excitons in bilayer graphene.

Excitons, the bound states of an electron and a hole in a solid material, play a key role in the optical properties of insulators and semiconductors. Here, we report the observation of excitons in bilayer graphene (BLG) using photocurrent spectroscopy of high-quality BLG encapsulated in hexagonal boron nitride. We observed two prominent excitonic resonances with narrow line widths that are tunable from the mid-infrared to the terahertz range. These excitons obey optical selection rules distinct from those in conventional semiconductors and feature an electron pseudospin winding number of 2. An external magnetic field induces a large splitting of the valley excitons, corresponding to a g-factor of about 20. These findings open up opportunities to explore exciton physics with pseudospin texture in electrically tunable graphene systems​.

Robust valley polarization of helium ion modified atomically thin MoS2

Atomically thin semiconductors have dimensions that are commensurate with critical feature sizes of future optoelectronic devices defined using electron/ion beam lithography. Robustness of their emergent optical and valleytronic properties is essential for typical exposure doses used during fabrication. Here, we explore how focused helium ion bombardement affects the intrinsic vibrational, luminescence and valleytronic properties of atomically thin . By probing the disorder dependent vibrational response we deduce the interdefect distance by applying a phonon confinement model. We show that the increasing interdefect distance correlates with disorder-related luminscence arising 180 meV below the neutral exciton emission. We perform ab initio density functional theory of a variety of defect related morphologies, which yield first indications on the origin of the observed additional luminescence. Remarkably, no significant reduction of free exciton valley polarization is observed until the interdefect distance approaches a few nanometers, namely the size of the free exciton Bohr radius. Our findings pave the way for direct writing of sub-10 nm nanoscale valleytronic devices and circuits using focused helium ions.

Exciton valley dynamics in monolayer Mo1-xWxSe2 (x = 0, 0.5, 1)

We study the exciton valley dynamics in monolayers MoSe2, Mo0.5W0.5Se2, and WSe2 by employing helicity-resolved two-color transient reflection spectroscopy. The valley depolarization dynamics as a function of the excitation laser energy is studied systematically at above-resonant excitation of excitons at 10 K. A longer intervalley scattering time is obtained as the excitation energy approaches the A exciton resonance for the three studied materials. The excitation energy dependence of exciton valley relaxation proves that the long-range electron-hole exchange interaction dominates the intervalley scattering in transition metal dichalcogenide monolayers. The longer valley scattering time and higher valley polarization degree commonly observed for WSe2 than for MoSe2 is discussed to result from the interplay between the intervalley electron-hole exchange interaction and dark-bright exciton scattering, where the existence of energetically lower lying dark excitonic states in monolayer WSe2 favors the suppression of the intervalley electron-hole exchange interaction.

Disorder-dependent valley properties in monolayer WSe2

We investigate the effect on disorder potential on exciton valley polarization and valley coherence in monolayer WSe2. By analyzing polarization properties of photoluminescence, the valley coherence (VC) and valley polarization (VP) is quantified across the inhomogeneously broadened exciton resonance. We find that disorder plays a critical role in the exciton VC, while minimally affecting VP. For different monolayer samples with disorder characterized by their Stokes Shift (SS), VC decreases in samples with higher SS while VP again remains unchanged. These two methods consistently demonstrate that VC as defined by the degree of linearly polarized photoluminescence is more sensitive to disorder potential, motivating further theoretical studies.

Valley dynamics of excitons in monolayer dichalcogenides

Monolayer transition‐metal dichalcogenides (TMDCs) have recently emerged as possible candidates for valleytronic applications, as the spin and valley pseudospin are directly coupled and stabilized by a large spin splitting. In these semiconducting materials, optically excited electron–hole pairs form tightly Coulomb‐bound excitons with large binding energies. The selection rules for excitonic transitions allow for direct optical generation of a valley‐polarized exciton population using resonant excitation. Here, we investigate the exciton valley dynamics in monolayers of three different TMDCs by means of time‐resolved Kerr rotation at low temperatures. We observe pronounced differences in the valley dynamics of tungsten‐ and molybdenum‐based TMDCs, which are directly related to the opposite order of the conduction‐band spin splitting in these materials.

Geometric decoherence of valley excitons in monolayer transition metal dichalcogenides

We study the effects of the Berry phases of the valley excitons in the monolayer transition metal dichalcogenides (TMDs) when the valley excitons are manipulated by an external terahertz field. We find that the decoherence of the valley degree of freedom of the valley excitons is spontaneously induced because of the different Berry phases of valley excitons accumulated along the opposite trajectories under the manipulation of the external field. It is called the geometric decoherence because it completely results from the geometric phases. The obvious phenomenon related to such spontaneous decoherence is the gradual decrement of the dipole moment matrix element of the valley exciton and consequently the decrement of the emitted signals after the valley excitons are recombined. Moreover, another effect due to the Berry phases is the giant Faraday rotation of the polarization of the emitted photons. Such imperfection of the valley degree of freedom is supposed to provide the potential limits of the valleytronics based on the TMDs optoelecronic devices.

Trion valley coherence in monolayer semiconductors

The emerging field of valleytronics aims to exploit the valley pseudospin of electrons residing near Bloch band extrema as an information carrier. Recent experiments demonstrating optical generation and manipulation of exciton valley coherence (the superposition of electron–hole pairs at opposite valleys) in monolayer transition metal dichalcogenides (TMDs) provide a critical step towards control of this quantum degree of freedom. The charged exciton (trion) in TMDs is an intriguing alternative to the neutral exciton for control of valley pseudospin because of its long spontaneous recombination lifetime, its robust valley polarization, and its coupling to residual electronic spin. Trion valley coherence has however been unexplored due to experimental challenges in accessing it spectroscopically. In this work, we employ ultrafast 2D coherent spectroscopy to resonantly generate and detect trion valley coherence in monolayer MoSe2 demonstrating that it persists for a few-hundred femtoseconds. We conclude that the underlying mechanisms limiting trion valley coherence are fundamentally different from those applicable to exciton valley coherence.

Apparent breakdown of Raman selection rule at valley exciton resonances in monolayerMoS2

The valley degree of freedom in atomically thin transition metal dichalcogenides (TMDCs) has generated great interest due to the possibility of using it to store and control information in analogy to the spin degree of freedom in spintronics. A signature of the valley pseudospin is the selective coupling of valley excitons to photons with defined helicity. This selectivity can have important consequences for a variety of optical phenomena associated with the valley excitons. Here we report that Raman features that seemingly violate the Raman selection rules can become prominent at valley exciton resonances in atomically thin $\mathrm{Mo}{\mathrm{S}}_{2}$. Specifically, the Raman selection rule requires the excitation and scattering photons to have opposite circular polarizations for the in-plane $E$\ensuremath{'} mode phonon, but we observe an apparent $E$\ensuremath{'} Raman peak for excitation and scattered photons with the same circular polarization at exciton resonances. We attribute this peak to a defect-assisted process that involves phonons in the transverse optical $E$\ensuremath{'} branch slightly away from the \ensuremath{\Gamma} point, a process that can be enhanced by the selective coupling of valley pseudospin to photon helicity. Thus, the valley pseudospin, in addition to the crystal symmetry, may be important in understanding the Raman scattering spectra for excitations close to valley exciton resonances.

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.

Raman-like resonant secondary emission causes valley coherence in CVD-grown monolayer MoS2

Monolayer transition metal dichalcogenides are promising materials for ``valleytronics.'' They have band gaps at energy-degenerate $K$ and ${K}^{\ensuremath{'}}$ valleys with opposite spins. Due to the lack of inversion symmetry, electron-hole pairs can be selectively created at $K$ or ${K}^{\ensuremath{'}}$ valleys by circularly polarized photons. In addition, linearly polarized light excitation creates the coherent superposition of exciton valley states, referred to as the generation of valley coherence. In this study we performed polarization resolved photoluminescence and resonant Raman spectroscopy of CVD-grown monolayer $\mathrm{Mo}{\mathrm{S}}_{2}$. We found that the lowest exciton photoluminescence becomes polarized, indicating the effective generation of valley polarization and valley coherence due to the resonant effect, accompanied by a drastic change of the polarization selection rule of Raman scattering. These results were theoretically explained from the viewpoint of the selection rules of resonant Raman scattering. We conclude that the Raman-like resonant second-order optical process should be the main mechanism of valley coherence.

Temporal and spatial valley dynamics in two-dimensional semiconductors probed via Kerr rotation

Monolayer transition metal dichalcogenides (TMDCs) offer a tantalizing platform for control of both spin and valley degrees of freedom, which may enable future optoelectronic devices with enhanced and novel functionalities. Here, we investigate the valley dynamics of two prototypical members of TMDCs, namely $\mathrm{Mo}{\mathrm{S}}_{2}$ and $\mathrm{WS}{\mathrm{e}}_{2}$, using time-resolved Kerr rotation (TRKR) at temperatures from 10 K to 300 K. This pump-probe technique enables sub-picosecond temporal resolution, providing insight into ultrafast valley dynamics, which is inaccessible by polarized and time-resolved photoluminescence spectroscopy. Bi-exponential decay dynamics were observed for both materials at low temperatures, and the fast decay component indicated a rapid exciton valley depolarization time $(l10\phantom{\rule{0.16em}{0ex}}\mathrm{ps})$ due to strong Coulomb exchange interactions between the $K$ valleys. However, the slow decay components (several tens of picoseconds) were attributed to different origins in the two materials, which were further elucidated by temperature-dependent TRKR measurements. Moreover, the spatial dependence of the TRKR intensity across $\mathrm{Mo}{\mathrm{S}}_{2}$ monolayer flakes indicated a weaker valley polarization near the edges, which is likely associated with quenched excitons near the grain boundaries or a disordered edge region in chemical vapor deposition--grown monolayers. These temporal and spatial TRKR measurements reveal insight into the complex dynamics of valley excitonic states, which will be critical for valleytronic applications of monolayer TMDCs.

Chiral topological excitons in the monolayer transition metal dichalcogenides

We theoretically investigate the chiral topological excitons emerging in the monolayer transition metal dichalcogenides, where a bulk energy gap of valley excitons is opened up by a position dependent external magnetic field. We find two emerging chiral topological nontrivial excitons states, which exactly connects to the bulk topological properties, i.e., Chern number = 2. The dependence of the spectrum of the chiral topological excitons on the width of the magnetic field domain wall as well as the magnetic filed strength is numerically revealed. The chiral topological valley excitons are not only important to the excitonic transport due to prevention of the backscattering, but also give rise to the quantum coherent control in the optoelectronic applications.

Dark excitons and the elusive valley polarization in transition metal dichalcogenides

A rate equation model for the dark and bright excitons kinetics is proposed which explains the wide variation in the observed degree of circular polarization of the PL emission in different TMDs monolayers. Our work suggests that the dark exciton states play an important, and previously unsuspected role in determining the degree of polarization of the PL emission. A dark exciton ground state provides a robust reservoir for valley polarization, which tries to maintain a Boltzmann distribution of the bright exciton states in the same valley via the intra valley bright dark exciton scattering mechanism. The dependence of the degree of circular polarization on the detuning energy of the excitation in MoSe2 suggests that the electron–hole exchange interaction dominates over two LA phonon emission mechanism for inter valley scattering in TMDs.

Exciton valley dynamics in monolayer WSe2 probed by the two-color ultrafast Kerr rotation.

The newly developed two-dimensional layered materials provide a perfect platform for valley-spintronics exploration. To determine the prospect of utilizing the valley degree of freedom, it is of great importance to directly detect and understand the valley dynamics in these materials. Here, the exciton valley dynamics in monolayer WSe2 is investigated by the two-color pump-probe magneto-optical Kerr technique. By tuning the probe photon energy in resonance with the free excitons and trions, the valley relaxation time of different excitonic states in monolayer WSe2 is determined. Valley relaxation time of the free exciton in monolayer WSe2 is confirmed to be several picoseconds. A slow valley polarization relaxation process is observed to be associated with the trions, showing that the valley lifetime for trions is one order of magnitude longer than that of free excitons. This finding suggests that trion can be a good candidate for valleytronics applications.

Excitonic Valley Effects in Monolayer WS2 under High Magnetic Fields.

Transition-metal dichalcogenides can be easily produced as atomically thin sheets, exhibiting the possibility to optically polarize and read out the valley pseudospin of extremely stable excitonic quasiparticles present in these 2D semiconductors. Here, we investigate a monolayer of tungsten disulfide in high magnetic fields up to 30 T via photoluminescence spectroscopy at low temperatures. The valley degeneracy is lifted for all optical features, particularly for excitons, singlet and triplet trions, for which we determine the g factor separately. While the observation of a diamagnetic shift of the exciton and trion resonances gives us insight into the real-space extension of these quasiparticles, magnetic field-induced valley polarization effects shed light onto the exciton and trion dispersion relations in reciprocal space. The field dependence of the trion valley polarizations is in line with the predicted trion splitting into singlet and triplet configurations.

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 9T. 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.

Optical manipulation of valley pseudospin

The coherent manipulation of spin and pseudospin underlies existing and emerging quantum technologies, including NMR, quantum communication, and quantum computation. Valley polarization, associated with the occupancy of degenerate, but quantum mechanically distinct valleys in momentum space, closely resembles spin polarization and has been proposed as a pseudospin carrier for the future quantum electronics. Valley exciton polarization has been created in the transition metal dichalcogenide (TMDC) monolayers using excitation by circularly polarized light and has been detected both optically and electrically. In addition, the existence of coherence in the valley pseudospin has been identified experimentally. The manipulation of such valley coherence has, however, remained out of reach. Here we demonstrate an all-optical control of the valley coherence by means of the pseudomagnetic field associated with the optical Stark effect. Using below-bandgap circularly polarized light, we experimentally rotate the valley exciton pseudospin in monolayer WSe2 on the femtosecond time scale. Both the direction and speed of the rotation can be optically manipulated by tuning the dynamic phase of excitons in opposite valleys. This study completes the generation-manipulation-detection paradigm for valley pseudospin, enabling the platform of excitons in 2D materials for the control of this novel degree of freedom in solids.

Exciton Dynamics in Monolayer Transition Metal Dichalcogenides.

Since the discovery of semiconducting monolayer transition metal dichalcogenides, a variety of experimental and theoretical studies have been carried out seeking to understand the intrinsic exciton population recombination and valley relaxation dynamics. Reports of the exciton decay time range from hundreds of femtoseconds to ten nanoseconds, while the valley depolarization time can exceed one nanosecond. At present, however, a consensus on the microscopic mechanisms governing exciton radiative and non-radiative recombination is lacking. The strong exciton oscillator strength resulting in up to ~ 20% absorption for a single monolayer points to ultrafast radiative recombination. However, the low quantum yield and large variance in the reported lifetimes suggest that non-radiative Auger-type processes obscure the intrinsic exciton radiative lifetime. In either case, the electron-hole exchange interaction plays an important role in the exciton spin and valley dynamics. In this article, we review the experiments and theory that have led to these conclusions and comment on future experiments that could complement our current understanding.

Direct measurement of exciton valley coherence in monolayer WSe2

In crystals, energy band extrema in momentum space can be identified by their valley index. The internal quantum degree of freedom associated with valley pseudospin indices can act as a useful information carrier analogous to electronic charge or spin. Interest in valleytronics has been revived in recent years following the discovery of atomically thin materials such as graphene and transition metal dichalcogenides. However, the valley coherence time, a key quantity for manipulating the valley pseudospin, has never been measured in any material. In this work, we use a sequence of laser pulses to resonantly generate a coherent superposition of excitons (Coulomb-bound electron-hole pairs) in opposite valleys of monolayer WSe$_2$. The imposed valley coherence persists for approximately one hundred femtoseconds. We propose that the electron-hole exchange interaction provides an important decoherence mechanism in addition to exciton population decay. Our work provides critical insight into the requirements and strategies for optical manipulation of the valley pseudospin for future valleytronics applications.