The geometry of electronic bands in a solid can drastically alter single-particle charge and spin transport. We show here that collective optical excitations arising from Coulomb interactions also exhibit unique signatures of Berry curvature and quantum geometric tensor. A non-zero Berry curvature mixes and lifts the degeneracy of $l \neq 0$ states, leading to a time-reversal-symmetric analog of the orbital Zeeman effect. The quantum geometric tensor, on the other hand, leads to $l$-dependent shifts of exciton states that is analogous to the Lamb shift. Our results provide an explanation of the non-hydrogenic exciton spectrum recently calculated for transition metal dichalcogenides. Numerically, we find a Berry curvature induced splitting of $\sim 10$ meV between the $2p_x \pm i2p_y$ states of WSe$_2$.
In transition metal dichalcogenides layers of atomic scale thickness, the electron-hole Coulomb interaction potential is strongly influenced by the sharp discontinuity of the dielectric function across the layer plane. This feature results in peculiar non-hydrogenic excitonic states, in which exciton-mediated optical nonlinearities are predicted to be enhanced as compared to their hydrogenic counterpart. To demonstrate this enhancement, we performed optical transmission spectroscopy of a MoSe$_2$ monolayer placed in the strong coupling regime with the mode of an optical microcavity, and analyz…
The physics of excitons, electron-hole pairs that are bound together by their mutual Coulomb attraction, can to great extent be understood in the framework of the quantum-mechanical hydrogen model. This model has recently been challenged by spectroscopic measurements on two-dimensional transition-metal dichalchogenides that unveil strong deviations from a hydrogenic spectrum. Here, we show that this deviation is due to the particular relativistic character of electrons in this class of materials. Indeed, their electrons are no longer described in terms of a Schroedinger but a massive Dirac equ…
Using an effective Dirac model, we study the orbital Hall effect (OHE) in bilayers of transition metal dichalcogenides with 2H stacking (2H-TMD). We use first-order perturbation theory in the interlayer coupling of the bilayer system to obtain analytical expressions for the orbital Hall conductivity in the linear response regime. We use two distinct descriptions of the orbital angular momentum (OAM) operator: The first one is the intra-atomic approximation that considers only the intrasite contribution to the OAM [Cysne et al. Phys. Rev. Lett. 126, 056601 (2021)]. The second one uses the Berry…
Converting solar energy into chemical energy by splitting water is a promising means to generate a sustainable and renewable solution without detrimental environmental impact. The two-dimensional semiconductors serve as potential catalysts in this regard, and here we combine Janus transition-metal dichalcogenides (MoXY, X/Y = S, Se, Te) and graphitic carbon nitride in a van der Waals heterostructure. Within the first-principles calculations, we investigate the electronic, optical and excitonic properties that determine the photocatalytic activity. Due to the internal electric field, the photog…
Recently, the celebrated Keldysh potential has been widely used to describe the Coulomb interaction of few-body complexes in monolayer transition-metal dichalcogenides. Using this potential to model charged excitons (trions), one finds a strong dependence of the binding energy on whether the monolayer is suspended in air, supported on SiO$_2$, or encapsulated in hexagonal boron-nitride. However, empirical values of the trion binding energies show weak dependence on the monolayer configuration. This deficiency indicates that the description of the Coulomb potential is still lacking in this impo…
A self-consistent scheme for the calculations of the interacting groundstate and the near bandgap optical spectra of mono- and multilayer transition-metal-dichalcogenide systems is presented. The approach combines a dielectric model for the Coulomb interaction potential in a multilayer environment, gap equations for the renormalized groundstate, and the Dirac-Wannier-equation to determine the excitonic properties. To account for the extension of the individual monolayers perpendicular to their basic plane, an effective thickness parameter in the Coulomb interaction potential is introduced. Num…
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…
Reflectance and magneto-reflectance experiments together with theoretical modelling based on the $\mathbf{k\cdot p}$ approach have been employed to study the evolution of direct bandgap excitons in MoS$_2$ layers with a thickness ranging from mono- to trilayer. The extra excitonic resonances observed in MoS$_2$ multilayers emerge as a result of the hybridization of Bloch states of each sub-layer due to the interlayer coupling. The properties of such excitons in bi- and trilayers are classified by the symmetry of corresponding crystals. The inter- and intralayer character of the reported excito…
The semiconducting two-dimensional transition metal dichalcogenides MX$_{2}$ show an abundance of one-dimensional metallic edges and grain boundaries. Standard techniques for calculating edge states typically model nanoribbons, and require the use of supercells. In this paper we formulate a Green$'$s function technique for calculating edge states of (semi-)infinite two-dimensional systems with a single well-defined edge or grain boundary. We express Green$'$s functions in terms of Bloch matrices, constructed from the solutions of a quadratic eigenvalue equation. The technique can be applied to…
Contact resistance of semiconducting transition metal dichalcogenides has been shown to decrease in lateral heterojunctions formed with their metallic phases but its origins remain elusive. Here we combine first principles and quantum transport calculations to rationalize the contact resistance of these structures in terms of phase, composition (WTe2, MoTe2, WSe2, and MoSe2), and length of the channel. We find that charge injection in metallic 1T'-WTe2/1T'-MoTe2 junctions is nearly ideal as electrode Bloch states remain delocalized through the channel. Mixtures of 1T' selenides and tellurides …
We present a model of the electronic properties of monolayer transition-metal dichalcogenides based on a tight binding approach which includes the effects of strain and curvature of the crystal lattice. Mechanical deformations of the lattice offer a powerful route for tuning the electronic structure of the transition-metal dichalcogenides, as changes to bond lengths lead directly to corrections in the electronic Hamiltonian while curvature of the crystal lattice mixes the orbital structure of the electronic Bloch bands. We first present an effective low energy Hamiltonian describing the electr…
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…
Orbital Hall effect from orbital magnetic moments of Bloch states: the role of a new correction term
Instituto de Física, Universidade Federal Fluminense（弗鲁米嫩塞联邦大学物理研究所）；Centro de Física de Materiales, Universidad del País Vasco（巴斯克大学材料物理中心）；Ikerbasque Foundation（伊克尔巴斯基基金会）；Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；Physics Center of Minho and Porto Universities (CF-UM-UP)（米尼奥与波尔图大学物理中心）；International Iberian Nanotechnology Laboratory (INL)（国际伊比利亚纳米技术实验室）
Monolayer transition metal dichalcogenides feature tightly bound bright excitons at the degenerate valleys, where electron-hole Coulomb exchange interaction strongly couples the valley pseudospin to the momentum of exciton. Placed on periodically structured dielectric substrate, the spatial modulation of the Coulomb interaction leads to the formation of exciton Bloch states with real-space valley pseudospin texture displayed in a mesoscopic supercell. We find this spatial valley texture in the exciton Bloch function is pattern-locked to the propagation direction, enabling nano-optical excitati…
We theoretically introduce the fundamentally fastest induction of a significant population and valley polarization in a monolayer of a transition metal dichalcogenide (i.e., $\mathrm{MoS_2}$ and $\mathrm{WS_2}$). This may be extended to other two-dimensional materials with the same symmetry. This valley polarization can be written and read-out by a pulse consisting of just a single optical oscillation with a duration of a few femtoseconds and an amplitude of $\sim0.2~\mathrm V/\mathrmÅ$. Under these conditions, we predict a new effect of {\em topological resonance}, which is due to Bloch motio…
An $\it{ab \,\, initio}$ based fully microscopic many-body approach is used to study the carrier relaxation dynamics in monolayer transition-metal dichalcogenides. Bandstructures and wavefunctions as well as phonon energies and coupling matrix elements are calculated using density functional theory. The resulting dipole and Coulomb matrix elements are implemented in the Dirac-Bloch equations to calculate carrier-carrier and carrier-phonon scatterings throughout the whole Brillouin zone. It is shown that carrier scatterings lead to a relaxation into hot quasi-Fermi distributions on a single fem…
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…
In this work, we provide an effective model to evaluate the one-electron dipole matrix elements governing optical excitations and the photoemission process of single-layer (SL) and bilayer (BL) transition metal dichalcogenides. By utilizing a $\vec{k} \cdot \vec{p}$ Hamiltonian, we calculate the photoemission intensity as observed in angle-resolved photoemission from the valence bands around the $\bar{K}$-valley of MoS$_2$. In SL MoS$_2$ we find a significant masking of intensity outside the first Brillouin zone, which originates from an in-plane interference effect between photoelectrons emit…
We study hot-electron cooling by acoustic and optical phonons in monolayer MoS$_2$. The cooling power $P$ ($P_e = P/n$) is investigated as a function of electron temperature $T_e$ (0-500 $\mathrm{K}$) and carrier density $n$ ($10^{10}$-$10^{13}$ $\mathrm{cm}^{-2}$) taking into account all relevant electron-phonon (el-ph) couplings. We find that the cross over from acoustic phonon dominated cooling at low $T_e$ to optical phonon dominated cooling at higher $T_e$ takes place at $T_e \sim 50$-$75$ $\mathrm{K}$. The unscreened deformation potential (DP) coupling to the TA phonon is shown to domina…
Angle-resolved photoemission spectroscopy (ARPES) is the most powerful technique to investigate the electronic band structure of crystalline solids. To completely characterize the electronic structure of topological materials, one needs to go beyond band structure mapping and access information about the momentum-resolved Bloch wavefunction, namely orbitals, Berry curvature, and topological invariants. However, because phase information is lost in the process of measuring photoemission intensities, retrieving the complex-valued Bloch wavefunction from photoemission data has yet remained elusiv…
Dzyaloshinskii-Moriya interaction (DMI) is vital to form various chiral spin textures, novel behaviors of magnons and permits their potential applications in energy-efficient spintronic devices. Here, we realize a sizable bulk DMI in a transition metal dichalcogenide (TMD) 2H-TaS2 by intercalating Fe atoms, which form the chiral supercells with broken spatial inversion symmetry and also act as the source of magnetic orderings. Using a newly developed protonic gate technology, gate-controlled protons intercalation could further change the carrier density and intensely tune DMI via the Ruderman-…
Increasing the speed limits of conventional electronics requires innovative approaches to manipulate other quantum properties of electrons besides their charge. An alternative approach utilizes the valley degree of freedom in low-dimensional semiconductors. Here we demonstrate that the valley degeneracy of exciton energies in transition metal dichalcogenide monolayers may be lifted by coherent optical interactions on timescales corresponding to few tens of femtoseconds. The optical Stark and Bloch-Siegert effects generated by strong nonresonant circularly-polarized light induce valley-selectiv…
The chirality of electronic Bloch bands is responsible for many intriguing properties of layered two-dimensional materials. We show that in bilayers of transition metal dichalcogenides (TMDCs), unlike in few-layer graphene and monolayer TMDCs, both intra-layer and inter-layer couplings give important contributions to the Berry-curvature in the $K$ and $-K$ valleys of the Brillouin zone. The inter-layer contribution leads to the stacking dependence of the Berry curvature and we point out the differences between the commonly available 3R type and 2H type bilayers. Due to the inter-layer contribu…
Interfaces of dye molecules and two-dimensional transition metal dichalcogenides (TMDCs) combine strong molecular dipole excitations with high carrier mobilities in semiconductors. Förster type energy transfer is one key mechanism for the coupling between both constituents. We report microscopic calculations of a spectrally resolved Förster induced transition rate from dye molecules to a TMDC layer. Our approach is based on microscopic Bloch equations which are solved self-consistently together with Maxwells equations. This approach allows to incorporate the dielectric environment of a TMDC se…
We investigate the optical transition selection rules for excitonic Rydberg series formed in massive Dirac cones. The entanglement of the exciton envelop function with the pseudospin texture leads to anomalous selection rules for one-photon generation of excitons, where $d$-orbitals can be excited with the opposite helicity selection rule from the $s$-orbitals in a given valley. The trigonal warping effects in realistic hexagonal lattices further renders more excited states bright, where $p$-orbitals can also be accessed by one-photon excitation with the opposite valley selection rules to the …
The Berry phase of Bloch states can have profound effects on electron dynamics lead to novel transport phenomena, such as the anomalous Hall effect and the valley Hall effect. Recently, it was predicted that the Berry phase effect can also modify the exciton states in transition metal dichalcogenide monolayers, and lift the energy degeneracy of exciton states with opposite angular momentum through an effective valley-orbital coupling. Here, we report the first observation and control of the Berry-phase induced splitting of the 2p-exciton states in monolayer molybdenum diselenide using the intr…
Resonant inelastic X-ray scattering (RIXS) can probe localized excitations at selected atoms in materials, including particle-hole transitions between the valence and conduction bands. These transitions are governed by fundamental properties of the corresponding Bloch wave-functions, including orbital and magnetic degrees of freedom, and quantum geometric properties such as the Berry curvature. In particular, orbital angular momentum (OAM), which is closely linked to the Berry curvature, can exhibit a nontrivial momentum dependence. We demonstrate how information on such OAM textures can be ex…
