Optical valley Hall effect for highly valley-coherent exciton-polaritons in an atomically thin semiconductor
Nils Lundt, Lukasz Dusanowski, Evgeny Sedov, Petr Stepanov, Mikhail M. Glazov, Sebastian Klembt, Martin Klaas, Johannes Beierlein, Ying Qin, Sefaattin Tongay, M… 展开作者
Nils Lundt, Lukasz Dusanowski, Evgeny Sedov, Petr Stepanov, Mikhail M. Glazov, Sebastian Klembt, Martin Klaas, Johannes Beierlein, Ying Qin, Sefaattin Tongay, Maxime Richard, Alexey V. Kavokin, Sven Höfling, Christian Schneider
Spin-orbit coupling is a fundamental mechanism that connects the spin of a charge carrier with its momentum. Likewise, in the optical domain, a synthetic spin-orbit coupling is accessible, for instance, by engineering optical anisotropies in photonic materials. Both, akin, yield the possibility to create devices directly harnessing spin- and polarization as information carriers. Atomically thin layers of transition metal dichalcogenides provide a new material platform which promises intrinsic spin-valley Hall features both for free carriers, two-particle excitations (excitons), as well as for photons. In such materials, the spin of an exciton is closely linked to the high-symmetry point in reciprocal space it emerges from. Here, we demonstrate, that spin, and hence valley selective propagation is accessible in an atomically thin layer of MoSe2, which is strongly coupled to a microcavity photon mode. We engineer a wire-like device, where we can clearly trace the flow, and the helicity of exciton-polaritons expanding along a channel. By exciting a coherent superposition of K and K- tagged polaritons, we observe valley selective expansion of the polariton cloud without neither any applied external magnetic fields nor coherent Rayleigh scattering. Unlike the valley Hall effect for TMDC excitons, the observed optical valley Hall effect (OVHE) strikingly occurs on a macroscopic scale, and clearly reveals the potential for applications in spin-valley locked photonic devices.
Atomically-thin transition metal dichalcogenide crystals (TMDCs) hold great promise for future semiconductor optoelectronics due to their unique electronic and optical properties. In particular, electron-hole pairs (excitons) in TMDCs are stable at room temperature and interact strongly with light. When TMDCs are embedded in an optical microcavity, the excitons can hybridise with cavity photons to form exciton polaritons (polaritons herein), which display both ultrafast velocities and strong interactions. The ability to manipulate and trap polaritons on a microchip is critical for future appli…
We investigate the interactions between exciton-polaritons in N two-dimensional semiconductor layers embedded in a planar microcavity. In the limit of low-energy scattering, where we can ignore the composite nature of the excitons, we obtain exact analytical expressions for the spin-triplet and spin-singlet interaction strengths, which go beyond the Born approximation employed in previous calculations. Crucially, we find that the strong light-matter coupling enhances the strength of polariton-polariton interactions compared to that of the exciton-exciton interactions, due to the Rabi coupling …
We present a numerical study of exciton-polariton (polariton) condensation in a staggered polariton graphene showing a gapped s-band at the $K$ and $K'$ valleys. The condensation occurs at $K$ or $K'$, at the kinetically-favorable negative mass extrema of the valence band. Considering attractive polariton-polariton interaction allows to generate a spatially extended condensate. Spontaneous symmetry breaking occurring during the condensate build-up leads to the formation of valley-polarized domains following the Kibble-Zurek scenario. The selection of a single valley breaks time-reversal symmet…
The newly discovered valley degree of freedom in atomically thin two-dimensional transition metal dichalcogenides (TMD) offers a promising platform to explore rich nonlinear physics, such as spinor Bose-Einstein condensate (BEC) and novel valleytronics applications. However, the critical nonlinear effect, such as valley polariton bosonic stimulation, has long remained an unresolved challenge due to the generation of limited polariton ground state densities necessary to induce the stimulated scattering of polaritons in specific valleys. Here, we report the self-induced valley bosonic stimulatio…
Atomically thin crystals of transition metal dichalcogenides are ideally suited to study the interplay of light-matter coupling, polarization and magnetic field effects. In this work, we investiagte the formation of exciton-polaritons in a MoSe2 monolayer, which is integrated in a fully-grown, monolithic microcavity. Due to the narrow linewidth of the polaritonic resonances, we are able to directly investigate the emerging valley Zeeman splitting of the hybrid light-matter resonances in the presence of a magnetic field. At a detuning of -54.5 meV (13.5 % matter constituent of the lower polarit…
Dispersion engineering is a powerful and versatile tool that can vary the speed of light signals and induce negative-mass effects in the dynamics of particles and quasiparticles. Here, we show that dissipative coupling between bound electron-hole pairs (excitons) and photons in an optical microcavity can lead to the formation of exciton polaritons with an inverted dispersion of the lower polariton branch and hence a negative mass. We perform direct measurements of the anomalous dispersion in atomically thin (monolayer) WS$_2$ crystals embedded in planar microcavities and demonstrate that the p…
Transition metal dichalcogenide semiconductors represent elementary components of layered heterostructures for emergent technologies beyond conventional opto-electronics. In their monolayer form they host electrons with quantized circular motion and associated valley polarization and valley coherence as key elements of opto-valleytronic functionality. Here, we introduce two-dimensional polarimetry as means of direct imaging of the valley pseudospin degree of freedom in monolayer transition metal dichalcogenides. Using MoS$_2$ as a representative material with valley-selective optical transitio…
We consider exciton-polaritons in a honeycomb lattice of micropillars subjected to circularly polarized (${σ_\pm}$) incoherent pumps, which are arranged to form two domains in the lattice. We predict that the nonlinear interaction between the polaritons and the reservoir excitons gives rise to the topological valley Hall effect where in each valley two counterpropagating helical edge modes appear. Under a resonant pump, ${σ_\pm}$ polaritons propagate in different directions without being reflected around bends. The polaritons propagating along the interface have extremely high effective lifeti…
Electrons hopping in two-dimensional honeycomb lattices possess a valley degree of freedom in addition to charge and spin. In the absence of inversion symmetry, these systems were predicted to exhibit opposite Hall effects for electrons from different valleys. Such valley Hall effects have been achieved only by extrinsic means, such as substrate coupling, dual gating, and light illuminating. Here, we report the first observation of intrinsic valley Hall transport without any extrinsic symmetry breaking in the non-centrosymmetric monolayer and trilayer MoS2, evidenced by considerable nonlocal r…
Anomalous valley Hall dynamics of exciton-polaritons
East China Normal University（华东师范大学）；Institute of Science and Technology Austria（奥地利科学技术研究所）；Tsinghua University（清华大学）；Aarhus University（奥胡斯大学）；Shanxi University（山西大学）
Two-dimensional transition metal dichalcogenide (TMD) semiconductors provide a unique possibility to access the electronic valley degree of freedom using polarized light, opening the way to valley information transfer between distant systems. Excitons with a well-defined valley index (or valley pseudospin) as well as superpositions of the exciton valley states can be created with light having circular and linear polarization, respectively. However, the generated excitons have short lifetimes (ps) and are also subject to the electron-hole exchange interaction leading to fast relaxation of the v…
Monolayer transition metal dichalcogenides, known for exhibiting strong excitonic resonances, constitute a very interesting and versatile platform for investigation of light-matter interactions. In this work we report on a strong coupling regime between excitons in monolayer WSe2 and photons confined in an open, voltage-tunable dielectric microcavity. The tunability of our system allows us to extend the exciton-polariton state over a wide energy range and, in particular, to bring the excitonic component of the lower polariton mode into resonance with other excitonic transitions in monolayer WS…
As hosts for tightly-bound electron-hole pairs carrying quantized angular momentum, atomically-thin semiconductors of transition metal dichalcogenides provide an appealing platform for optically addressing the valley degree of freedom. In particular, the valleytronic properties of neutral and charged excitons in these systems have been widely investigated. Meanwhile, correlated quantum states involving more particles are so far elusive and controversial. Here we present experimental evidence for valleytronic four-particle biexcitons and five-particle exciton-trions in high-quality monolayer tu…
We apply a microscopic theory of exciton-polaritons in cavity-confined monolayer transition-metal dichalcogenides including both optical polarizations in the monolayer plane, allowing to describe how chiral cavity photons interact with the valley degrees of freedom of the active material. Upon polariton formation, the degenerate excitons inhabiting the two inequivalent valleys are shown to assume bonding and antibonding superpositions as a result of cavity-mediated intravalley interactions combined with intervalley Coulomb interactions. This is representative of a polariton-induced coherent mi…
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 bombardment affects the intrinsic vibrational, luminescence and valleytronic properties of atomically thin MoS$_{2}$. By probing the disorder dependent vibrational response we deduce the interdefect distance by applying a phonon confinement model. We show…
Localization of charge carriers in monolayers (MLs) of transition metal dichalcogenides (TMDs) dramatically increases spin and valley coherence times, and, by analogy with other systems, the role of the hyperfine interaction should enhance. We perform theoretical analysis of the intervalley hyperfine interaction in TMD MLs based on the group representation theory. We demonstrate, that the spin-valley locking leads to the helical structure of the in-plane hyperfine interaction. In the upper valence band the hyperfine interaction is shown to be of the Ising type, which can be used for fabricatio…
The emergence of two-dimensional crystals has revolutionized modern solid-state physics. From a fundamental point of view, the enhancement of charge carrier correlations has sparked enormous research activities in the transport- and quantum optics communities. One of the most intriguing effects, in this regard, is the bosonic condensation and spontaneous coherence of many-particle complexes. Here, we find compelling evidence of bosonic condensation of exciton-polaritons emerging from an atomically thin crystal of MoSe2 embedded in a dielectric microcavity under optical pumping. The formation o…
Keldysh field theory of spin- and valley-distinguished polariton nonlinearities in transition-metal dichalcogenide monolayers
Abrikosov Center for Theoretical Physics, Moscow Center for Advanced Studies（阿布里科索夫理论物理中心，莫斯科高等研究中心）；National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)（国立研究核大学MEPhI（莫斯科工程物理学院））；Russian Quantum Center, Skolkovo IC（俄罗斯量子中心，斯科尔科沃创新中心）
In monolayers of transition metal dichalcogenides the nonlocal nature of the effective dielectric screening leads to large binding energies of excitons. Additional lateral confinement gives rise to exciton localization in quantum dots. By assuming parabolic confinement for both the electron and the hole, we derive model wave functions for the relative and the center-of-mass motions of electron-hole pairs, and investigate theoretically resonant energy transfer among excitons localized in two neighboring quantum dots. We quantify the probability of energy transfer for a direct-gap transition by …
Strong spin-orbit coupling and inversion symmetry breaking in transition metal dichalcogenide monolayers yield the intriguing effects of valley-dependent optical selection rules. As such, it is possible to substantially polarize valley excitons with chiral light and furthermore create coherent superpositions of K and K- polarized states. Yet, at ambient conditions dephasing usually becomes too dominant, and valley coherence typically is not observable. Here, we demonstrate that valley coherence is, however, clearly observable for a single monolayer of WSe2, if it is strongly coupled to the opt…
We show that a nonlinear optical response associated with a resonant, atomically thin material can be dramatically enhanced by placing it in front of a partially reflecting mirror, rendering otherwise weakly nonlinear systems suitable for experiments and applications involving quantum nonlinear optics. Our approach exploits the nonlinear response of long-lived polariton resonances that arise at particular distances between the material and the mirror. The scheme is entirely based on free-space optics, eliminating the need for cavities or complex nanophotonic structures. We analyze a specific i…
Twisted atomically thin semiconductors are characterized by moiré excitons. Their optical signatures and selection rules are well understood. However, their hybridization with photons in the strong coupling regime for heterostructures integrated in an optical cavity has not been in the focus of research yet. Here, we combine an excitonic density matrix formalism with a Hopfield approach to provide microscopic insights into moiré exciton polaritons. In particular, we show that exciton-light coupling, polariton energy, and even the number of polariton branches can be controlled via the twist ang…
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 momentu…
Systems with strong light-matter interaction opens up new avenues for studying topological phases of matter. Examples include exciton-polaritons, mixed light-matter quasiparticles, where the topology of the polaritonic band structure arises from the collective coupling between matter wave and optical fields strongly confined in periodic dielectric structures. Distinct from light-matter interaction in a uniform environment, the spatially varying nature of the optical fields leads to a fundamental modification of the well-known optical selection rules, which were derived under the plane wave app…
Atomically thin transition metal dichalcogenides (TMDs) possess a number of properties that make them attractive for realizing room-temperature polariton devices. An ideal platform for manipulating polariton fluids within monolayer TMDs is that of Bloch surface waves, which confine the electric field to a small volume near the surface of a dielectric mirror. Here we demonstrate that monolayer tungsten disulfide ($\text{WS}_2$) can sustain Bloch surface wave polaritons (BSWPs) with a Rabi splitting of 43 meV and propagation constants reaching 33 $μ$m. In addition, we evidence strong polariton-p…
Monolayers of transition metal dichalcogenides (TMDCs) exhibit an exceptionally strong Coulomb interaction between charge carriers due to the two-dimensional carrier confinement in connection with weak dielectric screening. High densities of excited charge carriers in the various band-structure valleys cause strong many-body renormalizations that influence both the electronic properties and the optical response of the material. We investigate electronic and optical properties of the typical monolayer TMDCs MoS$_2$, MoSe$_2$, WS$_2$ and WSe$_2$ in the presence of excited carriers by solving sem…
Recent experiments in exciton-polariton systems have provided high-precision measurements of the value of the polariton-polariton interaction constant, which is a key parameter that governs the nonlinear dynamics of polariton condensates and potentially enables quantum correlated polaritons. Yet, until now, this parameter has only been addressed theoretically using perturbative treatments or approximations that do not include the composite nature of the excitons. Here, we use a recently developed microscopic description of polaritons involving electrons, holes, and photons, where the interacti…
Nonlinear optical effects such as four-wave mixing and generation of squeezed light are ubiquitous in optical devices and light sources. For new devices operating at low optical power, the resonant nonlinearity arising from the two-photon sensitive bound biexciton in a semiconductor microcavity is an interesting prospective platform. Due to the particularly strong Coulomb interaction in atomically thin semiconductors, these materials have strongly bound biexcitons and operate in the visible frequency range of the electromagnetic spectrum. To remove the strong pump laser from the generated ligh…
Quantum emitters (QEs) in two-dimensional transition metal dichalcogenides (2D TMDCs) have advanced to the forefront of quantum communication and transduction research due to their unique potentials in accessing valley pseudo-spin degree of freedom (DOF) and facile integration into quantum-photonic, electronic and sensing platforms via the layer-by-layer-assembly approach. To date, QEs capable of operating in O-C telecommunication bands have not been demonstrated in TMDCs. Here we report a deterministic creation of such telecom QEs emitting over the 1080 to 1550 nm wavelength range via couplin…
The rise of quantum science and technologies motivates photonics research to seek new platforms with strong light-matter interactions to facilitate quantum behaviors at moderate light intensities. One promising platform to reach such strong light-matter interacting regimes is offered by polaritonic metasurfaces, which represent ultrathin artificial media structured on nano-scale and designed to support polaritons - half-light half-matter quasiparticles. Topological polaritons, or 'topolaritons', offer an ideal platform in this context, with unique properties stemming from topological phases of…
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 mome…
We develop a microscopic description of an electron-doped two-dimensional semiconductor embedded in a microcavity. Specifically, we investigate the interactions between exciton-polaritons and electrons for the case where the interactions between charges are strongly screened and the system is spin polarized. As a starting point, we obtain an analytic expression for the exciton-polariton wave function, and we relate the microscopic parameters of the light-matter system to experimentally measurable quantities, such as the Rabi coupling and the cavity photon frequency. We then derive the polarito…
In this paper, we present a novel route to tunable spontaneous valley coherence in heterostructures of two dimensional valleytronic materials with other layered materials hosting anisotropic polaritonic modes. We first discuss the dependence of this coherence on the conductivity tensor of the anisotropic part of a general heterostructure and on its geometrical configuration. Subsequently, we propose two implementations - one, using anisotropic plasmons in phosphorene and another with hyperbolic phonon polaritons in MoO3. In both these systems we show for the first time electrostatic tunability…
Plasmon polaritons in van der Waals (vdW) materials hold promise for next-generation photonics. The ability to deterministically imprint spatial patterns of high carrier density in cavities and circuitry with nanoscale features underlies future progress in nonlinear nanophotonics and strong light-matter interactions. Here, we demonstrate a general strategy to atomically imprint low-loss graphene plasmonic structures using oxidation-activated charge transfer (OCT). We cover graphene with a monolayer of WSe$_2$, which is subsequently oxidized into high work-function WOx to activate charge transf…
Atomically thin semiconductors such as transition metal dichalcogenide (TMD) monolayers exhibit a very strong Coulomb interaction, giving rise to a rich exciton landscape. This makes these materials highly attractive for efficient and tunable optoelectronic devices. In this article, we review the recent progress in the understanding of exciton optics, dynamics and transport, which crucially govern the operation of TMD-based devices. We highlight the impact of hBN-encapsulation, which reveals a plethora of many-particle states in optical spectra, and we outline the most novel breakthroughs in t…
The emergence of spatial and temporal coherence of light emitted from solid-state systems is a fundamental phenomenon, rooting in a plethora of microscopic processes. It is intrinsically aligned with the control of light-matter coupling, and canonical for laser oscillation. However, it also emerges in the superradiance of multiple, phase-locked emitters, and more recently, coherence and long-range order have been investigated in bosonic condensates of thermalized light, as well as in exciton-polaritons driven to a ground state via stimulated scattering. Here, we experimentally show that the in…
We develop the theory of the spin and valley Hall effects in two-dimensional systems caused by asymmetric -- skew -- scattering of the quasiparticles. The collision integral is derived in the third order in the particle-particle interaction with account for the spin-orbit coupling both for bosons and fermions. It is shown that the scattering asymmetry appears only in the processes where the interaction between the particles in the initial and intermediate state is present. We show that for degenerate electrons or nondegenerate particles the spin and valley currents induced by interparticle col…
