In this note, we reply to the comment made by E.I.Kats and V.V.Lebedev [arXiv:1407.4298] on our recent work Thermodynamics of quantum crystalline membranes [Phys. Rev. B 89, 224307 (2014)]. Kats and Lebedev question the validity of the calculation pr
esented in our work, in particular on the use of a Debye momentum as a ultra-violet regulator for the theory. We address and counter argue the criticisms made by Kats and Lebedev to our work.
Imperfections in the crystal structure, such as point defects, can strongly modify the optical and transport properties of materials. Here, we study the effect of point defects on the optical and DC conductivities of single layers of semiconducting t
ransition metal dichalcogenides with the form $M$S$_2$, where $M$=Mo or W. The electronic structure is considered within a six bands tight-binding model, which accounts for the relevant combination of $d$ orbitals of the metal $M$ and $p$ orbitals of the chalcogen $S$. We use the Kubo formula for the calculation of the conductivity in samples with different distributions of disorder. We find that $M$ and/or S defects create mid-gap states that localize charge carriers around the defects and which modify the optical and transport properties of the material, in agreement with recent experiments. Furthermore, our results indicate a much higher mobility for $p$-doped WS$_2$ in comparison to MoS$_2$.
We investigate the thermodynamic properties and the lattice stability of two-dimensional crystalline membranes, such as graphene and related compounds, in the low temperature quantum regime $Trightarrow0$. A key role is played by the anharmonic coupl
ing between in-plane and out-of plane lattice modes that, in the quantum limit, has very different consequences than in the classical regime. The role of retardation, namely of the frequency dependence, in the effective anharmonic interactions turns out to be crucial in the quantum regime. We identify a crossover temperature, $T^{*}$, between classical and quantum regimes, which is $sim 70 - 90$ K for graphene. Below $T^{*}$, the heat capacity and thermal expansion coefficient decrease as power laws with decreasing temperature, tending to zero for $Trightarrow0$ as required by the third law of thermodynamics.
The electrodynamics of a two-dimensional gas of massless fermions in graphene is studied by a collisionless hydrodynamic approach. A low-energy dispersion relation for the collective modes (plasmons) is derived both in the absence and in the presence
of a perpendicular magnetic field. The results for graphene are compared to those for a standard two-dimensional gas of massive electrons. We further compare the results within the classical hydrodynamic approach to the full quantum mechanical calculation in the random phase approximation. The low-energy dispersion relation is shown to be a good approximation at small wave vectors. The limitations of this approach at higher order is also discussed.
The recent spectacular progress in the experimental and theoretical understanding of graphene, the basic constituent of graphite, is applied here to compute, from first principles, the UV extinction of nano-particles made of stacks of graphene layers
. The theory also covers cases where graphene is affected by structural, chemical or orientation disorder, each disorder type being quantitatively defined by a single parameter. The extinction bumps carried by such model materials are found to have positions and widths falling in the same range as the known astronomical 2175 AA features: as the disorder parameter increases, the bump width increases from 0.85 to 2.5 $mu$m$^{-1}$, while its peak position shifts from 4.65 to 4.75 $mu$m$^{-1}$. Moderate degrees of disorder are enough to cover the range of widths of the vast majority of observed bumps (0.75 to 1.3 $mu$m$^{-1}$). Higher degrees account for outliers, also observed in the sky. The introduction of structural or chemical disorder amounts to changing the initial $sp^{2}$ bondings into $sp^{3}$ or $sp^{1}$, so the optical properties of the model material become similar to those of the more or less amorphous carbon-rich materials studied in the laboratory: a-C, a-C:H, HAC, ACH, coals etc. The present treatment thus bridges gaps between physically different model materials.
We study the intra-valley spin-orbit mediated spin relaxation in monolayers of MoS2 within a two bands effective Hamiltonian. The intrinsic spin splitting of the valence band as well as a Rashba-like coupling due to the breaking of the out-of-plane i
nversion symmetry are considered. We show that, in the hole doped regime, the out-of-plane spin relaxation is not very efficient since the spin splitting of the valence band tends to stabilize the spin polarization in this direction. We obtain spin lifetimes larger than nanoseconds, in agreement with recent valley polarization experiments.
We present a theoretical description of Bernstein modes that arise as a result of the coupling between plasmon-like collective excitations (upper-hybrid mode) and inter-Landau-level excitations, in graphene in a perpendicular magnetic field. These mo
des, which are apparent as avoided level crossings in the spectral function obtained in the random-phase approximation, are described to great accuracy in a phenomenological model. Bernstein modes, which may be measured in inelastic light-scattering experiments or in photo-conductivity spectroscopy, are a manifestation of the Coulomb interaction between the electrons and may be used for a high-precision measurement of the upper-hybrid mode at small non-zero wave vectors.
We study collective electronic excitations in graphene in the integer quantum Hall regime, concentrating mainly on excitations with spin reversal such as spin-flip and spin-wave excitations. We show that these excitations are correctly accounted for
in the time-dependent Hartree-Fock and strong magnetic field approximations, in contrast to spin-conserving (magneto-exciton) modes which involve a strong Landau-level mixing at non-zero wave vectors. The collective excitations are discussed in view of prominent theorems, such as Kohns and Larmors. Whereas the latter remains valid in graphene and yields insight into the understanding of spin-dependent modes, Kohns theorem does not apply to relativistic electrons in graphene. We finally calculate the exchange correction to the chemical potential in the weak magnetic field limit.
The particle-hole excitation spectrum for doped graphene is calculated from the dynamical polarizability. We study the zero and finite magnetic field cases and compare them to the standard two-dimensional electron gas. The effects of electron-electro
n interaction are included within the random phase approximation. From the obtained polarizability, we study the screening effects and the collective excitations (plasmon, magneto-excitons, upper-hybrid mode and linear magneto-plasmons). We stress the differences with the usual 2DEG.
A doped graphene layer in the integer quantum Hall regime reveals a highly unusual particle-hole excitation spectrum, which is calculated from the dynamical polarizability in the random phase approximation. We find that the elementary neutral excitat
ions in graphene in a magnetic field are unlike those of a standard two-dimensional electron gas (2DEG): in addition to the upper-hybrid mode, the particle-hole spectrum is reorganized in linear magneto-plasmons that disperse roughly parallel to $omega=v_F q$, instead of the usual horizontal (almost dispersionless) magneto-excitons. These modes could be detected in an inelastic light scattering experiment.
