Three-particle correlation from a Many-Body Perspective: Trions in a Carbon Nanotube

Exact Quantum Virial Expansion for the Optical Response of Doped Two-Dimensional Semiconductors

We introduce a quantum virial expansion for the optical response of a doped two-dimensional semiconductor. As we show, this constitutes a perturbatively exact theory in the high-temperature or low-doping regime, where the electrons' thermal wavelength is smaller than their interparticle spacing. We obtain exact analytic expressions for the photoluminescence and we predict new features such as a nontrivial shape of the attractive branch peak related to universal resonant exciton-electron scattering and an associated energy shift from the trion energy. Our theory furthermore allows us to formally unify the two distinct theoretical pictures that have been applied to this system, where we reveal that the predictions of the conventional trion picture correspond to a high-temperature and weak-interaction limit of Fermi-polaron theory. Our results are in excellent agreement with recent experiments on doped monolayer MoSe_{2} and they provide the foundation for modeling a range of emerging optically active materials such as van der Waals heterostructures.

Electrostatic and Environmental Control of the Trion Fine Structure in Transition Metal Dichalcogenide Monolayers

Charged excitons or trions are essential for optical spectra in low-dimensional doped monolayers (ML) of transitional metal dichalcogenides (TMDC). Using a direct diagonalization of the three-body Hamiltonian, we calculate the low-lying trion states in four types of TMDC MLs as a function of doping and dielectric environment. We show that the fine structure of the trion is the result of the interplay between the spin-valley fine structure of the single-particle bands and the exchange interaction. We demonstrate that by variations of the doping and dielectric environment, the fine structure of the trion energy can be tuned, leading to anticrossing of the bright and dark states, with substantial implications for the optical spectra of the TMDC ML.

Computational methods for 2D materials modelling

Materials with thickness ranging from a few nanometers to a single atomic layer present unprecedented opportunities to investigate new phases of matter constrained to the two-dimensional plane. Particle-particle Coulomb interaction is dramatically affected and shaped by the dimensionality reduction, driving well-established solid state theoretical approaches to their limit of applicability. Methodological developments in theoretical modelling and computational algorithms, in close interaction with experiments, led to the discovery of the extraordinary properties of two-dimensional materials, such as high carrier mobility, Dirac cone dispersion and bright exciton luminescence, and inspired new device design paradigms. This review aims to describe the computational techniques used to simulate and predict the optical, electronic and mechanical properties of two-dimensional materials, and to interpret experimental observations. In particular, we discuss in detail the particular challenges arising in the simulation of two-dimensional constrained fermions and quasiparticles, and we offer our perspective on the future directions in this field.

Signatures of Dimensionality and Symmetry in Exciton Band Structure: Consequences for Exciton Dynamics and Transport

Exciton dynamics, lifetimes, and scattering are directly related to the exciton dispersion or band structure. Here, we present a general theory for exciton band structure within both ab initio and model Hamiltonian approaches. We show that contrary to common assumption, the exciton band structure contains nonanalytical discontinuities-a feature which is impossible to obtain from the electronic band structure alone. These discontinuities are purely quantum phenomena, arising from the exchange scattering of electron-hole pairs. We show that the degree of these discontinuities depends on materials' symmetry and dimensionality, with jump discontinuities occurring in 3D and different orders of removable discontinuities in 2D and 1D, whose details depend on the exciton degeneracy and material thickness. We connect these features to the early stages of exciton dynamics, radiative lifetimes, and diffusion constants, in good correspondence with recent experimental observations, revealing that the discontinuities in the band structure lead to ultrafast ballistic transport and suggesting that measured exciton diffusion and dynamics are influenced by the underlying exciton dispersion.

sp3-Functionalization of Single-Walled Carbon Nanotubes Creates Localized Spins

Chemical functionalization-introduced sp³ quantum defects in single-walled carbon nanotubes (SWCNTs) have shown compelling optical properties for their potential applications in quantum information science and bioimaging. Here, we utilize temperature- and power-dependent electron spin resonance measurements to study the fundamental spin properties of SWCNTs functionalized with well-controlled densities of sp³ quantum defects. Signatures of isolated spins that are highly localized at the sp³ defect sites are observed, which we further confirm with density functional theory calculations. Applying temperature-dependent line width analysis and power-saturation measurements, we estimate the spin-lattice relaxation time T₁ and spin dephasing time T₂ to be around 9 μs and 40 ns, respectively. These findings of the localized spin states that are associated with the sp³ quantum defects not only deepen our understanding of the molecular structures of the quantum defects but could also have strong implications for their applications in quantum information science.

Light-matter interaction in van der Waals hetero-structures

Even if individual two-dimensional materials own various interesting and unexpected properties, the stacking of such layers leads to van der Waals solids which unite the characteristics of two dimensions with novel features originating from the interlayer interactions. In this topical review, we cover fabrication and characterization of van der Waals hetero-structures with a focus on hetero-bilayers made of monolayers of semiconducting transition metal dichalcogenides. Experimental and theoretical techniques to investigate those hetero-bilayers are introduced. Most recent findings focusing on different transition metal dichalcogenides hetero-structures are presented and possible optical transitions between different valleys, appearance of moiré patterns and signatures of moiré excitons are discussed. The fascinating and fast growing research on van der Waals hetero-bilayers provide promising insights required for their application as emerging quantum-nano materials.

Enhanced Carrier-Exciton Interactions in Monolayer MoS2 under Applied Voltages

Carrier-exciton interactions in two-dimensional transition metal dichalcogenides (TMDs) is one of the crucial elements for limiting the performance of their optoelectronic devices. Here, we have experimentally studied the carrier-exciton interactions in a monolayer MoS₂-based two-terminal device. Such two-terminal device without a gate electrode is generally considered as invalid to modulate the carrier concentration in active materials, while the photoluminescence peak exhibits a red shift and decay with increasing applied voltages. Time-resolved photoluminescence spectroscopy and photoluminescence multipeak fittings verify that such changes of photoluminescence peaks result from enhanced carrier-exciton interactions with increasing electron concentration induce the charged exciton increasing. To characterize the level of the carrier-exciton interactions, a quantitative relationship between the Raman shift of out-of-plane mode and changes in electron concentration has been established using the mass action model. This work provides an appropriate supplement for understanding the carrier-exciton interactions in TMD-based two-terminal optoelectronic devices.

Erratum: Three-Particle Correlation from a Many-Body Perspective: Trions in a Carbon Nanotube [Phys. Rev. Lett. 116, 196804 (2016)]

This corrects the article DOI: 10.1103/PhysRevLett.116.196804.

Excited-State Trions in Monolayer WS_{2}

We discover an excited bound three-particle state, the 2s trion, appearing energetically below the 2s exciton in monolayer WS_{2}, using absorption spectroscopy and ab initio GW and Bethe-Salpeter equation calculations. The measured binding energy of the 2s trion (22 meV) is smaller compared to the 1s intravalley and intervalley trions (37 and 31 meV). With increasing temperature, the 1s and 2s trions transfer their oscillator strengths to the respective neutral excitons, establishing an optical fingerprint of trion-exciton resonance pairs. Our discovery underlines the importance of trions for the entire excitation spectrum of two-dimensional semiconductors.

Many-particle excitations in non-covalently doped single-walled carbon nanotubes

Doping of single-walled carbon nanotubes leads to the formation of new energy levels which are able to participate in optical processes. Here, we investigate (6,5)-single walled carbon nanotubes doped in a solution of hydrochloric acid using optical absorption, photoluminescence, and pump-probe transient absorption techniques. We find that, beyond a certain level of doping, the optical spectra of such nanotubes exhibit the spectral features related to two doping-induced levels, which we assign to a localized exciton [Formula: see text] and a trion T, appearing in addition to an ordinary exciton [Formula: see text]. We evaluate the formation and relaxation kinetics of respective states and demonstrate that the kinetics difference between E1 and X energy levels perfectly matches the kinetics of the state T. This original finding evidences the formation of trions through nonradiative relaxation via the [Formula: see text] level, rather than via a direct optical excitation from the ground energy state of nanotubes.

Polarity Tunable Trionic Electroluminescence in Monolayer WSe2

Monolayer WSe₂ exhibits luminescence arising from various types of exciton complexes due to strong many-body effects. Here, we demonstrate selective electrical excitation of positive and negative trions in van der Waals metal-insulator-semiconductor (MIS) heterostructure consisting of few-layer graphene (FLG), hexagonal boron nitride (hBN), and monolayer WSe₂. Intentional unbalanced injection of electrons and holes is achieved via field-emission tunneling and electrostatic accumulation. The device exhibits planar electroluminescence from either positive trion X⁺ or negative trion X^- depending on the bias conditions. We show that hBN serves as a tunneling barrier material allowing selective injection of electron or holes into WSe₂ from FLG layer. Our observation offers prospects for hot carrier injection, trion manipulation, and on-chip excitonic devices based on two-dimensional semiconductors.

Many-body simulation of two-dimensional electronic spectroscopy of excitons and trions in monolayer transition metal dichalcogenides

Indications of coherently interacting excitons and trions in doped transition metal dichalcogenides have been measured as quantum beats in two-dimensional electronic spectroscopy, but the microscopic principles underlying the optical signals of exciton-trion coherence remain to be clarified. Here we present calculations of two-dimensional spectra of such monolayers based on a microscopic many-body formalism. We use a parameterized band structure and a static model dielectric function, although a full ab initio implementation of our formalism is possible in principle. Our simulated spectra are in excellent agreement with experiments, including the quantum beats, while revealing the interplay between excitons and trions in molybdenum- and tungsten-based transition metal dichalcogenides. Quantum beats are confirmed to unambiguously reflect the exciton-trion coherence time in molybdenum compounds, but are shown to provide a lower bound to the coherence time for tungsten analogues due to a destructive interference from coexisting singlet and triplet trions.

2D electronic spectroscopy found experimental indications of coherently interacting excitons and trions in doped transition metal dichalcogenides (TMDCs). Here, the authors perform simulations of 2D spectra of monolayer TMDCs based on a many-body formalism, allowing to relate exciton-trion coherence to quantum beats based on microscopic principles.

Benchmark study of ionization potentials and electron affinities of armchair single-walled carbon nanotubes using density functional theory

The intrinsic parameters of carbon nanotubes (CNTs) such as ionization potential (IP) and electron affinity (EA) are closely related to their unique properties and associated applications. In this work, we demonstrated the success of optimal tuning method based on range-separated (RS) density functionals for both accurate and efficient prediction of vertical IPs and electron affinities (EAs) of a series of armchair single-walled carbon nanotubes C_20n H₂₀ (n  =  2-6) compared to the high-level IP/EA equation-of-motion coupled-cluster method with single and double substitutions (IP/EA-EOM-CCSD). Notably, the resulting frontier orbital energies (-ε _HOMO and -ε _LUMO) from the tuning method exhibit an excellent approximation to the corresponding IPs and EAs, that significantly outperform other conventional density functionals. In addition, it is suggested that the RS density functionals that possess both a fixed amount of exact exchange in the short-range and a correct long-range asymptotic behavior are suitable for calculating electronic structures of finite-sized CNTs. Next the performance of density functionals for description of various molecular properties such as chemical potential, hardness and electrophilicity are assessed as a function of tube length. Thanks to the efficiency and accuracy of this tuning method, the related behaviors of much longer armchair single-walled CNTs until C₂₀₀H₂₀ were studied. Lastly, the present work is proved to provide an efficient theoretical tool for future materials design and reliable characterization of other interesting properties of CNT-based systems.

Interlayer Trions in the MoS2/WS2 van der Waals Heterostructure

Electronic excitations in van der Waals heterostructures can have interlayer or intralayer character depending on the spatial localization of the involved charges (electrons and holes). In the case of neutral electron-hole pairs (excitons), both types of excitations have been explored theoretically and experimentally. In contrast, studies of charged trions have so far been limited to the intralayer type. Here we investigate the complete set of interlayer excitations in a MoS₂/WS₂ heterostructure using a novel ab initio method, which allows for a consistent treatment of both excitons and trions at the same theoretical footing. Our calculations predict the existence of bound interlayer trions below the neutral interlayer excitons. We obtain binding energies of 18/28 meV for the positive/negative interlayer trions with both electrons/holes located on the same layer. In contrast, a negligible binding energy is found for trions which have the two equally charged particles on different layers. Our results advance the understanding of electronic excitations in doped van der Waals heterostructures and their effect on the optical properties.

Diversity of trion states and substrate effects in the optical properties of an MoS2 monolayer

Almost all experiments and future applications of transition metal dichalcogenide monolayers rely on a substrate for mechanical stability, which can significantly modify the optical spectra of the monolayer. Doping from the substrate might lead to the domination of the spectra by trions. Here we show by ab initio many-body theory that the negative trion (A⁻) splits into three excitations, with both inter- and intra-valley character, while the positive counterpart (A⁺) consists of only one inter-valley excitation. Furthermore, the substrate enhances the screening, which renormalizes both band gap and exciton as well as the trion-binding energies. We verify that these two effects do not perfectly cancel each other, but lead to red-shifts of the excitation energies for three different substrates ranging from a wide-bandgap semiconductor up to a metal. Our results explain recently found experimental splittings of the lowest trion line as well as excitation red-shifts on substrates.

The optical and electrical properties of atomically thin transition metal dichalcogenides critically depend on the underlying substrate. Here, the authors develop an abinitio many-body formalism to investigate the full spectrum of negative and positive trions in these layered semicondutors.

Huge Trionic Effects in Graphene Nanoribbons

One- and two-dimensional materials are being intensively investigated due to their interesting properties for next-generation optoelectronic devices. Among these, armchair-edged graphene nanoribbons are very promising candidates with optical properties that are dominated by excitons. In the presence of additional charges, trions (i.e., charged excitons) can occur in the optical spectrum. With our recently developed first-principle many-body approach (Phys. Rev. Lett. 116, 196804), we predict strongly bound trions in free-standing nanoribbons with large binding energies of 140-660 meV for widths of 14.6-3.6 Å. Both for the trions and for the excitons, we observe an almost linear dependency of their binding energies on the band gap. We observe several trion states with different character derived from the corresponding excitons. Because of the large bindings energies, this opens a route to applications by which optical properties are easily manipulated, for example, by electrical fields.