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 transport, are analyzed in detail for different frequency, temperature, chemical potential and scattering rate limits. We obtain analytical expressions for the conductivity that reproduce previous expressions used to fit experimental measurements in graphene and compare with direct numerical evaluations of the Kubo formula, finding great agreement. The optical absorption arising from intervalley transitions displays a maximum at a special frequency that can be tuned by doping. Our results show how the single parameter describing the valley coupling in this system could be obtained by measuring graphene's optical absorbance in the region where interband transitions are blocked by the impurities. Finally, we use Fermi's golden rule to independently verify some of the previous results.
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…
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 hundre…
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…
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 …
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 …
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 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…
Intervalley scattering of carriers in graphene at `top' adatoms may give rise to a hidden Kekulé ordering pattern in the adatom positions. This ordering is the result of a rapid modulation in the electron-mediated interaction between adatoms at the wavevector $K- K'$, which has been shown experimentally and theoretically to dominate their spatial distribution. Here we show that the adatom interaction is extremely sensitive to strain in the supporting graphene, which leads to a characteristic spatial modulation of the Kekulé order as a function of adatom distance. Our results suggest that the s…
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…
Band structure and optical response of Kekulé-modulated $α-\mathcal{T}_3$ model
Facultad de Ciencias, Universidad Autónoma de Baja California（下加利福尼亚自治大学理学院）；Department of Physics and Astronomy and Nanoscale and Quantum Phenomena Institute, Ohio University（俄亥俄大学物理与天文学系及纳米量子现象研究所）；Centro de Nanociencias y Nanotecnología, Universidad Nacional Autónoma de México（墨西哥国立自治大学纳米科学与纳米技术中心）
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…
A Kekulé bond texture in graphene modifies the electronic band structure by folding the Brillouin zone and bringing the two inequivalent Dirac points to the center. This can result, in the opening of a gap (Kek-O) or the locking of the valley degree of freedom with the direction of motion (Kek-Y). We analyze the effects of uniaxial strain on the band structure of Kekulé-distorted graphene for both textures. Using a tight-binding approach, we introduce strain by considering the hopping renormalization and corresponding geometrical modifications of the Brillouin zone. We numerically evaluate the…
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…
The dynamic polarization for kekulé-patterned graphene is studied within the Random Phase Approximation (RPA). It is shown how the breaking of the valley degeneracy by the lattice modulation is manifested through the dielectric spectrum, the plasmonic dispersion, the static screening and the optical conductivity. The valley-dependent splitting of the Fermi velocities due to the kekulé distortion leads to a similar splitting in the dielectric spectrum of graphene, introducing new characteristic frequencies, which are given in terms of the valley-coupling amplitude. The valley coupling also spli…
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…
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…
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…
A growing body of experimental work suggests that magic angle twisted bilayer graphene exhibits a "cascade" of spontaneous symmetry breaking transitions, sparking interest in the potential relationship between symmetry-breaking and superconductivity. However, it has proven difficult to find experimental probes which can unambiguously identify the nature of the symmetry breaking. Here we show how atomically-resolved scanning tunneling microscopy can be used as a fingerprint of symmetry breaking order. By analyzing the pattern of sublattice polarization and "Kekulé" distortions in small magnetic…
The interaction between electrons in graphene under high magnetic fields drives the formation of a rich set of quantum Hall ferromagnetic phases (QHFM), with broken spin or valley symmetry. Visualizing atomic scale electronic wavefunctions with scanning tunneling spectroscopy (STS), we resolve microscopic signatures of valley ordering in QHFM and fractional quantum Hall phases of graphene. At charge neutrality, we observe a field-tuned continuous quantum phase transition from a valley polarized state to an intervalley coherent state, with a Kekule distortion of its electronic density. Mapping …
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…
