Electron-hole generation and recombination rates for intravalley and intervalley phonon scattering in Graphene are presented. The transverse and the longitudinal optical phonon modes ($E_{2g}$-modes) near the zone center ($Γ$-point) contribute to intravalley interband carrier scattering. At the zone edge ($K(K')$-point), only the transverse optical phonon mode ($A'_{1}$-mode) contributes significantly to intervalley interband scattering with recombination rates faster than those due to zone center phonons. The calculated recombination times range from less than a picosecond to more than hundreds of picoseconds and are strong functions of temperature and electron and hole densities. The theoretical calculations agree well with experimental measurements of the recombination rates of photoexcited carriers in graphene.
We investigate the in-plane spin relaxation of electrons due to the D'yakonov-Perel' and Elliot-Yafet mechanisms including the intra- and inter-valley processes in monolayer MoS$_2$. We construct the effective Hamiltonian for the conduction band using the Löwdin partition method from the anisotropic two-band Hamiltonian with the intrinsic spin-orbit coupling of the conduction band included. The spin-orbit coupling of the conduction band induces the intra- and inter-valley D'yakonov-Perel' spin relaxation. In addition, the Elliot-Yafet spin relaxation also takes place due to the interband spin …
The magnetic-field dependence of the energy spectrum, wave function, binding energy and oscillator strength of exciton states confined in a circular graphene quantum dot (CGQD) are obtained within the configuration interaction (CI) method. We predict that: (1) excitonic effects are very significant in the CGQD as a consequence of a combination of geometric confinement, magnetic confinement and reduced screening; (2) two types of excitons (intravalley and intervalley excitons) are present in the CGQD because of the valley degree of freedom in graphene; (3) the intravalley and intervalley excito…
By considering analytical expressions for the self-energies of intervalley and intravalley phonons in graphene, we describe the behavior of D, 2D, and D$'$ Raman bands with changes in doping ($μ$) and light excitation energy ($E_L$). Comparing the self-energy with the observed $μ$ dependence of the 2D bandwidth, we estimate the wavevector $q$ of the constituent intervalley phonon at $\hbar vq\simeq E_L/1.6$ ($v$ is electron's Fermi velocity) and conclude that the self-energy makes a major contribution (60%) to the dispersive behavior of the D and 2D bands. The estimation of $q$ is based on an …
A Kubo formalism is used to calculate the electronic and optical conductivity of a graphene superlattice with Y-shaped kekulé bond texture, similar to that visualized in recent experiments. We show that new conduction channels between the valleys in graphene are opened by the kekulé distortion. This intervalley contribution to the electronic transport is not present in pristine graphene and here appears due to the folding of the Dirac cones $K$, $K'$ on top of each other. The contribution of intervalley transport to the conductivity of graphene, as well as the modification of the intravalley t…
Excitons and trions (or exciton-polarons) in transition metal dichalcogenides (TMDs) are known to decay predominantly through intravalley transitions. Electron-hole recombination across different valleys can also play a significant role in the excitonic dynamics, but intervalley transitions are rarely observed in monolayer TMDs, because they violate the conservation of momentum. Here we reveal the intervalley recombination of dark excitons and trions through more than one path in monolayer WSe$_2$. We observe the intervalley dark excitons, which can recombine by the assistance of defect scatte…
We propose an analytical model describing Fermi arc surface states observed in the recent investigations of Weyl semimetals. The effective two-valley Hamiltonian is supplemented by the boundary conditions taking into account both the intravalley and intervalley interfacial interaction. We demonstrate that the latter is crucial for the formation of the surface states having the form consistent with the experimental data. Depending on the magnitude and interplay between the intravalley and intervalley interactions, the Fermi arc connects two nearby or distant valleys. Moreover, the emergence of …
Band gap engineering in graphene may open the routes towards transistor devices in which electric current can be switched off and on at will. One may, however, ask if a semiconducting band gap alone is sufficient to quench the current in graphene. In this paper we demonstrate that despite a bulk band gap graphene can still have metallic conductance along the sample edges (provided that they are shorter than the localization length). We find this for single-layer graphene with a zigzag-type boundary which hosts gapless propagating edge states even in the presence of a bulk band gap. By generati…
The coherent third-order nonlinear response of monolayer transition-metal dichalcogenide (TMD) semiconductors, such as MoSe$_2$ is dominated by the nonlinear exciton response, as well as biexciton and trion resonances. The fact that these resonances may be spectrally close together makes identification of the signatures, for example in differential transmission (DT), challenging. Instead of focusing on explaining a given set of experimental data, a systematic study aimed at elucidating the roles of intravalley and intervalley electron-hole (e-h) exchange on the DT spectra is presented. Previou…
The interactions between electrons and lattice vibrational modes play the key role in determining the carrier transport properties, thermoelectric performance and other physical quantities related to phonons in semiconductors. However, for two-dimensional (2D) materials, the widely-used models for carrier transport only consider the interactions between electrons and some specific phonon modes, which usually leads to inaccruate predictions of electrons/phonons transport properties. In this work, comprehensive investigations on full electron-phonon couplings and their influences on carrier mobi…
The power loss $P$ of hot Dirac fermions through the coupling to the intrinsic intravalley and intervalley acoustic and optical phonons is analytically investigated in silicene as a function of electron temperature $T_e$ and density $n_s$. At very low $T_e$, the power dissipation is found to follow the Bloch-Grüneisen power-law $\propto T_e^4$ and $n_s^{-0.5}$, as in graphene, and for $T_e \lesssim20-30$ K, the power loss is predominantly due to the intravalley acoustic phonon scattering. On the other hand, dispersionless low energy intervalley acoustic phonons begin to dominate the power tran…
The variety of excitonic states in tungsten-based dichalcogenide monolayers stems from unique interplay between the spin and valley degrees of freedom. One of the exciton species is the indirect exciton (momentum or valley dark), which is responsible to a series of resonances when the monolayer is charge neutral. We investigate the short-range electron-hole exchange interaction of the indirect exciton, as well as its recombination mechanism mediated by impurities. The analysis provides thorough understanding of the energy and polarization of the zero-phonon indirect exciton resonance in the em…
We consider mutual effect of the electron-phonon and strong Coulomb interactions on each other by summing up leading logarithmic corrections via the renormalization group approach. We find that the Coulomb interaction enhances electron coupling to the intervalley A1 optical phonons, but not to the intravalley E2 phonons.
The electronic properties of twisted bilayer graphene on SiC substrate were studied via combination of transport measurements and scanning tunneling microscopy. We report the observation of enhanced intervalley scattering from one Dirac cone to the other, which contributes to weak localization, of the twisted bilayer graphene by increasing the interlayer coupling strength. Our experiment and analysis demonstrate that the enhanced intervalley scattering is closely related to the periodic AB stacked atoms (the A atom of layer 1 and the B atom of layer 2 that have the same horizontal positions) t…
We report magneto-photoluminescence spectroscopy of gated MoS$_2$ monolayers in high magnetic fields to 28 T. At B = 0T and electron density $n_s\sim 10^{12}cm^-2$, we observe three trion resonances that cannot be explained within a single-particle picture. Employing ab initio calculations that take into account three-particle correlation effects as well as local and non-local electron-hole exchange interaction, we identify those features as quantum superpositions of inter- and intravalley spin states. We experimentally investigate the mixed character of the trion wave function via the filling…
We study the quantum diffusive transport of multivalley massive Dirac cones, where time-reversal symmetry requires opposite spin orientations in inequivalent valleys. We show that the intervalley scattering and intravalley scattering can be distinguished from the quantum conductivity that corrects the semiclassical Drude conductivity, due to their distinct symmetries and localization trends. In immediate practice, it allows transport measurements to estimate the intervalley scattering rate in hole-doped monolayers of group-VI transition metal dichalcogenides (e.g., molybdenum dichalcogenides a…
Effect of spin-dependent tunneling and intervalley scattering in magnetic-semiconductor van der Waals heterostructures on exciton and trion polarization
Moiré superlattice created by twist stacking has multiple physical properties. These physical properties depend on the twist angle, hence investigation of the twist angle dependency is important for the deep understanding of physical phenomena in moiré superlattice. In this work, negative magnetoresistance owing to weak localization (WL) was investigated in twisted double bilayer graphene (TDBG) as a function of the twist angle. The ratio of the intervalley scattering time to the intravalley scattering time, estimated using the WL formula for bilayer graphene, tended to decrease as the twist a…
We have carried out scanning tunneling spectroscopy measurements on exfoliated monolayer graphene on SiO$_2$ to probe the correlation between its electronic and structural properties. Maps of the local density of states are characterized by electron and hole puddles that arise due to long range intravalley scattering from intrinsic ripples in graphene and random charged impurities. At low energy, we observe short range intervalley scattering which we attribute to lattice defects. Our results demonstrate that the electronic properties of graphene are influenced by intrinsic ripples, defects and…
Graphitic nitrogen-doped graphene is an excellent platform to study scattering processes of massless Dirac fermions by charged impurities, in which high mobility can be preserved due to the absence of lattice defects through direct substitution of carbon atoms in the graphene lattice by nitrogen atoms. In this work, we report on electrical and magnetotransport measurements of high-quality graphitic nitrogen-doped graphene. We show that the substitutional nitrogen dopants in graphene introduce atomically sharp scatters for electrons but long-range Coulomb scatters for holes and, thus, graphitic…
Here we report a facile method to generate a high density of point defects in graphene on metal foil and show how the point defects affect the electronic structures of graphene layers. Our scanning tunneling microscopy (STM) measurements, complemented by first principle calculations, reveal that the point defects result in both the intervalley and intravalley scattering of graphene. The Fermi velocity is reduced in the vicinity area of the defect due to the enhanced scattering. Additionally, our analysis further points out that periodic point defects can tailor the electronic properties of gra…
Mesoscopic conductance fluctuations in graphene samples at energies not very close to the Dirac point are studied analytically. We demonstrate that the conductance variance $<[δG]^2>$ is very sensitive to the elastic scattering breaking the valley symmetry. In the absence of such scattering (disorder potential smooth at atomic scales, trigonal warping negligible), the variance $<[δG]^2 > = 4 < [δG]^2 >_\text{metal}$ is four times greater than that in conventional metals, which is due to the two-fold valley degeneracy. In the absence of intervalley scattering, but for strong intravalley scatter…
Atomically thin materials, like semiconducting transition metal dichalcogenides, are highly sensitive to the environment. This opens up an opportunity to externally control their properties by changing their surroundings. In this work, high-quality van der Waals heterostructures assembled from hBN-encapsulated monolayer MoS$_2$ are studied with the aid of photoluminescence, photoluminescence excitation, and reflectance contrast experiments. We demonstrate that carrier concentration in MoS$_2$ monolayers, arising from charge transfer from impurities in the substrate, can be significantly tuned …
We investigate the hole spin relaxation due to the Rashba spin-orbit coupling induced by an external perpendicular electric field in bilayer WSe$_2$. The Rashba spin-orbit coupling coefficients in bilayer WSe$_2$ are constructed from the corresponding monolayer ones. In contrast to monolayer WSe$_2$, the out-of-plane component of the bilayer Rashba spin-orbit coupling acts as a Zeeman-like field with opposite directions but identical values in the two valleys. For in-plane spins, this Zeeman-like field, together with the intervalley hole-phonon scattering, opens an intervalley spin relaxation …
Early experiments on alkali-doped graphene demonstrated that the dopant adatoms modify the conductivity of graphene significantly, as extra carriers enhance conductivity while Coulomb scattering off the adatoms suppresses it. However, conductivity probes the overall scattering rate, so a dominant channel associated with long-range Coulomb scattering will mask weaker short-range channels. We present weak localization measurements of epitaxial graphene with lithium adatoms that separately quantify intra- and intervalley scattering rates, then compare the measurements to tight-binding calculation…
Vertical graphene heterostructures made up of graphene layers separated by BN spacers allow for novel ways of tuning the interactions between electrons. We study the possibility of electron pairing mediated by modified repulsive interactions. Long range intravalley and short range intervalley interactions give rise to different anisotropic phases. We show that a superconducting state with gaps of opposite signs in different valleys, an odd momentum pairing state, can exist above carrier densities of $5-10 \times 10^{13} {\rm cm}^{-2}$. The dependence of the transition temperature on the differ…
Monolayer transition metal dichalcogenides offer the possibility of optical control of the valley degree of freedom. In order to asses the potential of these materials in applications, detailed knowledge of the valley dynamics is essential. In this work, we apply low temperature time-resolved photoluminescence (PL) measurements to investigate exciton valley relaxation dynamics and, in particular, its behavior under strong excitation. At the lowest excitation powers the inter valley scattering time is $\simeq 50$ ps, but shortens by more than a factor of two at the highest powers. We attribute …
The recently-discovered monolayer transition metal dichalcogenides (TMDCs) provide a fertile playground to explore new coupled spin-valley physics. Although robust spin and valley degrees of freedom are inferred from polarized photoluminescence (PL) experiments, PL timescales are necessarily constrained by short-lived (3-100ps) electron-hole recombination. Direct probes of spin/valley polarization dynamics of resident carriers in electron (or hole) doped TMDCs, which may persist long after recombination ceases, are at an early stage. Here we directly measure the coupled spin-valley dynamics in…
The scattering of two-dimensional massless Dirac fermions from local spin-orbit interactions with an origin in dilute concentrations of physisorbed atomic species on graphene is theoretically investigated. The hybridization between graphene and the adatoms' orbitals lifts spin and valley degeneracies of the pristine host material, giving rise to rich spin-orbit coupling mechanisms with features determined by the exact adsorption position on the honeycomb lattice - bridge, hollow or top position - and the adatoms' outer-shell orbital type. Effective graphene-only Hamiltonians are derived from s…
Spin-forbidden intravalley dark exciton in tungsten-based transition metal dichalcogenides (TMDCs), owing to its unique spin texture and long lifetime, has attracted intense research interest. Here, we show that we can control the dark exciton electrostatically by dressing it with one free electron or free hole, forming the dark trions. The existence of the dark trions is suggested by the unique magneto-photoluminescence spectroscopy pattern of the boron nitride (BN) encapsulated monolayer WSe2 device at low temperature. The unambiguous evidence of the dark trions is further obtained by direct…
