Electron-phonon ($e$-ph) interactions are key to understanding the dynamics of electrons in materials, and can be modeled accurately from first-principles. However, when electrons and holes form Coulomb-bound states (excitons), quantifying their interactions and scattering processes with phonons remains an open challenge. Here we show a rigorous approach for computing exciton-phonon (ex-ph) interactions and the associated exciton dynamical processes from first principles. Starting from the ab initio Bethe-Salpeter equation, we derive expressions for the ex-ph matrix elements and relaxation times. We apply our method to bulk hexagonal boron nitride, for which we map the ex-ph relaxation times as a function of exciton momentum and energy, analyze the temperature and phonon-mode dependence of the ex-ph scattering processes, and accurately predict the phonon-assisted photoluminescence. The approach introduced in this work is general and provides a framework for investigating exciton dynamics in a wide range of materials.
We report a photoluminescence observation of robust excitonic polarons due to strong coupling of exciton and longitudinal optical (LO) phonon as well as Fano-type interference in high quality ZnO crystal. At low enough temperatures, the strong coupling of excitons and LO phonons leads to not only traditional Stokes lines (SLs) but also up to second-order anti-Stokes lines (ASLs) besides the zero-phonon line (ZPL). The SLs and ASLs are found to be not mirror symmetric with respect to the ZPL, strongly suggesting that they are from different coupling states of exciton and phonons. It is more int…
We analyse the interaction of exciton and exciton-polariton condensates in semiconductor microcavity with a coherent acoustic wave. An analytical solution for the dispersion of excitations of coupled condensate-phonon system is found in the approximation of k-independent interactions. Accounting for k-dependence results in a stronger modification of the dispersion, and even in the appearance of the "roton instability" region.
Temperature-dependent radiative recombination of free excitons involving one or two LO phonons in GaN is investigated in detail. It is found that both phonon sidebands possess asymmetric lineshape and their energy spacings from the zero phonon line strongly deviate from the characteristic energy of LO phonons as the temperature increases. Furthermore, the deviation rates of one and two phonon sidebands are significantly different. Segall-Mahan theory, taking the exciton-photon and exciton-phonon interactions into account, is employed to calculate the sidebands of one or two LO phonons for free…
Moiré patterns with angular mismatch in van der Waals heterostructures composed of atomically thin semiconducting materials are a fascinating platform to engineer the optically generated excitonic properties towards novel quantum phenomena. The moiré pattern as a periodic trap potential can give rise to spatially ordered zero-dimensional (0D) exciton ensembles, which offers the possibility for dense coherent quantum emitters and quantum simulation of many-body physics. The intriguing moiré exciton properties are affected by their dynamics and exciton-phonon interaction. However, the moiré exci…
We study theoretically the contribution of quantum effects to the exciton diffusion coefficient in atomically thin crystals. It is related to the weak localization caused by the interference of excitonic wavefunctions on the trajectories with closed loops. Due to a weak inelasticity of the exciton-phonon interaction the effect is present even if the excitons are scattered by long-wavelength acoustic phonons. We consider exciton interaction with longitudinal acoustic phonons with linear dispersion and with flexural phonons with quadratic dispersion. We identify the regimes where the weak locali…
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…
We develop a theory of the linear optical spectrum of excitons in quantum dot molecules, including the effect of exciton-phonon coupling beyond the Markov limit. The model reproduces the general trend of the zero-phonon line broadening as a function of interdot distance, that were recently measured. The unexpectedly broad linewidths and their large variation are explained in terms of both the non-Markov nature of the coupling and of the matching of the phonon wavelength to the interdot distance.
Single-layer transition metal dichalcogenides are at the center of an ever increasing research effort both in terms of fundamental physics and applications. Exciton-phonon coupling plays a key role in determining the (opto)electronic properties of these materials. However, the exciton-phonon coupling strength has not been measured at room temperature. Here, we develop two-dimensional micro-spectroscopy to determine exciton-phonon coupling of single-layer MoSe2. We detect beating signals as a function of waiting time T, induced by the coupling between the A exciton and the A'1 optical phonon. A…
We report resonant Raman spectroscopy of neutral excitons X$^0$ and intravalley trions X$^-$ in hBN-encapsulated MoS$_2$ monolayer embedded in a nanobeam cavity. By temperature tuning the detuning between Raman modes of MoS$_2$ lattice phonons and X$^0$/X$^-$ emission peaks, we probe the mutual coupling of excitons, lattice phonons and cavity vibrational phonons. We observe an enhancement of X$^0$-induced Raman scattering and a suppression for X$^-$-induced, and explain our findings as arising from the tripartite exciton-phonon-phonon coupling. The cavity vibrational phonons provide intermedia…
Moiré Phonons and Emergent Exciton-Phonon Coupling in a Moiré Heterobilayer
University of California, Berkeley（加州大学伯克利分校）；Kavli Energy NanoScience Institute（卡弗里能源纳米科学研究所）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Indian Institute of Science（印度科学学院）；Newcastle University（纽卡斯尔大学）；National Institute for Materials Science（国立材料研究所）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；Northeastern University（东北大学）
Atomically thin layer transition metal dichalcogenides have been intensively investigated for their rich optical properties and potential applications in nano-electronics. In this work, we study the incoherent optical phonon and exciton population dynamics in monolayer WS2 by time-resolved spontaneous Raman scattering spectroscopy. Upon excitation of the exciton transition, both the Stokes and anti-Stokes optical phonon scattering strength exhibit a large reduction. Based on the detailed balance, the optical phonon population is retrieved, which shows an instant build-up and a relaxation lifet…
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…
In monolayer semiconductor transition metal dichalcogenides, the exciton-phonon interaction is expected to strongly affect the photocarrier dynamics. Here, we report on an unusual oscillatory enhancement of the neutral exciton photoluminescence with the excitation laser frequency in monolayer MoSe2. The frequency of oscillation matches that of the M-point longitudinal acoustic phonon, LA(M). Oscillatory behavior is also observed in the steady-state emission linewidth and in timeresolved photoluminescence excitation data, which reveals variation with excitation energy in the exciton lifetime. T…
The coupling between spin, charge, and lattice degrees of freedom plays an important role in a wide range of fundamental phenomena. Monolayer semiconducting transitional metal dichalcogenides have emerged as an outstanding platform for studying these coupling effects because they possess unique spin-valley locking physics for hosting rich excitonic species and the reduced screening for strong Coulomb interactions. Here, we report the observation of multiple valley phonons, phonons with momentum vectors pointing to the corners of the hexagonal Brillouin zone, and the resulting exciton complexes…
We discuss how excitons can affect the generation of coherent radial breathing modes in ultrafast spectroscopy of single wall carbon nanotubes. Photoexcited excitons can be localized spatially and give rise to a spatially distributed driving force in real space which involves many phonon wavevectors of the exciton-phonon interaction. The equation of motion for the coherent phonons is modeled phenomenologically by the Klein-Gordon equation, which we solve for the oscillation amplitudes as a function of space and time. By averaging the calculated amplitudes per nanotube length, we obtain time-de…
We study theoretically the non-equilibrium exciton transport in monolayer transition metal dichalcogenides. We consider the situation where excitons interact with non-equilibrium phonons, e.g., under the conditions of localized excitation where a ``hot spot'' in formed. We develop the theory of the exciton drag by the phonons and analyze in detail the regimes of diffusive propagation of phonons and ballistic propagation of phonons where the phonon wind is formed. We demonstrate that a halo-like spatial distribution of excitons akin observed in [Phys. Rev. Lett. 120, 207401 (2018)] can be forme…
We present an \textit{ab initio} method to calculate phonon-assisted absorption and emission spectra in the presence of strong excitonic effects. We apply the method to bulk hexagonal BN which has an indirect band gap and is known for its strong luminescence in the UV range. We first analyse the excitons at the wave vector $\overline{q}$ of the indirect gap. The coupling of these excitons with the various phonon modes at $\overline{q}$ is expressed in terms of a product of the mean square displacement of the atoms and the second derivative of the optical response function with respect to atomi…
Excitonic quasi-particles, excitons/trions/bi-excitons, and their coupling with phonons and charge carriers play a crucial role in controlling the optical properties of atomically thin semiconducting 2D materials. In this work, we unravelled the dynamics of excitons/trions and their coupling with phonons and charge carriers in a few layers vertically and horizontally aligned MoS2. We observed trion signature up to the highest recorded temperature (330 K) in both systems and have shown that the dynamics of excitons/trions and their coupling with phonons and electrons are more affected in vertic…
In organic semiconductors working under ambient circumstance, there are remarkable quantum effects lack of comprehensive understanding, and an exotic composite particle named charge transfer (CT) exciton is normally regarded as the key ingredient. Another essential substance is the phonons stemming from intra- and inter-molecular vibrations, and the relevant diagonal electron-phonon couplings give rise to spatial localization and the off-diagonal couplings refer to the dispersion of electron wavefunctions. In this work, we first propose a toy model based upon the fracton physics to phenomenolo…
Hexagonal boron nitride (hBN) is a wide band gap material with both strong excitonic light emission in the ultraviolet and strong exciton-phonon coupling. Luminescence experiments performed on the recently synthesized monolayer form (m-hBN) present emission spectra that differ from one another, with some suggesting a coexistence between phonon-assisted and direct emission channels. Motivated by these results, we investigated the optical response of (m-hBN) using a new \textit{ab initio} approach that takes into account the effects of atomic vibrations on the luminescence spectra. We construct …
We calculate the acoustic phonon-assisted exciton spin relaxation in single self-assembled In$_{1-x}$Ga$_x$As/GaAs quantum dots using an atomic empirical pseudopotential method. We show that the transition from bright to dark exciton states is induced by Coulomb correlation effects. The exciton spin relaxation time obtained from sophisticated configuration interaction calculations is approximately 15--55 $μ$s in pure InAs/GaAs QDs and even longer in alloy dots. These results contradict previous theoretical and experimental results, which suggest very short exciton spin times (a few ns), but ag…
Far from resonance, the coupling of the G-band phonon to magneto-excitons in single layer graphene displays kinks and splittings versus filling factor that are well described by Pauli blocking and unblocking of inter- and intra- Landau level transitions. We explore the non-resonant electron-phonon coupling by high-magnetic field Raman scattering while electrostatic tuning of the carrier density controls the filling factor. We show qualitative and quantitative agreement between spectra and a linearized model of electron-phonon interactions in magnetic fields. The splitting is caused by dichrois…
The dephasing time of the lowest bright exciton in CdSe/ZnS wurtzite quantum dots is measured from 5 K to 170 K and compared with density dynamics within the exciton fine structure using a sensitive three-beam four-wave-mixing technique unaffected by spectral diffusion. Pure dephasing via acoustic phonons dominates the initial dynamics, followed by an exponential zero-phonon line dephasing of 109 ps at 5 K, much faster than the ~10 ns exciton radiative lifetime. The zero-phonon line dephasing is explained by phonon-assisted spin-flip from the lowest bright state to dark exciton states. This is…
Moire-Engineered Excitonic Landscape and Phonon-Mediated Recombination in Twisted WSe2 Bilayers
Indian Institute of Technology Mandi（印度技术学院曼迪分校）；CSIR-National Physical Laboratory（印度科学工业研究理事会国家物理实验室）；Academy of Scientific and Innovative Research (AcSIR)（科学与创新研究学院）；Indian Institute of Science（印度科学学院）；National Institute of Material Science（国家物质科学研究所）
The effects of the electron-phonon interaction on optical excitations can be understood in terms of exciton-phonon coupling, and require a careful treatment in low-dimensional materials with strongly bound excitons or strong electron-hole interaction in general. Through phonon absorption and emission processes, the optically accessible excitons are scattered into otherwise optically dark finite-momentum exciton states. We derive a practical expression for the phonon-induced term of the exciton self-energy (denoted as the exciton-phonon self-energy) that gives the temperature dependence of the …
We examine a mechanism by which excitons undergo ultrafast relaxation in common monolayer transition metal dichalcogenides. It is shown that at densities $\approx$ 1$\times$ 10$^{11}$ cm$^{-2}$ and temperatures $ \le 60$ K, excitons in well known monolayers (MoS$_2$, MoSe$_2$, WS$_2$ and WSe$_2$) exist as point-like structureless electron-hole quasi-particles. We evaluate the average rate of exciton energy relaxation due to acoustic phonons via the deformation potential and the piezoelectric coupling mechanisms and examine the effect of spreading of the excitonic wavefunction into the region p…
The optical properties of the two-dimensional (2D) crystals are dominated by tightly bound electron-hole pairs (excitons) and lattice vibration modes (phonons). The exciton-phonon interaction is fundamentally important to understand the optical properties of 2D materials and thus help develop emerging 2D crystal based optoelectronic devices. Here, we presented the excitonic resonant Raman scattering (RRS) spectra of few-layer WS$_2$ excited by 11 lasers lines covered all of A, B and C exciton transition energies at different sample temperatures from 4 to 300 K. As a result, we are not only abl…
The ability to assemble layers of two-dimensional (2D) materials to form permutations of van der Waals heterostructures provides significant opportunities in materials design and synthesis. Interlayer interactions provide a path to new properties and functionality, and understanding such interactions is essential to that end. Here we report formation of interlayer exciton-phonon bound states in Bi2Se3/WS2 heterostructures, where the Bi2Se3 A1(3) surface phonon, a mode particularly susceptible to electron-phonon coupling, is imprinted onto the excitonic emission of the WS2. The exciton-phonon b…
The excitonic luminescence of an isolated polydiacetylene polymer chain in its monomer matrix is studied by micro-photoluminescence. These chains behave as perfect 1D excitonic systems with the expected 1/sqrt{E} density of states between 5 and 50 K. The temperature dependence of the homogeneous width is quantitatively explained by interaction with longitudinal acoustic phonons of the crystal in the range of temperature explored.
We find that the optical properties of carbon nanotubes reflect remarkably strong effects of exciton-phonon coupling. Tight-binding calculations show that a significant fraction of the spectral weight of the absorption peak is transferred to a distinct exciton+phonon sideband, which is peaked at around 200 meV above the main absorption peak. This sideband provides a distinctive signature of the excitonic character of the optical transition. The exciton-phonon coupling is reflected in a dynamical structural distortion, which contributes a binding energy of up to 100 meV. The distortion is surpr…
Single-walled carbon nanotubes (SWCNTs) are quasi-one-dimensional systems with poor Coulomb screening and enhanced electron-phonon interaction, and are good candidates for excitons and exciton-phonon couplings in metallic state. Here we report back scattering reflection experiments on individual metallic SWCNTs. An exciton-phonon sideband separated by 0.19 eV from the first optical transition peak is observed in a metallic SWCNT of chiral index (13,10), which provides clear evidences of excitons in metallic SWCNTs. A static dielectric constant of 10 is estimated from the reflectance spectrum.
A full quantum mechanical theory for the spontaneous emission from excitons simultaneously coupled to electronic excitations and anharmonic phonons in solid is developed. Origin of detailed structures, such as zero-phonon line splitting, Fano lineshape near one phonon sideband, strong second-order phonon Stokes line, asymmetric phonon anti-Stokes lines, and two-electron satellites as well as their phonon replicas recently revealed in the low-temperature photoluminescence of ZnO, has been identified by quantitative calculations from the theory.
We report on the exciton formation and relaxation dynamics following photocarrier injection in a single-layer two-dimensional lead-iodide perovskite. We probe the time evolution of four distinct exciton resonances by means of time-resolved photoluminescence and transient absorption spectroscopies, and find that at 5\,K a subset of excitons form on a $\lesssim$ 1-ps timescale, and that these relax subsequently to lower-energy excitons on $\sim$ 5--10\,ps with a marked temperature dependence over $<$ 100\,K. We implement a mode projection analysis that determines the relative contribution of all…
We study experimentally and theoretically the exciton-phonon interaction in MoSe2 monolayers encapsulated in hexagonal BN, which has an important impact on both optical absorption and emission processes. The exciton transition linewidth down to 1 meV at low temperatures makes it possible to observe high energy tails in absorption and emission extending over several meV, not masked by inhomogeneous broadening. We develop an analytical theory of the exciton-phonon interaction accounting for the deformation potential induced by the longitudinal acoustic phonons, which plays an important role in e…
The excitonic absorption spectrum for a disordered quantum well in presence of exciton-acoustic phonon interaction is treated beyond the Markov approximation. Realistic disorder exciton states are taken from a microscopic simulation, and the deformation potential interaction is implemented. The exciton Green's function is solved with a self energy in second order Born quality. The calculated spectra differ from a superposition of Lorentzian lineshapes by enhanced inter-peak absorption. This is a manifestation of pure dephasing which should be possible to measure in near-field experiments.
High degree of preservation of spin states during energy relaxation processes mediated by optical phonons is demonstrated in a single quantum dot. Optical-phonon resonance and relevant suppression of spin relaxation are clearly identified as dip structures in photoluminescence excitation spectra probed by the positive trion emission. The absence of continuum states makes this observation possible under the cross-circularly polarized detection with respect to a circularly polarized pumping. Consequently, distinguishably high degree of circular polarization up to ~0.85 is achieved without applyi…
The novel method of observation and controlling of Bose-Einstein condensation in the system of spatially and momentum-space indirect excitons in coupled quantum wells using in-plane magnetic and normal electric fields is proposed. Fields are used for exciton dispersion engeneering. In the presence of in-plane magnetic field ground state of spatially indirect exciton becomes also indirect in the momentum space. Manipulation of electric field magnitude is used for tuning to resonance of transition of "dark" long-life spatially and momentum-space indirect exciton in condensate into spatially and …
The temperature-dependent optical response of excitons in semiconductors is controlled by the exciton-phonon interaction. When the exciton-lattice coupling is weak, the excitonic line has a Lorentzian profile resulting from motional narrowing, with a width increasing linearly with the lattice temperature $T$. In contrast, when the exciton-lattice coupling is strong, the lineshape is Gaussian with a width increasing sublinearly with the lattice temperature, proportional to $\sqrt{T}$. While the former case is commonly reported in the literature, here the latter is reported for the first time, f…
The concept of \textit{optical} exciton - a photo-excited bound electron-hole pair within a crystal - is routinely used to interpret and model a wealth of excited-state phenomena in semiconductors. Beside originating sub-band gap signatures in optical spectra, optical excitons have also been predicted to condensate, diffuse, recombine, relax. However, all these phenomena are rooted on a theoretical definition of the excitonic state based on the following simple picture: "excitons" are actual particles that both appear as peaks in the linear absorption spectrum and also behave as well-defined q…
We demonstrate that the optical linewidth of Rydberg excitons in Cu2O can be completely explained by scattering with acoustical and optical phonons, whereby the dominant contributions stems from the non-polar optical modes. The consequences for the observation of polariton effects are discussed. We find that an anti-crossing of photon and exciton dispersions exists only for states with main quantum numbers n>28, so polariton effects do not play any role in the experiments reported up to now.
Micro-photoluminescence spectroscopy at variable temperature, excitation intensity and energy was performed on a single InAs/AlAs self-assembled quantum dot. The exciton emission line (zero-phonon line, ZPL) exhibits a broad sideband due to exciton-acoustic phonon coupling by the deformation potential mechanism. Additionally, narrow low-energy sidebands at about 0.25 meV of the ZPL are attributed to exciton-acoustic phonon piezoelectric coupling. In lowering the excitation energy or intensity these bands gradually dominate the emission spectrum of the quantum dot while the ZPL disappears. At h…
We investigate the spin dynamics of excitons interacting with acoustic phonons in quantum wells, quantum wires and quantum disks by employing a multiband model based on the $4\times4$ Luttinger Hamiltonian. We also use the Bir-Pikus Hamiltonian to model the coupling of excitons to both longitudinal acoustic phonons and transverse acoustic phonons, thereby providing us with a realistic framework in which to determine details of the spin dynamics of excitons. We use a fractional dimensional formulation to model the excitonic wavefunctions and we demonstrate explicitly the decrease of spin relaxa…
We performed detailed photoluminescence (PL) spectroscopy studies of three different types of single-walled carbon nanotubes (SWNTs) by using samples that contain essentially only one chiral type of SWNT, (6,5), (7,5), or (10,5). The observed PL spectra unambiguously show the existence of an emission sideband at ~ 145 meV below the lowest singlet excitonic (E11) level, whose identity and origin are now under debate. We find that the energy separation between the E11 level and the sideband is almost independent of the SWNT diameter. Based on this, we ascribe the origin of the observed sideband …
