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Excitons and Phonons in Two-Dimensional Materials: From Fundamental to Applications

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A special issue of Nanomaterials (ISSN 2079-4991). This special issue belongs to the section "2D and Carbon Nanomaterials".

Deadline for manuscript submissions: closed (20 August 2023) | Viewed by 19269

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Dr. Maciej Molas

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Institute of Experimental Physics, Faculty of Physics, University of Warsaw, 02-093 Warsaw, Poland
Interests: two-dimensional layered materials; transition metal dichalcogenides; post-transition metal chalcogenides; van der Waals heterostructures; photoluminescence; reflectance contrast; Raman scattering; magneto-optics
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Dear Colleagues,

The isolation of graphene opened up the gate to investigate a vast family of two-dimensional (2D) layered materials. A concept of an exciton, an electron-hole pair (e–h) bound by Coulomb interactions, lies at the foundation of solid state physics. Excitons are responsible for the electronic and optical response of many semiconductors. Particularly, an optical response of the semiconducting transition metal dichalcogenides, e.g. MoS₂, WS₂, and WSe₂, is dominated by the emergence of excitons even at room temperature. Simultaneously, lattice dynamics in solids is described by the phonons. They not only characterize the vibrations of atoms, but can also significantly influence the light−matter interaction due to the electron-phonon or exciton-phonon (e-p) coupling. As recently, a variety of intriguing excitonic complexes have been identified and described in monolayers of 2D materials: so‑called bright and dark complexes, neutral and charged excitons, biexcitons, etc. A family of excitons is even larger in multilayered specimens and artificial van der Waals (vdW) heterostructures. Phonons are also present in the optical response of different layered materials, apparent as phonon replicas. Consequently, the investigation of the phonon modes in 2D materials on account of e-p coupling is essential in terms of potential applications of layered materials.

This Special Issue, entitled “Excitons and Phonons in Two-Dimensional Materials: From Fundamental to Applications”, aims to cover the entire range of fundamental and applied research associated with excitonic complexes and phonon modes in two-dimensional layered materials.

Dr. Maciej Molas
Guest Editor

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Keywords

Neutral excitons, charged excitons, trions, biexcitons, multiexcitonic complexes
Dark excitons, phonon replicas
Van der Waals heterostructures, moiré phenomena, interlayer excitons
Vibrations, phonon modes, lattice dynamics
Acoustic and optical phonons
Emission, absorption, up-conversion processes
Photoluminescence, electroluminescence
Raman scattering
Theoretical calculations
2D devices and applications
2D layered materials
Graphene
Transition metal dichalcogenides: MoS₂, ReS₂, WS₂, MoSe₂, ReSe₂, WSe₂, MoTe₂, etc.
Post-transition metal chalcogenides: GaS, InS, GaSe, InSe, GaTe, etc.
Black phosphorous, silicene, germanene
Layered perovskites: CsPbCl₃, (PEA)₂SnI₄, (PEA)₂PbI₄, (PEA)₂PbBr₄, (PEA)₂(MA)_n−1Pb_nI_3n+1

Related Special Issue

Advances in Two-Dimensional Layered Materials: From Excitonic Complexes to Optoelectronics in Nanomaterials

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Editorial

Jump to: Research, Review

3 pages, 204 KiB

Open AccessEditorial

Excitons and Phonons in Two-Dimensional Materials: From Fundamental to Applications

by Maciej R. Molas

Nanomaterials 2023, 13(23), 3047; https://doi.org/10.3390/nano13233047 - 29 Nov 2023

Viewed by 717

Abstract

The isolation of graphene opened the gate to investigate a vast family of two-dimensional (2D) layered materials [...] Full article

(This article belongs to the Special Issue Excitons and Phonons in Two-Dimensional Materials: From Fundamental to Applications)

Research

Jump to: Editorial, Review

10 pages, 2732 KiB

Open AccessArticle

Exciton–Phonon Interactions in Strained Domes of Monolayer MoS₂ Studied by Resonance Raman Spectroscopy

by Jessica S. Lemos, Elena Blundo, Antonio Polimeni, Marcos A. Pimenta and Ariete Righi

Nanomaterials 2023, 13(19), 2722; https://doi.org/10.3390/nano13192722 - 07 Oct 2023

Cited by 3 | Viewed by 927

Abstract

This work describes a resonance Raman study performed in the domes of monolayer MoS₂ using 23 different laser excitation energies covering the visible and near-infrared (NIR) ranges. The multiple excitation results allowed us to investigate the exciton–phonon interactions of different phonons (A [...] Read more.

^{'}

₁, E

^{'}

, and LA) with different excitonic optical transitions in biaxially strained monolayer MoS

_{2}

. The analysis of the intensities of the two first-order peaks, A

^{'}

₁ and E

^{'}

, and the double-resonance 2LA Raman band as a function of the laser excitation furnished the values of the energies of the indirect exciton and the direct excitonic transitions in the strained MoS

_{2}

domes. It was noticed that the out-of-plane A

^{'}

₁ phonon mode is significantly enhanced only by the indirect exciton I and the C exciton, whereas the in-plane E

^{'}

mode is only enhanced by the C exciton of the MoS₂ dome, thus revealing the weak interaction of these phonons with the A and B excitons in the strained MoS

_{2}

domes. On the other hand, the 2LA Raman band is significantly enhanced at the indirect exciton I and by the A (or B) exciton but not enhanced by the C exciton, thus showing that the LA edge phonons that participate in the double-resonance process in MoS

_{2}

have a weak interaction with the C exciton. Full article

(This article belongs to the Special Issue Excitons and Phonons in Two-Dimensional Materials: From Fundamental to Applications)

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15 pages, 1247 KiB

Open AccessEditor’s ChoiceArticle

The Key Role of Non-Local Screening in the Environment-Insensitive Exciton Fine Structures of Transition-Metal Dichalcogenide Monolayers

by Wei-Hua Li, Jhen-Dong Lin, Ping-Yuan Lo, Guan-Hao Peng, Ching-Yu Hei, Shao-Yu Chen and Shun-Jen Cheng

Nanomaterials 2023, 13(11), 1739; https://doi.org/10.3390/nano13111739 - 26 May 2023

Cited by 4 | Viewed by 1894

Abstract

In this work, we present a comprehensive theoretical and computational investigation of exciton fine structures of WSe

_{2}

In this work, we present a comprehensive theoretical and computational investigation of exciton fine structures of WSe

_{2}

-monolayers, one of the best-known two-dimensional (2D) transition-metal dichalcogenides (TMDs), in various dielectric-layered environments by solving the first-principles-based Bethe–Salpeter equation. While the physical and electronic properties of atomically thin nanomaterials are normally sensitive to the variation of the surrounding environment, our studies reveal that the influence of the dielectric environment on the exciton fine structures of TMD-MLs is surprisingly limited. We point out that the non-locality of Coulomb screening plays a key role in suppressing the dielectric environment factor and drastically shrinking the fine structure splittings between bright exciton (BX) states and various dark-exciton (DX) states of TMD-MLs. The intriguing non-locality of screening in 2D materials can be manifested by the measurable non-linear correlation between the BX-DX splittings and exciton-binding energies by varying the surrounding dielectric environments. The revealed environment-insensitive exciton fine structures of TMD-ML suggest the robustness of prospective dark-exciton-based optoelectronics against the inevitable variation of the inhomogeneous dielectric environment. Full article

(This article belongs to the Special Issue Excitons and Phonons in Two-Dimensional Materials: From Fundamental to Applications)

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14 pages, 2048 KiB

Open AccessArticle

Ultrafast Dynamics of Valley-Polarized Excitons in WSe₂ Monolayer Studied by Few-Cycle Laser Pulses

by Petr Koutenský, Artur Slobodeniuk, Miroslav Bartoš, František Trojánek, Petr Malý and Martin Kozák

Nanomaterials 2023, 13(7), 1207; https://doi.org/10.3390/nano13071207 - 28 Mar 2023

Cited by 1 | Viewed by 1265

Abstract

We report on the experimental investigation of the ultrafast dynamics of valley-polarized excitons in monolayer WSe

_{2}

using transient reflection spectroscopy with few-cycle laser pulses with 7 fs duration. We observe that at room temperature, the anisotropic valley population of excitons decays on [...] Read more.

We report on the experimental investigation of the ultrafast dynamics of valley-polarized excitons in monolayer WSe

_{2}

using transient reflection spectroscopy with few-cycle laser pulses with 7 fs duration. We observe that at room temperature, the anisotropic valley population of excitons decays on two different timescales. The shorter decay time of approximately 120 fs is related to the initial hot exciton relaxation related to the fast direct recombination of excitons from the radiative zone, while the slower picosecond dynamics corresponds to valley depolarization induced by Coloumb exchange-driven transitions of excitons between two inequivalent valleys. Full article

(This article belongs to the Special Issue Excitons and Phonons in Two-Dimensional Materials: From Fundamental to Applications)

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26 pages, 1572 KiB

Open AccessArticle

Signatures of Electric Field and Layer Separation Effects on the Spin-Valley Physics of MoSe₂/WSe₂ Heterobilayers: From Energy Bands to Dipolar Excitons

by Paulo E. Faria Junior and Jaroslav Fabian

Nanomaterials 2023, 13(7), 1187; https://doi.org/10.3390/nano13071187 - 27 Mar 2023

Cited by 8 | Viewed by 1913

Abstract

Multilayered van der Waals heterostructures based on transition metal dichalcogenides are suitable platforms on which to study interlayer (dipolar) excitons, in which electrons and holes are localized in different layers. Interestingly, these excitonic complexes exhibit pronounced valley Zeeman signatures, but how their spin-valley physics can be further altered due to external parameters—such as electric field and interlayer separation—remains largely unexplored. Here, we perform a systematic analysis of the spin-valley physics in MoSe

_{2}

/WSe

_{2}

heterobilayers under the influence of an external electric field and changes of the interlayer separation. In particular, we analyze the spin (

S_{z}

) and orbital (

L_{z}

) degrees of freedom, and the symmetry properties of the relevant band edges (at K, Q, and

Γ

points) of high-symmetry stackings at 0° (R-type) and 60° (H-type) angles—the important building blocks present in moiré or atomically reconstructed structures. We reveal distinct hybridization signatures on the spin and the orbital degrees of freedom of low-energy bands, due to the wave function mixing between the layers, which are stacking-dependent, and can be further modified by electric field and interlayer distance variation. We find that H-type stackings favor large changes in the g-factors as a function of the electric field, e.g., from

- 5

to 3 in the valence bands of the H

_{h}^{h}

stacking, because of the opposite orientation of

S_{z}

and

L_{z}

of the individual monolayers. For the low-energy dipolar excitons (direct and indirect in k-space), we quantify the electric dipole moments and polarizabilities, reflecting the layer delocalization of the constituent bands. Furthermore, our results show that direct dipolar excitons carry a robust valley Zeeman effect nearly independent of the electric field, but tunable by the interlayer distance, which can be rendered experimentally accessible via applied external pressure. For the momentum-indirect dipolar excitons, our symmetry analysis indicates that phonon-mediated optical processes can easily take place. In particular, for the indirect excitons with conduction bands at the Q point for H-type stackings, we find marked variations of the valley Zeeman (∼4) as a function of the electric field, which notably stands out from the other dipolar exciton species. Our analysis suggests that stronger signatures of the coupled spin-valley physics are favored in H-type stackings, which can be experimentally investigated in samples with twist angle close to 60°. In summary, our study provides fundamental microscopic insights into the spin-valley physics of van der Waals heterostructures, which are relevant to understanding the valley Zeeman splitting of dipolar excitonic complexes, and also intralayer excitons. Full article

(This article belongs to the Special Issue Excitons and Phonons in Two-Dimensional Materials: From Fundamental to Applications)

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8 pages, 513 KiB

Open AccessEditor’s ChoiceArticle

Fine Structure Splitting of Phonon-Assisted Excitonic Transition in (PEA)₂PbI₄ Two-Dimensional Perovskites

by Katarzyna Posmyk, Mateusz Dyksik, Alessandro Surrente, Katarzyna Zalewska, Maciej Śmiertka, Ewelina Cybula, Watcharaphol Paritmongkol, William A. Tisdale, Paulina Plochocka and Michał Baranowski

Nanomaterials 2023, 13(6), 1119; https://doi.org/10.3390/nano13061119 - 21 Mar 2023

Cited by 5 | Viewed by 2354

Abstract

Two-dimensional van der Waals materials exhibit particularly strong excitonic effects, which causes them to be an exceptionally interesting platform for the investigation of exciton physics. A notable example is the two-dimensional Ruddlesden–Popper perovskites, where quantum and dielectric confinement together with soft, polar, and low symmetry lattice create a unique background for electron and hole interaction. Here, with the use of polarization-resolved optical spectroscopy, we have demonstrated that the simultaneous presence of tightly bound excitons, together with strong exciton–phonon coupling, allows for observing the exciton fine structure splitting of the phonon-assisted transitions of two-dimensional perovskite (PEA)

_{2}

PbI

_{4}

, where PEA stands for phenylethylammonium. We demonstrate that the phonon-assisted sidebands characteristic for (PEA)

_{2}

PbI

_{4}

are split and linearly polarized, mimicking the characteristics of the corresponding zero-phonon lines. Interestingly, the splitting of differently polarized phonon-assisted transitions can be different from that of the zero-phonon lines. We attribute this effect to the selective coupling of linearly polarized exciton states to non-degenerate phonon modes of different symmetries resulting from the low symmetry of (PEA)

_{2}

PbI

_{4}

lattice. Full article

(This article belongs to the Special Issue Excitons and Phonons in Two-Dimensional Materials: From Fundamental to Applications)

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13 pages, 3376 KiB

Open AccessArticle

Investigation of a Multi-Layer Absorber Exhibiting the Broadband and High Absorptivity in Red Light and Near-Infrared Region

by Guoxiang Peng, Wei-Zheng Li, Ling-Chieh Tseng and Cheng-Fu Yang

Nanomaterials 2023, 13(4), 766; https://doi.org/10.3390/nano13040766 - 18 Feb 2023

Cited by 5 | Viewed by 1159

Abstract

In this study, an absorber with the characteristics of high absorptivity and ultra-wideband (UWB), which was ranged from the visible light range and near-infrared band, was designed and numerically analyzed using COMSOL Multiphysics^® simulation software (version 6.0). The designed absorber was constructed by using two-layer square cubes stacked on the four-layer continuous plane films. The two-layer square cubes were titanium dioxide (TiO₂) and titanium (Ti) (from top to bottom) and the four-layer continuous plane films were Poly(N-isopropylacrylamide) (PNIPAAm), Ti, silica (SiO₂), and Ti. The analysis results showed that the first reason to cause the high absorptivity in UWB is the anti-reflection effect of top TiO₂ layer. The second reason is that the three different resonances, including localized surface plasmon resonance, the propagating surface plasmon resonance, and the Fabry-Perot (FP) cavity resonance, are coexisted in the absorption peaks of the designed absorber and at least two of them can be excited at the same time. The third reason is that two FP resonant cavities were formed in the PNIPAAm and SiO₂ dielectric layers. Because of the combination of the anti-reflection effect and the three different resonances, the designed absorber presented the properties of UWB and high absorptivity. Full article

(This article belongs to the Special Issue Excitons and Phonons in Two-Dimensional Materials: From Fundamental to Applications)

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18 pages, 6779 KiB

Open AccessFeature PaperArticle

Stress-Tuned Optical Transitions in Layered 1T-MX₂ (M=Hf, Zr, Sn; X=S, Se) Crystals

by Miłosz Rybak, Tomasz Woźniak, Magdalena Birowska, Filip Dybała, Alfredo Segura, Konrad J. Kapcia, Paweł Scharoch and Robert Kudrawiec

Nanomaterials 2022, 12(19), 3433; https://doi.org/10.3390/nano12193433 - 30 Sep 2022

Cited by 4 | Viewed by 1640

Abstract

Optical measurements under externally applied stresses allow us to study the materials’ electronic structure by comparing the pressure evolution of optical peaks obtained from experiments and theoretical calculations. We examine the stress-induced changes in electronic structure for the thermodynamically stable 1T polytype of [...] Read more.

_{2}

compounds (M=Hf, Zr, Sn; X=S, Se), using the density functional theory. We demonstrate that considered 1T-MX

_{2}

materials are semiconducting with indirect character of the band gap, irrespective to the employed pressure as predicted using modified Becke–Johnson potential. We determine energies of direct interband transitions between bands extrema and in band-nesting regions close to Fermi level. Generally, the studied transitions are optically active, exhibiting in-plane polarization of light. Finally, we quantify their energy trends under external hydrostatic, uniaxial, and biaxial stresses by determining the linear pressure coefficients. Generally, negative pressure coefficients are obtained implying the narrowing of the band gap. The semiconducting-to-metal transition are predicted under hydrostatic pressure. We discuss these trends in terms of orbital composition of involved electronic bands. In addition, we demonstrate that the measured pressure coefficients of HfS

_{2}

and HfSe

_{2}

absorption edges are in perfect agreement with our predictions. Comprehensive and easy-to-interpret tables containing the optical features are provided to form the basis for assignation of optical peaks in future measurements. Full article

(This article belongs to the Special Issue Excitons and Phonons in Two-Dimensional Materials: From Fundamental to Applications)

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12 pages, 1737 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Anisotropic Optical and Vibrational Properties of GeS

by Natalia Zawadzka, Łucja Kipczak, Tomasz Woźniak, Katarzyna Olkowska-Pucko, Magdalena Grzeszczyk, Adam Babiński and Maciej R. Molas

Nanomaterials 2021, 11(11), 3109; https://doi.org/10.3390/nano11113109 - 18 Nov 2021

Cited by 8 | Viewed by 2192

Abstract

The optical response of bulk germanium sulfide (GeS) is investigated systematically using different polarization-resolved experimental techniques, such as photoluminescence (PL), reflectance contrast (RC), and Raman scattering (RS). It is shown that while the low-temperature (T = 5 K) optical band-gap absorption is governed by a single resonance related to the neutral exciton, the corresponding emission is dominated by the disorder/impurity- and/or phonon-assisted recombination processes. Both the RC and PL spectra are found to be linearly polarized along the armchair direction. The measured RS spectra over a broad range from 5 to 300 K consist of six Raman peaks identified with the help of Density Functional Theory (DFT) calculations: A

_{g}^{1}

, A

_{g}^{2}

, A

_{g}^{3}

, A

_{g}^{4}

, B

_{1 g}^{1}

, and B

_{1 g}^{2}

, which polarization properties are studied under four different excitation energies. We found that the polarization orientations of the A

_{g}^{2}

and A

_{g}^{4}

modes under specific excitation energy can be useful tools to determine the GeS crystallographic directions: armchair and zigzag. Full article

(This article belongs to the Special Issue Excitons and Phonons in Two-Dimensional Materials: From Fundamental to Applications)

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Review

Jump to: Editorial, Research

37 pages, 9069 KiB

Open AccessFeature PaperReview

Theory of Excitons in Atomically Thin Semiconductors: Tight-Binding Approach

by Maciej Bieniek, Katarzyna Sadecka, Ludmiła Szulakowska and Paweł Hawrylak

Nanomaterials 2022, 12(9), 1582; https://doi.org/10.3390/nano12091582 - 06 May 2022

Cited by 7 | Viewed by 3475

Abstract

Atomically thin semiconductors from the transition metal dichalcogenide family are materials in which the optical response is dominated by strongly bound excitonic complexes. Here, we present a theory of excitons in two-dimensional semiconductors using a tight-binding model of the electronic structure. In the first part, we review extensive literature on 2D van der Waals materials, with particular focus on their optical response from both experimental and theoretical points of view. In the second part, we discuss our ab initio calculations of the electronic structure of MoS₂, representative of a wide class of materials, and review our minimal tight-binding model, which reproduces low-energy physics around the Fermi level and, at the same time, allows for the understanding of their electronic structure. Next, we describe how electron-hole pair excitations from the mean-field-level ground state are constructed. The electron–electron interactions mix the electron-hole pair excitations, resulting in excitonic wave functions and energies obtained by solving the Bethe–Salpeter equation. This is enabled by the efficient computation of the Coulomb matrix elements optimized for two-dimensional crystals. Next, we discuss non-local screening in various geometries usually used in experiments. We conclude with a discussion of the fine structure and excited excitonic spectra. In particular, we discuss the effect of band nesting on the exciton fine structure; Coulomb interactions; and the topology of the wave functions, screening and dielectric environment. Finally, we follow by adding another layer and discuss excitons in heterostructures built from two-dimensional semiconductors. Full article

(This article belongs to the Special Issue Excitons and Phonons in Two-Dimensional Materials: From Fundamental to Applications)

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