We have examined the electronic structure evolution in transition metal dichalcogenides MX$_2$, where M=Mo,W and X=S,Se and Te. These are generally referred to as van der Waals heterostructures on the one hand, yet one has band gap changes as large as 0.6 eV with thickness in some instances. This does not seem to be consistent with a description where the dominant interactions are van der Waals interactions. Mapping onto a tight binding model allows us to quantify the electronic structure changes which are found to be dictated solely by interlayer hopping interactions. Different environments that an atom encounters could change the Madelung potential and therefore the onsite energies. This could happen while going from monolayer to bilayer as well as in cases where the stackings are different from what is found in 2H structures. These effects are quantitatively found to be negligible, enabling us to quantify the thickness dependent electronic structure changes as arising from interlayer interactions alone.
In this paper we develop a fully microscopic theory of the polarizability of excitons in transition metal dichalcogenides. We apply our method to the description of the excitation $2$p dark states. These states are not observable in absorption experiments but can be excited in a pump-probe experiment. As an example we consider $2$p dark states in WSe\textsubscript{2}. We find a good agreement between recent experimental measurements and our theoretical calculations.
Using an equation of motion (EOM) approach, we calculate excitonic properties of monolayer transition metal dichalcogenides (TMDs) perturbed by an external magnetic field. We compare our findings to the widely used Wannier model for excitons in two-dimensional materials and to recent experimental results. We find good agreement between the calculated excitonic transition energies and the experimental results. In addition, we find that the exciton energies calculated using the EOM approach are slightly lower than the ones calculated using the Wannier model. Finally, we also show that the effect…
Microscopic origin of Rashba coupling from first principles: Layer-resolved orbital asymmetry in transition metal dichalcogenides
University of Hamburg（汉堡大学）；Max Planck Institute for the Structure and Dynamics of Matter（马克斯·普朗克物质结构与动力学研究所）；The Hamburg Centre for Ultrafast Imaging（汉堡超快成像中心）
A fully microscopic model of the doping-dependent exciton and trion line widths in the absorption spectra of monolayer transition metal dichalcogenides in the low temperature and low doping regime is explored. The approach is based on perturbation theory and avoids the use of phenomenological parameters. In the low-doping regime, we find that the trion line width is relatively insensitive to doping levels while the exciton line width increases monotonically with doping. On the other hand, we argue that the trion line width shows a somewhat stronger temperature dependence. The magnitudes of the…
The band structure of many semiconducting monolayer transition metal dichalcogenides (TMDs) possesses two degenerate valleys, with equal and opposite Berry curvature. It has been predicted that, when illuminated with circularly polarized light, interband transitions generate an unbalanced non-equilibrium population of electrons and holes in these valleys, resulting in a finite Hall voltage at zero magnetic field when a current flows through the system. This is the so-called valley Hall effect that has recently been observed experimentally. Here, we show that this effect is mediated by photo-ge…
We present a microscopic study on higher excitonic states in transition metal dichalcogenides in the presence of disorder. We show that the geometric phase cancels the degeneration of 2s and 2p states and that a significant disorder-induced coupling of bright and dark states offers a strategy to circumvent optical selection rules. As a prove, we show a direct fingerprint of dark 2p states in absorption spectra of WS$_2$. The predicted softening of optical selection rules through exciton-disorder coupling is of general nature and therefore applicable to related two-dimensional semiconductors.
Atomically thin transition metal dichalcogenides (TMDs) are direct-gap semiconductors with strong light-matter and Coulomb interaction. The latter accounts for tightly bound excitons, which dominate the optical properties of these technologically promising materials. Besides the optically accessible bright excitons, these systems exhibit a variety of dark excitonic states. They are not visible in optical spectra, but can strongly influence the coherence lifetime and the linewidth of the emission from bright exciton states. In a recent study, an experimental evidence for the existence of such d…
We analyze the properties of strongly coupled excitons and photons in systems made of semiconducting two-dimensional transition-metal dichalcogenides embedded in optical cavities. Through a detailed microscopic analysis of the coupling we unveil novel, highly tunable features of the spectrum, that result in polariton splitting and a breaking of light-matter selection rules. The dynamics of the composite polaritons is influenced by the Berry phase arising both from their constituents and from the confinement-enhanced coupling. We find that light-matter coupling emerges as a mechanism that enhan…
Using a multiscale computational approach, we probe the origin and evolution of ultraflatbands in moiré superlattices of twisted bilayer MoS$_2$, a prototypical transition metal dichalcogenide. Unlike twisted bilayer graphene, we find no unique magic angles in twisted bilayer MoS$_2$ for flatband formation. Ultraflatbands form at the valence band edge for twist angles ($θ$) close to 0$^\circ$ and at both the valence and conduction band edges for $θ$ close to 60$^\circ$, and have distinct origins. For$ θ$ close to 0$^\circ$, inhomogeneous hybridization in the reconstructed moiré superlattice is…
We investigate the spin-nonconserving relaxation channel of excitons by their couplings with phonons in two-dimensional transition metal dichalcogenides using $\textit{ab initio}$ approaches. Combining $\text{GW}$-Bethe-Salpeter equation method and density functional perturbation theory, we calculate the electron-phonon and exciton-phonon coupling matrix elements for the spin-flip scattering in monolayer WSe$_{\text{2}}$, and further analyze the microscopic mechanisms influencing these scattering strengths. We find that phonons could produce effective in-plane magnetic fields which flip spin o…
The photoluminescence (PL) spectrum of transition metal dichalcogenides (TMDs) shows a multitude of emission peaks below the bright exciton line and not all of them have been explained yet. Here, we study the emission traces of phonon-assisted recombinations of momentum-dark excitons. To this end, we develop a microscopic theory describing simultaneous exciton, phonon and photon interaction and including consistent many-particle dephasing. We explain the drastically different PL below the bright exciton in tungsten- and molybdenum-based materials as result of different configurations of bright…
The recent accessibility of high quality, charge neutral monolayer transition metal dichalcogenides with narrow exciton linewidths at the homogeneous limit provides an ideal platform to study excitonic many-body interactions. In particular, the possibility to manipulate coherent exciton-exciton interactions, which govern the ultrafast nonlinear optical response, by applying an external magnetic field has not been considered so far. We address this discrepancy by presenting a nonlinear microscopic theory in the coherent limit for optical excitations in the presence of out-of-plane, in-plane, an…
Monolayer transition metal dichalcogenides (TMDs) have been in focus of current research, among others due to their remarkable exciton landscape consisting of bright and dark excitonic states. Although dark excitons are not directly visible in optical spectra, they have a large impact on exciton dynamics and hence their understanding is crucial for potential TMD-based applications. Here, we study brightening mechanisms of dark excitons via interaction with phonons and in-plane magnetic fields. We show clear signatures of momentum- and spin-dark excitons in WS$_2$, WSe$_2$ and MoS$_2$, while th…
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 decay 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% ab…
We have addressed the microscopic transport mechanism at the switching or on-off transition in transition metal dichalcogenide (TMDC) field-effect transistors (FET), which has been a controversial topic in TMDC electronics, especially at room temperature. With simultaneous measurement of channel conductivity and its slow time-dependent fluctuation (or noise) in ultra-thin WSe2 and MoS2 FETs on insulating SiO2 substrates, where noise arises from McWhorter-type carrier number fluctuations, we establish that the switching in conventional backgated TMDC FETs is a classical percolation transition i…
We study theoretically effects of an anisotropic elastic strain on the exciton energy spectrum fine structure and optical selection rules in atom-thin crystals based on transition-metal dichalcogenides. The presence of strain breaks the chiral selection rules at the $\bm K$-points of the Brillouin zone and makes optical transitions linearly polarized. The orientation of the induced linear polarization is related to the main axes of the strain tensor. Elastic strain provides an additive contribution to the exciton fine structure splitting in agreement with experimental evidence obtained from un…
Cooperative effects allow for fascinating characteristics in light-matter interacting systems. Here, we study naturally occurring superradiant coupling in a class of quasi-two-dimensional, layered semiconductor systems. We perform optical absorption experiments of the lowest exciton for transition-metal dichalcogenides with different numbers of atomic layers. We examine two representative materials, MoSe$_2$ and WSe$_2$, using incoherent broadband white light. The measured transmission at the A exciton resonance does not saturate for optically thick samples consisting of hundreds of atomic lay…
Due to a strong Coulomb interaction, excitons dominate the excitation kinetics in 2D materials. While Coulomb-scattering between electrons has been well studied, the interaction of excitons is more challenging and remains to be explored. As neutral composite bosons consisting of electrons and holes, excitons show a non-trivial scattering dynamics. Here, we study on microscopic footing exciton-exciton interaction in transition-metal dichalcogenides and related van der Waals heterostructures. We demonstrate that the crucial criterion for efficient scattering is a large electron/hole mass asymmet…
Atomically thin layers of transition metal dichalcogenides (TMDCs) exhibit exceptionally strong Coulomb interaction between charge carriers due to the two-dimensional carrier confinement in connection with weak dielectric screening. The van der Waals nature of interlayer coupling makes it easy to integrate TMDC layers into heterostructures with different dielectric or metallic substrates. This allows to tailor electronic and optical properties of these materials, as Coulomb interaction inside atomically thin layers is very susceptible to screening by the environment. Here we theoretically inve…
Manipulating materials properties far from equilibrium recently garnered significant attention, with experimental emphasis on transient melting, enhancement, or induction of electronic order. A more tantalizing aspect of the matter-light interaction regards the possibility to access dynamical steady states with distinct non-equilibrium phase transitions to affect electronic transport. Here, we show that the interplay of crystal symmetry and optical pumping of monolayer transition-metal dichalcogenides (TMDCs) provides a novel avenue to engineer topologically-protected chiral edge modes. In sta…
Monolayer transition metal dichalcogenides (TMDs) are known to be highly sensitive to externally applied tensile or compressive strain. In particular, strain can be exploited as a tool to control the optical response of TMDs. However, the role of excitonic effects under strain has not been fully understood yet. Utilizing the strain-induced modification of electron and phonon dispersion obtained by first principle calculations, we present in this work microscopic insights into the strain-dependent optical response of various TMD materials. In particular, we explain recent experiments on the cha…
Probing valley quantum oscillations via the spin Seebeck effect in transition metal dichalcogenide/ferromagnet hybrids
Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学）；Waseda Institute for Advanced Study, Waseda University（早稻田大学）；CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences（中国科学院大学）；Advanced Science Research Center, Japan Atomic Energy Agency（日本原子能机构）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所）
Nanolasers operate with a minimal amount of active material and low losses. In this regime, single layers of transition-metal dichalcogenides (TMDs) are being investigated as next generation gain materials due to their high quantum efficiency. We provide results from microscopic gain calculations of highly excited TMD monolayers and specify requirements to achieve lasing with four commonly used TMD semiconductors. Our approach includes band-structure renormalizations due to excited carriers that trigger a direct-to-indirect band-gap transition. As a consequence, we predict a rollover for the g…
Persistent electrical polarized states are fundamentally important to the electric industry as they can be used in the non-volatile memory, the artificial neuromorphic network, and negative capacitors, making ultralow energy consumption electronic devises possible. With the recent development in low dimensional ferroelectric materials, emerging 2D out-of-plane ferroelectric materials like MoTe2 have great potential for future development. Despite previous phenomenological studies, the underlying microscopic origin of ferroelectricity is still missing. Here, using density functional theory and …
Excitons dominate the optical properties of monolayer transition metal dichalcogenides (TMDs). Besides optically accessible bright exciton states, TMDs exhibit also a multitude of optically forbidden dark excitons. Here, we show that efficient exciton-phonon scattering couples bright and dark states and gives rise to an asymmetric excitonic line shape. The observed asymmetry can be traced back to phonon-induced sidebands that are accompanied by a polaron redshift. We present a joint theory-experiment study investigating the microscopic origin of these sidebands in different TMD materials takin…
We developed a Landau type theory for the description of polar phenomena in low-dimensional transition metal dichalcogenides (TMDs), specifically exploring flexoelectric origin of the polarization induced by a spontaneous bending and by inversion symmetry breaking due to the interactions with substrate. We consider the appearance of the spontaneous out-of-plane polarization due to the flexoelectric coupling with the strain gradient of the spontaneous surface rippling and surface-induced piezoelectricity. Performed calculations proved that the out-of-plane spontaneous polarization, originated f…
We develop a microscopic and atomistic theory of electron spin-based qubits in gated quantum dots in a single layer of transition metal dichalcogenides. The qubits are identified with two degenerate locked spin and valley states in a gated quantum dot. The two-qubit states are accurately described using a multi-million atom tight-binding model solved in wavevector space. The spin-valley locking and strong spin-orbit coupling result in two degenerate states, one of the qubit states being spin-down located at the $+K$ valley of the Brillouin zone, and the other state located at the $-K$ valley w…
In recent years, transition metal dichalcogenides (TMDs) have garnered great interest as topological materials -- monolayers of centrosymmetric $β$-phase TMDs have been identified as 2D topological insulators (TIs), and bulk crystals of noncentrosymmetric $γ$-phase MoTe$_2$ and WTe$_2$ have been identified as type-II Weyl semimetals. However, ARPES and STM probes of these TMDs have revealed huge, "arc-like" surface states that overwhelm, and are sometimes mistaken for, the much smaller topological surface Fermi arcs of bulk type-II Weyl points. In this letter, we use first-principles calculati…
In transition-metal dichalcogenides, electrons in the K-valleys can experience both Ising and Rashba spin-orbit couplings. In this work, we show that the coexistence of Ising and Rashba spin-orbit couplings leads to a special type of valley Hall effect, which we call spin-orbit coupling induced valley Hall effect. Importantly, near the conduction band edge, the valley-dependent Berry curvatures generated by spin-orbit couplings are highly tunable by external gates and dominate over the intrinsic Berry curvatures originating from orbital degrees of freedom under accessible experimental conditio…
The remarkably strong Coulomb interaction in atomically thin transition metal dichalcogenides (TMDs) results in an extraordinarily rich many-particle physics including the formation of tightly bound excitons. Besides optically accessible bright excitonic states, these materials also exhibit a variety of dark excitons. Since they can even lie below the bright states, they have a strong influence on the exciton dynamics, lifetimes, and photoluminescence. While very recently, the presence of dark excitonic states has been experimentally demonstrated, the origin of these states, their formation, a…
We report on a novel mechanism of BCS-like superconductivity, mediated by a pair of Bogoliubov quasiparticles (bogolons). It takes place in hybrid systems consisting of a two-dimensional electron gas in a transition metal dichalcogenide monolayer in the vicinity of a Bose-Einstein condensate. Taking a system of two-dimensional indirect excitons as a testing ground we show, that the bogolon-pair-mediated electron pairing mechanism is stronger than phonon-mediated and single bogolon-mediated ones. We develop a microscopic theory of bogolon-pair-mediated superconductivity, based on the Schrieffer…
Just as photons are the quanta of light, plasmons are the quanta of orchestrated charge-density oscillations in conducting media. Plasmon phenomena in normal metals, superconductors and doped semiconductors are often driven by long-wavelength Coulomb interactions. However, in crystals whose Fermi surface is comprised of disconnected pockets in the Brillouin zone, collective electron excitations can also attain a shortwave component when electrons transition between these pockets. Here, we show that the band structure of monolayer transition-metal dichalcogenides gives rise to an intriguing mec…
We examine the full static non-linear optical response of uniaxially strained transition metal dichalcogenide monolayers doped with a finite carrier density in the conduction band, in the presence of disorder. We find that the customary shift current is suppressed, yet we identify a strong, valley-dependent non-reciprocal response, which we term a \textit{unidirectional valley-contrasting photo-current} (UVCP). This DC current originates from the combined effect of strain and Kramers symmetry breaking by trigonal warping, while the contributions due to individual valleys can be separated by in…
Recent experimental progresses have demonstrated the great potential of electronic and excitonic moiré superlattices in transition metal dichalcogenides (TMDs) for quantum many-body simulations and quantum optics applications. Here we reveal that the moiré potential landscapes in the TMDs heterostructures have an electrostatic origin from the spontaneous charge transfer across the heterointerfaces dependent on the atomic registry. This allows engineering tunable multi-chromatic superlattices through the interference of moiré potentials from independently configurable heterointerfaces in multil…
Monolayers of transition metal dichalcogenides (TMDs) have a remarkable excitonic landscape with deeply bound bright and dark exciton states. Their properties are strongly affected by lattice distortions that can be created in a controlled way via strain. Here, we perform a joint theory-experiment study investigating exciton diffusion in strained tungsten disulfide (WS$_2$) monolayers. We reveal a non-trivial and non-monotonic influence of strain. Lattice deformations give rise to different energy shifts for bright and dark excitons changing the excitonic landscape, the efficiency of intervall…
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…
Strain presents a straightforward tool to tune electronic properties of atomically thin nanomaterials that are highly sensitive to lattice deformations. While the influence of strain on the electronic band structure has been intensively studied, there are only few works on its impact on optical properties of monolayer transition metal dichalcogenides (TMDs). Combining microscopic theory based on Wannier and Bloch equations with nearestneighbor tight-binding approximation, we present an analytical view on how uni- and biaxial strain influences the optical fingerprint of TMDs including their exc…
Assessing atomic defect states and their ramifications on the electronic properties of two dimensional van der Waals semiconducting transition metal dichalcogenides (SC TMDs) is the primary task to expedite multi disciplinary efforts in the promotion of next generation electrical and optical device applications utilizing these low dimensional materials. Here, with electron tunneling and optical spectroscopy measurements with density functional theory, we spectroscopically locate the midgap states from chalcogen atom vacancies in four representative monolayer SC TMDs (MoS2, WS2, MoSe2, WSe2), a…
Dissecting intervalley coupling mechanisms in monolayer transition metal dichalcogenides
Politecnico di Milano（米兰理工大学）；Technische Universität Berlin（柏林工业大学）；Columbia University（哥伦比亚大学）；University of Luxembourg（卢森堡大学）；CNR-IFN（意大利国家研究委员会纳米科学研究所）
Exciton optical transitions in transition-metal dichalcogenides offer unique opportunities to study rich many-body physics. Recent experiments in monolayer WSe$_2$ and WS$_2$ have shown that while the low-temperature photoluminescence from neutral excitons and three-body complexes is suppressed in the presence of elevated electron densities or strong photoexcitation, new dominant peaks emerge in the low-energy side of the spectrum. I present a theory that elucidates the nature of these optical transitions showing the role of the intervalley Coulomb interaction. After deriving a compact dynamic…
