arXiv subjects

A. O. Slobodeniuk

Publications and source records attributed to A. O. Slobodeniuk.

18 recordsLinked to original sources

arXiv2026

The impact of intraband carrier dynamics on the optical properties of two-dimensional materials: I. General theory

We consider the generation of microscopic polarization in two-dimensional semiconductors under intense optical fields in the non-resonant regime. We demonstrate that the intraband motion of quasiparticles, driven by the electric field of the laser pulse, contributes substantially to the system's polarization. The effects of intraband motion are analyzed using the semiconductor Bloch equations. We propose a method for solving these equations by considering them in a reference frame co-moving along the direction of the electric field of the optical pulse. We demonstrate the developed technique on transition metal dichalcogenide monolayers irradiated by strong circularly-polarized infrared light. The solution is provided in the form of a power series expansion in a small parameter that naturally emerges in the system. The implications of the results are examined, and the limitations of the approach are discussed.

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arXiv2023

Exciton spectrum in atomically thin monolayers: The role of hBN encapsulation

The high-quality structures containing semiconducting transition metal dichalcogenides (S-TMDs) monolayer (MLs) required for optical and electrical studies are achieved by their encapsulation in hexagonal BN (hBN) flakes. To examine the effect of hBN thickness in these systems, we consider a model with an S-TMD ML placed between a semi-infinite in the out-of-plane direction substrate and complex top cover layers: a layer of finite thickness, adjacent to the ML, and a semi-infinite in the out-of-plane direction top part. We obtain the expression for the Coulomb potential for such a structure. Using this result, we demonstrate that the energies of excitonic $s$ states in the structure with WSe$_2$ ML change significantly for the top hBN with thickness less than 30 layers for different substrate cases, such as hBN and SiO$_2$. For the larger thickness of the top hBN flake, the binding energies of the excitons are saturated to their values of the bulk hBN limit.

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arXiv2023

Ultrafast valley-selective coherent optical manipulation with excitons in WSe$_2$ and MoS$_2$ monolayers

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-selective blue shifts of exciton quantum levels by more than 30 meV. We show these phenomena by studying the two most intensive exciton resonances in transiton metal dichalcogenide monolayers and compare the results to a theoretical model, which properly includes the Coulomb interaction and exciton dispersion. These results open the door for ultrafast valleytronics working at multiterahertz frequencies.

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arXiv2022

Semiconductor Bloch equation analysis of optical Stark and Bloch-Siegert shifts in monolayers WSe$_2$ and MoS$_2$

We report on the theoretical and experimental investigation of valley-selective optical Stark and Bloch-Siegert shifts of exciton resonances in monolayers WSe$_2$ and MoS$_2$ induced by strong circularly polarized nonresonant optical fields. We predict and observe transient shifts of both 1sA and 1sB exciton transitions in the linear interaction regime. The theoretical description is based on semiconductor Bloch equations. The solutions of the equations are obtained with a modified perturbation technique, which takes into account many-body Coulomb interaction effects. These solutions allow to explain the polarization dependence of the shifts and calculate their values analytically. We found experimentally the limits of the applicability of the theoretical description by observing the transient exciton spectra change due to many-body effects at high field amplitudes of the driving wave.

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arXiv2022

Exchange-split multiple Rydberg series of excitons in anisotropic quasi two-dimensional ReS$_{2}$

We perform a polarization-resolved magnetoluminescence study of excitons in ReS$_2$. We observe that two linearly polarized Rydberg series of excitons are accompanied by two other Rydberg series of dark excitons, brightened by an in-plane magnetic field. All series extrapolate to the same single-electron bandgap, indicating that the observed excitons originate either from the same valley or from two valleys related by the inversion symmetry, and are split by exchange interaction. To interpret our observations of the magnetic brightening, we have to assume the dominant spin-orbit coupling to be Ising-like, which hints at an approximate symmetry of the electronic states in ReS$_2$ which is higher than the crystal symmetry $C_i$.

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arXiv2021

The optical response of artificially twisted MoS$_2$ bilayers

Two-dimensional layered materials offer the possibility to create artificial vertically stacked structures possessing an additional degree of freedom - $the$ $interlayer$ $twist$. We present a comprehensive optical study of artificially stacked bilayers (BLs) MoS$_2$ encapsulated in hexagonal BN with interlayer twist angle ranging from 0 to 60 degrees using Raman scattering and photoluminescence spectroscopies. It is found that the strength of the interlayer coupling in the studied BLs can be estimated using the energy dependence of indirect emission versus the A$_\textrm{1g}$-E$_\textrm{2g}^1$ energy separation. Due to the hybridization of electronic states in the valence band, the emission line related to the interlayer exciton is apparent in both the natural (2H) and artificial (62$^\circ$) MoS$_2$ BLs, while it is absent in the structures with other twist angles. The interlayer coupling energy is estimated to be of about 50 meV. The effect of temperature on energies and intensities of the direct and indirect emission lines in MoS$_2$ bilayers is also quantified.

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arXiv2020

Neutral and charged dark excitons in monolayer WS$_2$

Low temperature and polarization resolved magneto-photoluminescence experiments are used to investigate the properties of dark excitons and dark trions in a monolayer of WS$_2$ encapsulated in hexagonal BN (hBN). We find that this system is an $n$-type doped semiconductor and that dark trions dominate the emission spectrum. In line with previous studies on WSe$_2$, we identify the Coulomb exchange interaction coupled neutral dark and grey excitons through their polarization properties, while an analogous effect is not observed for dark trions. Applying the magnetic field in both perpendicular and parallel configurations with respect to the monolayer plane, we determine the g-factor of dark trions to be $g\sim$-8.6. Their decay rate is close to 0.5 ns, more than 2 orders of magnitude longer than that of bright excitons.

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arXiv2020

Valley polarization of singlet and triplet trions in WS$_2$ monolayer in magnetic fields

The spectral signatures associated with different negatively charged exciton complexes (trions) in a WS$_2$ monolayer encapsulated in hBN, are analyzed from low temperature and polarization resolved reflectance contrast (RC) and photoluminescence (PL) experiments, with an applied magnetic field. Based on results obtained from the RC experiment, we show that the valley Zeeman effect affects the optical response of both the singlet and the triplet trion species through the evolution of their energy and of their relative intensity, when applying an external magnetic field. Our analysis allows us to estimate a free electron concentration of $\sim 1.3 \cdot 10^{11}$ cm$^{-2}$. The observed evolutions based on PL experiments on the same sample are different and can hardly be understood within the same simple frame highlighting the complexity of relaxation processes involved in the PL response.

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arXiv2019

Energy spectrum of two-dimensional excitons in a non-uniform dielectric medium

We demonstrate that, in monolayers (MLs) of semiconducting transition metal dichalcogenides, the $s$-type Rydberg series of excitonic states follows a simple energy ladder: $ε_n=-Ry^*/(n+δ)^2$, $n$=1,2,\ldots, in which $Ry^*$ is very close to the Rydberg energy scaled by the dielectric constant of the medium surrounding the ML and by the reduced effective electron-hole mass, whereas the ML polarizability is only accounted for by $δ$. This is justified by the analysis of experimental data on excitonic resonances, as extracted from magneto-optical measurements of a high-quality WSe$_2$ ML encapsulated in hexagonal boron nitride (hBN), and well reproduced with an analytically solvable Schrödinger equation when approximating the electron-hole potential in the form of a modified Kratzer potential. Applying our convention to other, MoSe$_2$, WS$_2$, MoS$_2$ MLs encapsulated in hBN, we estimate an apparent magnitude of $δ$ for each of the studied structures. Intriguingly, $δ$ is found to be close to zero for WSe$_2$ as well as for MoS$_2$ monolayers, what implies that the energy ladder of excitonic states in these two-dimensional structures resembles that of Rydberg states of a three-dimensional hydrogen atom.

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arXiv2019

Probing and manipulating valley coherence of dark excitons in monolayer WSe$_2$

Monolayers of semiconducting transition metal dichalcogenides are two-dimensional direct-gap systems which host tightly-bound excitons with an internal degree of freedom corresponding to the valley of the constituting carriers. Strong spin-orbit interaction and the resulting ordering of the spin-split subbands in the valence and conduction bands makes the lowest-lying excitons in WX$_2$ (X~being S or Se) spin-forbidden and optically dark. With polarization-resolved photoluminescence experiments performed on a WSe$_2$ monolayer encapsulated in a hexagonal boron nitride, we show how the intrinsic exchange interaction in combination with the applied in-plane and/or out-of-plane magnetic fields enables one to probe and manipulate the valley degree of freedom of the dark excitons.

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arXiv2019

Spin-flip processes and radiative decay of dark intravalley excitons in transition metal dichalcogenide monolayers

We perform a theoretical study of radiative decay of dark intravalley excitons in transition metal dichalcogenide monolayers. This decay necessarily involves an electronic spin flip. The intrinsic decay mechanism due to interband spin-flip dipole moment perpendicular to the monolayer plane, gives a rate about 100--1000 times smaller than that of bright excitons. However, we find that this mechanism also introduces an energy splitting due to a local field effect, and the whole oscillator strength is contained in the higher-energy component, while the lowest-energy state remains dark and needs an extrinsic spin-flip mechanism for the decay. Rashba effect due to a perpendicular electric field or a dielectric substrate, gives a negligible radiative decay rate (about $10^7$ times slower than that of bright excitons). Spin flip due to Zeeman effect in a sufficiently strong in-plane magnetic field can give a decay rate comparable to that due to the intrinsic interband spin-flip dipole.

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arXiv2018

Fine structure of $\mathrm{K}$-excitons in multilayers of transition metal dichalcogenides

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 excitonic resonances is fingerprinted with the magneto-optical measurements: the excitonic $g$-factors of opposite sign and of different amplitude are revealed for these two types of resonances. The parameters describing the strength of the spin-orbit interaction are estimated for bi- and trilayer MoS$_2$.

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arXiv2018

Singlet and triplet trions in WS$_2$ monolayer encapsulated in hexagonal boron nitride

Embedding a WS$_2$ monolayer in flakes of hexagonal boron nitride allowed us to resolve and study the photoluminescence response due to both singlet and triplet states of negatively charged excitons (trions) in this atomically thin semiconductor. The energy separation between the singlet and triplet states has been found to be relatively small reflecting rather weak effects of the electron-electron exchange interaction for the trion triplet in a WS$_2$ monolayer, which involves two electrons with the same spin but from different valleys. Polarization-resolved experiments demonstrate that the helicity of the excitation light is better preserved in the emission spectrum of the triplet trion than in that of the singlet trion. Finally, the singlet (intravalley) trions are found to be observable even at ambient conditions whereas the emission due to the triplet (intervalley) trions is only efficient at low temperatures.

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arXiv2016

Optical properties of atomically thin transition metal dichalcogenides: Observations and puzzles

Recent results on the optical properties of mono- and few-layers of semiconducting transition metal dichalcogenides are reviewed. Experimental observations are presented and discussed in the frame of existing models, highlighting the limits of our understanding in this emerging field of research. We first introduce the representative band structure of these systems and their interband optical transitions. The effect of an external magnetic field is then considered to discuss Zeeman spectroscopy and optical pumping experiments, both revealing phenomena related to the valley degree of freedom. Finally, we discuss the observation of single photon emitters in different types of layered materials, including wide band gap hexagonal boron nitride. While going through these topics, we try to focus on open questions and on experimental observations, which do not yet have a clear explanation.

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arXiv2016

Brightening of dark excitons in monolayers of semiconducting transition metal dichalcogenides

We present low temperature magneto-photoluminescence experiments which demonstrate the brightening of dark excitons by an in-plane magnetic field $B$ applied to monolayers of different semiconducting transition metal dichalcogenides. For both WSe$_2$ and WS$_2$ monolayers, the dark exciton emission is observed at $\sim$50 meV below the bright exciton peak and displays a characteristic doublet structure which intensity is growing with $B^2$, while no magnetic field induced emission peaks appear for MoSe$_2$ monolayer. Our experiments also show that the MoS$_2$ monolayer has a dark exciton ground state with a dark-bright exciton splitting energy of $\sim$100 meV.

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arXiv2016

Exciton-phonon relaxation bottleneck and radiative decay of thermal exciton reservoir in two-dimensional materials

We study exciton radiative decay in a two-dimensional material, taking into account large thermal population in the non-radiative states, from which excitons are scattered into the radiative states by acoustic phonons. We find an analytical solution of the kinetic equation for the non-equilibrium distribution function of excitons in the radiative states. Our estimates for bright excitons in transition metal dichalcogenides indicate a strong depletion of radiative state population due to insufficient exciton-phonon scattering rate at low temperatures.

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arXiv2011

Density of states of relativistic and nonrelativistic two-dimensional electron gases in a uniform magnetic and Aharonov-Bohm fields

We study the electronic properties of 2D electron gas (2DEG) with quadratic dispersion and with relativistic dispersion as in graphene in the inhomogeneous magnetic field consisting of the Aharonov-Bohm flux and a constant background field. The total and local density of states (LDOS) are obtained on the base of the analytic solutions of the Schrödinger and Dirac equations in the inhomogeneous magnetic field. It is shown that as it was in the situation with a pure Aharonov-Bohm flux, in the case of graphene there is an excess of LDOS near the vortex, while in 2DEG the LDOS is depleted. This results in excess of the induced by the vortex DOS in graphene and in its depletion in 2DEG.

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arXiv2010

Aharonov-Bohm effect in relativistic and nonrelativistic 2D electron gas: a comparative study

We carry out a comparative study of electronic properties of 2D electron gas (2DEG) in a magnetic field of an infinitesimally thin solenoid with relativistic dispersion as in graphene and quadratic dispersion as in semiconducting heterostructures. The problem of ambiguity of the zero mode solutions of the Dirac equation is treated by considering of a finite radius flux tube which allows to select unique solutions associated with each $\mathbf{K}$ point of graphene's Brillouin zone. Then this radius is allowed to go to zero. On the base of the obtained in this case analytical solutions in the Aharonov-Bohm potential the local and total density of states (DOS) are calculated. It is shown that in the case of graphene there is an excess of LDOS near the vortex, while in 2DEG the LDOS is depleted. This results in excess of the induced by the vortex DOS in graphene and in its depletion in 2DEG. We discuss the application of the results for the local density of states for the scanning tunneling spectroscopy done on graphene.

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