Using recently developed numerical method we compute charge stiffness and optical conductivity of the t-J model coupled to optical phonons. Coherent hole motion is most strongly influenced by the electron-phonon coupling within the physically relevant regime of the exchange interaction. We find unusual non-monotonous dependence of the charge stiffness as a function of the exchange coupling near the crossover to the strong electron-phonon coupling regime. Optical conductivity in this regime shows a two-peak structure. The low-frequency peak represents local magnetic excitation, attached to the hole, while the higher-frequency peak corresponds to the mid infrared band that originates from coupling to spin-wave excitations, broadened and renormalized by phonon excitations. We observe no separate peak at or slightly above the phonon frequency. This finding suggests that the two peak structure seen in recent optical measurements is due to magnetic excitations coupled to lattice degrees of freedom via doped charge carriers.
The Momentum Average approximation is used to derive a new kind of non-perturbational analytical expression for the optical conductivity (OC) of a Holstein polaron at zero temperature. This provides insight into the shape of the OC, by linking it to the structure of the polaron's phonon cloud. Our method works in any dimension, properly enforces selection rules, can be systematically improved, and also generalizes to momentum-dependent couplings. Its accuracy is demonstrated by a comparison with the first detailed set of three-dimensional numerical OC results, obtained using the approximation-…
We employ dynamical mean-field theory to study the optical conductivity $σ(ω)$ of one hole in the Holstein-t-J model. We provide an exact solution for $σ(ω)$ in the limit of infinite connectivity. We apply our analysis to Nd$_{2-x}$Ce$_x$CuO$_4$. We show that our model can explain many features of the optical conductivity in this compounds in terms of magnetic/lattice polaron formation.
The effects of quantum lattice fluctuations on the Peierls transition and the optical conductivity in the one-dimensional Holstein model of spinless fermions have been studied by developing an analytical approach, based on the unitary transformation method. We show that when the electron-phonon coupling constant decreases to a finite critical value the Peierls dimerization is destroyed by the quantum lattice fluctuations. The dimerization gap is much more reduced by the quantum lattice fluctuations than the phonon order parameter. The calculated optical conductivity does not have the inverse-s…
An interacting electron-phonon system is considered within the Extended Holstein model at strong coupling regime and nonadiabatic approximation. It is assumed that screening of an electron-phonon interaction is due to the excess electrons in a lattice. An influence of the screening on the mass and optical conductivity of a lattice polarons is studied. A more general form Yukawa-type electron-phonon interaction potential potential is accepted and corresponding forces are derived in a lattice. It is emphasized that the screening effect is more pronounced at the values of screening radius compara…
Thermal and optical conductivity in the Holstein model at half filling and at finite temperature in the Luttinger-liquid and charge-density-wave regime
A comprehensive picture of polaron and bipolaron physics is essential to understand the optical absorption spectrum in many materials with electron-phonon interactions. In particular, the finite-temperature properties are of interest since they play an important role in many experiments. Here, we combine the parallel two-site time-dependent variational principle algorithm (p2TDVP) with local basis optimization (LBO) and purification to calculate time-dependent current-current correlation functions. From this information, we extract the optical conductivity for the Holstein polaron and bipolaro…
Applying newly developed dynamical density matrix renormalization group techniques at zero and finite temperatures to a Hubbard-Holstein model at half-filling, we examine the optical conductivity of a typical one-dimensional Mott insulator Sr_2CuO_3. We find a set of parameters in the Hubbard-Holstein model, which can describe optical conductivity for both Mott-gap excitation in the high-energy region and phonon-assisted spin excitation in the low-energy region. We also find that electron-phonon interaction gives additional broadening in the temperature dependence of the Mott-gap excitation.
We derive the exact solution for the optical conductivity $σ(ω)$ of one hole in the Holstein-t-J model in the framework of dynamical mean-field theory (DMFT). We investigate the magnetic and phonon features associated with polaron formation as a function of the exchange coupling $J$, of the electron-phonon interaction $λ$ and of the temperature. Our solution directly relates the features of the optical conductivity to the excitations in the single-particle spectral function, revealing two distinct mechanisms of closing and filling of the optical pseudogap that take place upon varying the micro…
Employing the Lanczos algorithm in combination with a kernel polynomial moment expansion (KPM) and the maximum entropy method (MEM), we show a way of calculating charge and spin excitations in the Holstein t-J model, including the full quantum nature of phonons. To analyze polaron band formation we evaluate the hole spectral function for a wide range of electron-phonon coupling strengths. For the first time, we present results for the optical conductivity of the 2D Holstein t-J model.
We use the approximation-free Bold Diagrammatic Monte Carlo technique to study the effects of a finite dispersion of the optical phonon mode on the properties of the Holstein polaron, especially its effective mass. For weak electron-phonon coupling the effect is very small, but it becomes significant for moderate and large electron-phonon coupling. The effective mass is found to increase (decrease) if the phonon dispersion has a negative (positive) curvature at the centre of the Brillouin zone.
We investigate the optical response of a charge-transfer complex in a condensed phase driven by an external laser field. Our model includes an instantaneous short-range Coulomb interaction and a local optical vibrational mode described by the Holstein-Hubbard (HH) model. Although characterization of the HH model for a bulk system has typically been conducted using a complex phase diagram, this approach is not sufficient for investigations of dynamical behavior at finite temperature, in particular for studies of nonlinear optical properties, where the time irreversibility of the dynamics that a…
A classical analog simulator of the two-site Hubbard-Holstein model, describing the dynamics of two correlated electrons coupled with local phonons, is proposed based on light transport in engineered optical waveguide arrays. Our photonic analog simulator enables to map the temporal dynamics of the quantum system in Fock space into spatial propagation of classical light waves in the evanescently-coupled waveguides of the array. In particular, in the strong correlation regime the periodic temporal dynamics, related to the excitation of Holstein polarons with equal energy spacing, can be visuali…
We study experimentally the Raman response of the undoped high-Tc parent compound $YBa_2Cu_3O_6$, and give a unified theory of the two-magnon Raman peak and optical conductivity based on the Hubbard-Holstein model with electron-phonon coupling (EPC). The Hubbard model without EPC can qualitatively account for the experimentally observed resonance of the Raman response, but only the Hubbard-Holstein model (i) reproduces asymmetry of the Raman spectrum, (ii) validates experimental visibility of the two-magnon peak, and (iii) predicts the correct shape and energy of the lower edge of the charge t…
We derive an effective d-dimensional Hamiltonian for a system of hard-core-bosons coupled to optical phonons in a lattice. At non-half-fillings, a superfluid-supersolid transition occurs at intermediate boson-phonon couplings, while at strong-couplings the system phase separates. We demonstrate explicitly that the presence of next-nearest-neighbor hopping and nearest-neighbor repulsion leads to supersolidity. Thus we present a microscopic mechanism for the homogeneous coexistence of charge-density-wave and superfluid orders.
The effects of quantum lattice fluctuations on the Peierls transition are studied within the one--dimensional Holstein molecular crystal model by means of exact diagonalization methods. Applying a very efficient variational Lanczos technique, the ground--state phase diagram is obtained in excellent agreement with predictions of recent density matrix renormalization group calculations. The transition to the charge--density--wave regime is signaled by a strong increase in the charge structure factor. In the metallic regime, the non--universal Luttinger liquid parameters (charge velocity and coup…
We use continuous-time quantum Monte Carlo simulations to study retardation effects in the metallic, quarter-filled Holstein model in one dimension. Based on results which include the one- and two-particle spectral functions as well as the optical conductivity, we conclude that with increasing phonon frequency the ground state evolves from one with dominant diagonal order---2k_F charge correlations---to one with dominant off-diagonal fluctuations, namely s-wave pairing correlations. In the parameter range of this crossover, our numerical results support the existence of a spin gap for all phon…
To discuss the interplay of electronic and lattice degrees of freedom in systems with strong Coulomb correlations we have performed an extensive numerical study of the two-dimensional Holstein t-J model. The model describes the interaction of holes, doped in a quantum antiferromagnet, with a dispersionsless optical phonon mode. We apply finite-lattice Lanczos diagonalization, combined with a well-controlled phonon Hilbert space truncation, to the Hamiltonian. The focus is on the dynamical properties. In particular we have evaluated the single-particle spectral function and the optical conducti…
The spectral response and physical features of the 2D Hubbard-Holstein model are calculated both in equilibrium at zero and low chemical dopings, and after an ultra short powerful light pulse, in undoped systems. At equilibrium and at strong charge-lattice couplings, the optical conductivity reveals a 3-peak structure in agreement with experimental observations. After an ultra short pulse and at nonzero electron-phonon interaction, phonon and spin subsystems oscillate with the phonon period $T_{ph} \approx 80$ fs. The decay time of the phonon oscillations is about 150-200 fs, similar to the re…
We generalize the Momentum Average approximations MA$^{(0)}$ and MA$^{(1)}$ to study the effects of coupling to multiple optical phonons on the properties of a Holstein polaron. As for a single phonon mode, these approximations are numerically very efficient. They become exact for very weak or very strong couplings, and are highly accurate in the intermediate regimes, {\em e.g.} the spectral weights obey exactly the first six, respectively eight, sum rules. Our results show that the effect on ground-state properties is cumulative in nature. In particular, if the effective coupling to one mode …
The spectral weight functions and the optical conductivity of the Holstein model are studied on a one-dimensional six-site lattice with periodic boundary conditions for three different electron concentrations: a single electron, two electrons of opposite spins, and half filling. A density matrix approach is used to obtain an optimal phonon basis and to truncate the phonon Hilbert space without significant loss of accuracy. This approach allows us to calculate spectral functions for electrons dressed locally by the optimal phonons as well as for bare electrons. We obtain evidence for a smooth c…
Calculations of one-electron spectral functions, optical conductivity and spin-wave energy in the Holstein double-exchange model are made using the many-body coherent potential approximation. Satisfactory agreement is obtained with angle-resolved photoemission results on La_1.2Sr_1.8Mn_2O_7 and optical measurements on Nd_0.7Sr_0.3MnO_3. A pseudogap in the one-electron spectrum at the Fermi level plays an important role in both systems, but a small-polaron band is only predicted to exist in the La system. A rigorous upper bound on spin-wave energies at T=0 is derived. The spin-wave stiffness co…
Spectral, optical and transport properties of an anisotropic three-dimensional Holstein model are studied within the adiabatic approximation. The parameter regime is appropriate for organic semiconductors used in single crystal based field effect transistors. Different approaches have been used to solve the model: self-consistent Born approximation valid for weak electron-phonon coupling, coherent potential approximation exact for infinite dimensions, and numerical diagonalization for finite lattices. With increasing temperature, the width of the spectral functions gets larger and larger makin…
We investigate the dynamics of an electron coupled to dispersionless optical phonons in the Holstein model, at high temperatures. The dynamics is conventionally believed to be diffusive, as the electron is repeatedly scattered by optical phonons. In a semiclassical approximation, however, the motion is not diffusive. In one dimension, the electron moves in a constant direction and does not turn around. In two dimensions, the electron follows and then continues to retrace a fractal trajectory. Aspects of these nonstandard dynamics are retained in more accurate calculations, including a fully qu…
We derive an effective d-dimensional Hamiltonian for a system of hard-core-bosons coupled to optical phonons in a lattice. Away from half-filling, we show that the presence of next-nearest-neighbor hopping in the effective Hamiltonian leads to a superfluid-to-supersolid transition at intermediate boson-phonon (b-p) couplings, while at strong-couplings the system phase separates. However, at half-filling and at a critical b-p coupling (as in the xxz-model), the system undergoes a superfluid-to-charge-density-wave transition without any signature of supersolidity. Our analyses is based on extens…
The optical conductivity of charge carriers coupled to quantum phonons is studied in the framework of the one-dimensional spinless Holstein model. For one electron, variational diagonalisation yields exact results in the thermodynamic limit, whereas at finite carrier density analytical approximations based on previous work on single-particle spectral functions are obtained. Particular emphasis is put on deviations from weak-coupling, small-polaron or one-electron theories occurring at intermediate coupling and/or finite carrier density. The analytical results are in surprisingly good agreement…
Exact results for the density of states and the ac conductivity of the spinless Holstein model at finite carrier density are obtained combining Lanczos and kernel polynomial methods.
The molecular-crystal model, that describes a one-dimensional electron gas interacting with quartic anharmonic lattice vibrations, offers great potentials in the mapping of a relatively wide range of low-dimensional fermion systems coupled to optical phonons onto quantum liquids with retarded interactions. Following a non-perturbative approach involving non-Gaussian partial functional integrations of lattice degrees of freedom, the exact expression of the phonon-mediated two-electron action for this model is derived. With the help of Hubbard-Stratonovich transformation the charge-density-wave …
We present numerically exact solutions to the problem of a single electron interacting through a long range interaction with optical phonons in two and three dimensions. Comparisons are made with results for the standard Holstein model, and with perturbative approaches from both the weak coupling and strong coupling sides. We find, in agreement with earlier work, that the polaron effective mass increases (decreases) in the weak (strong) coupling regime, respectively. However, in two dimensions, the decrease in effective mass still results in too large an effective mass to be relevant in realis…
The optical conductivity (OC) of cuprates is studied theoretically in the low density limit of the t-t'-J-Holstein model. By developing a limited phonon basis exact diagonalization (LPBED) method capable of treating the lattice of largest size 4x4 ever considered, we are able to discern fine features of the mid-infrared (MIR) part of the OC revealing three-peak structure. The two lowest peaks are observed in experiments and the highest one is tacitly resolved in moderately doped cuprates. Comparison of OC with the results of semianalytic approaches and detailed analysis of the calculated isoto…
The optical properties of the charge-ordering ($CO$) phase of the one-dimensional (1D) half-filled spinless Holstein model are derived at zero temperature within a well-known variational approach improved including second-order lattice fluctuations. Within the $CO$ phase, the static lattice distortions give rise to the optical interband gap, that broadens as the strength of the electron-phonon ($el-ph$) interaction increases. The lattice fluctuation effects induce a long subgap tail in the infrared conductivity and a wide band above the gap energy. The first term is due to the multi-phonon emi…
We performed an extensive numerical analysis of the Holstein model. Combining variational Lanczos diagonalisation, density matrix renormalisation group, kernel polynomial expansion, and cluster perturbation theory techniques we solved for properties of the Holstein polaron and bipolaron problems. Numerical solution of the Holstein model means that we determined the ground-state and low-lying excited states with arbitrary precision in the thermodynamic limit for any dimension. Moreover, we calculated the spectral properties (e.g. photoemission and phonon spectra), optical response and thermal t…
We investigate the temperature and doping dependence of the optical conductivity $σ(ω)$ of Nd$_{2-x}$Ce$_x$CuO$_4$ in terms of magnetic/lattice polaron formation. We employ dynamical mean-field theory in the context of the Holstein-t-J model where an exact analytical solution is available in the limit of infinite connectivity. We show that the pseudogap features in the optical conductivity of this compound can be associated to the formation of lattice polarons assisted by the magnetic interaction.
We study the effect of strong DC and pulsed electric fields on a Mott insulating system with coupling to optical phonons. A DC field of the order of the gap induces a metallic state characterized by polaronic features in the gap region and a partially inverted population. In this quasi-steady state, the field-induced doublon-hole production is balanced by a phonon-enhanced doublon-hole recombination. The photo-excitation of carriers by a pulsed field leads to similar modifications of the electronic structure in the gap region, and an associated reduction of the doublon life-time. We demonstrat…
We investigate the physical properties of the Ba$_{1-x}$K$_x$BiO$_3$ compounds with a focus on the optical properties. Results from the simple Holstein model, describing a single band coupled to an oxygen breathing mode with parameters derived from first principles calculations, are in excellent agreement with a broad range of experimental information. It accounts for an insulating parent compound at $x=0$ %, with a direct- (optical) and an indirect-gap, and a metal insulator transition around $x = 0.38$. Strong electron-phonon coupling leads to spectral weight redistribution over a frequency …
Exploring supersolidity in naturally occurring and artificially designed systems has been and will continue to be an area of immense interest. Here, we study how superfluid and charge-density-wave (CDW) states cooperate or compete in a minimal model for hard-core-bosons (HCBs) coupled locally to optical phonons: a two-dimensional Bose-Holstein model. Our study is restricted to the parameter regimes of strong HCB-phonon coupling and non-adiabaticity. We use Quantum Monte Carlo simulation (involving stochastic-series-expansion technique) to study phase transitions and to investigate whether we h…
We present calculation of optical conductivity in a simple model of electronic spectrum of two-dimensional system with "hot patches" on the Fermi surface, leading to non Fermi-liquid renormalization of the spectral density (pseudogap) on these patches. It is shown that this model qualitatively reproduces basic anomalies of optical experiments in the pseudogap state of copper oxides.
The response of charge stripes to an external electric field applied perpendicular to the stripe direction is studied within a diagrammatic approach for both weak and strong pinning by random impurities. The sound-like mode of the stripes described as elastic strings moves to finite frequency due to impurity pinning. By calculating the optical conductivity we determine this characteristic energy scale for both a single stripe and an array of interacting stripes. The results explain the anomalous far-infrared peak observed recently in optical-conductivity measurements on cuprates.
We present a theory of optical conductivity in systems with finite-momentum Cooper pairs. In contrast to the BCS pairing where AC conductivity is purely imaginary in the clean limit, there is nonzero AC absorption across the superconducting gap for finite-momentum pairing if we break the Galilean symmetry explicitly in the electronic Hamiltonian. Vertex correction is crucial for maintaining the gauge invariance in the mean-field formalism and dramatically changes the optical conductivity in the direction of the pairing momentum. We carried out a self-consistent calculation and gave an explicit…
The doping and temperature dependent conductivity of electron-doped cuprates is analysed. The variation of kinetic energy with doping is shown to imply that the materials are approximately as strongly correlated as the hole-doped materials. The optical spectrum is fit to a quasiparticle scattering model; while the model fits the optical data well, gross inconsistencies with photoemission data are found, implying the presence of a large, strongly doping dependent Landau parameter.
We compute the optical conductivity of 2D f-wave superconductors and also of the multigap model proposed recently by Zhitomirsky and Rice at T=0K in the Born limit. The presence of interband impurity scattering was found to play an important role: the contributions from the two bands mix up, and new structures are seen in the tunneling density of states and in the optical spectrum as well, corresponding to interband transitions. This will provide a sensitive test in selecting the competing models for the triplet superconductivity in Sr_2RuO_4.
Journal ref.: J. Phys.: Condens. Matter 25, 065602 (2013): We investigated the optical reflectivity of the heavy-fermion metal CeCu2Si2 in the energy range 3 meV - 30 eV for temperatures between 4K - 300K. The results for the charge dynamics indicate a behavior that is expected for the formation of a coherent heavy quasiparticle state: Upon cooling the spectra of the optical conductivity indicate a narrowing of the coherent response. Below temperatures of 30 K a considerable suppression of conductivity evolves below a peak structure at 13 meV. We assign this gap-like feature to strong electron…
We begin with an overview of the experimental results for the temperature and doping dependences of the optical-conductivity spectral weight in cuprate superconductors across the whole phase diagram. Then we discuss recent attempts to explain the observed behavior of the spectral weight using reduced and full models with unconventional $d_{x^2-y^2}$ charge-density waves.
We study theoretically the optical conductivity of d-wave superconductors like in high temperature cuprates in the presence of impurities. We limit ourselves at T=0K and focus on the frequency dependence of both sigma_1(omega) and ω*σ_2(omega) for omega<2Delta. When the impurity scattering is in the unitary limit, we find a peak in sigma_1(omega) with omega/Delta\simeq 0.1\sim 0.5$, which may account for the peak seen by Basov et al. in Zn-substituted YBCO.
For electronic states and photoinduced charge dynamics near the neutral-ionic transition in the mixed-stack charge-transfer complex tetrathiafulvalene-$p$-chloranil (TTF-CA), we review the effects of Peierls coupling to lattice phonons modulating transfer integrals and Holstein couplings to molecular vibrations modulating site energies. The former stabilizes the ionic phase and reduces discontinuities in the phase transition, while the latter stabilizes the neutral phase and enhances the discontinuities. To reproduce the experimentally observed ionicity, optical conductivity and photoinduced c…
We describe the formation and properties of Holstein polarons in the entire parameter regime. Our presentation focuses on the polaron mass and radius, which we obtain with an improved numerical technique. It is based on the combination of variational exact diagonalization with an improved construction of phonon states, providing results even for the strong coupling adiabatic regime. In particular we can describe the formation of large and heavy adiabatic polarons. A comparison of the polaron mass for the one and three dimensional situation explains how the different properties in the static os…
Disorder Suppression of Charge Density Waves in the Honeycomb Holstein Model
School of Physical Science and Technology, Beijing University of Posts and Telecommunications（北京邮电大学物理科学与技术学院）；School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）；Key Laboratory of Multiscale Spin Physics (Ministry of Education), Beijing Normal University（北京师范大学多尺度自旋物理教育部重点实验室）
A non-equilibrium theory of optical conductivity of dirty-limit superconductors and commensurate charge density wave is presented. We discuss the current response to different experimentally relevant light-field probe pulses and show that a single frequency definition of the optical conductivity $σ(ω)\equiv j(ω)/E(ω)$ is difficult to interpret out of the adiabatic limit. We identify characteristic time domain signatures distinguishing between superconducting, normal metal and charge density wave states. We also suggest a route to directly address the instantaneous superfluid stiffness of a sup…
The polaron optical conductivity is derived within the strong-coupling expansion, which is asymptotically exact in the strong-coupling limit. The polaron optical conductivity band is provided by the multiphonon optical transitions. The polaron optical conductivity spectra calculated within our analytic strong-coupling approach and the numerically accurate Diagrammatic Quantum Monte Carlo (DQMC) data are in a good agreement with each other at large $α\gtrapprox 9$.
We study a pseudogap Anderson-Holstein model of a magnetic impurity level that hybridizes with a conduction band whose density of states vanishes in power-law fashion at the Fermi energy, and couples, via its charge, to a nondispersive bosonic mode (e.g., an optical phonon). The model, which we treat using poor-man's scaling and the numerical renormalization group, exhibits quantum phase transitions of different types depending on the strength of the impurity-boson coupling. For weak impurity-boson coupling, the suppression of the density of states near the Fermi energy leads to quantum phase …
The optical conductivity of a system of electrons on the honeycomb lattice interacting through an electromagnetic field is computed by truncated exact Renormalization Group (RG) methods. We find that the conductivity has the universal value pi/2 times the conductivity quantum up to negligible corrections vanishing as a power law in the limit of low frequencies.
We present exact results for the optical response in the one-dimensional Holstein model. In particular, by means of a refined kernel polynomial method, we calculate the ac and dc electrical conductivities at finite temperatures for a wide parameter range of electron phonon interaction. We analyze the deviations from the results of standard small polaron theory in the intermediate coupling regime and discuss non-adiabaticity effects in detail.
We show how coupling to an Einstein phonon $ω_E$ affects the absorption peaks seen in the optical conductivity of graphene under a magnetic field $B$. The energies and widths of the various lines are shifted, and additional peaks arise in the spectrum. Some of these peaks are Holstein sidebands, resulting from the transfer of spectral weight in each Landau level (LL) into phonon-assisted peaks in the spectral function. Other additional absorption peaks result from transitions involving split LLs, which occur when a LL falls sufficiently close to a peak in the self-energy. We establish the sele…
We present results for the optical conductivity of Na2IrO3 within density functional theory by including spin-orbit (SO) and correlation effects (U) as implemented in GGA+SO+U. We identify the various interband transitions and show that the underlying quasi-molecular-orbital nature of the electronic structure in Na2IrO3 translates into distinct features in the optical conductivity. Most importantly, the parity of the quasi-molecular orbitals appears to be the main factor in determining strong and weak optical transitions. We also present optical conductivity calculations for Li2IrO3 and discus…
Transient quantum dynamics in an interacting fermion-phonon system are investigated. In particular, a charge order (CO) melting after a short optical-pulse irradiation and roles of the quantum phonons on the transient dynamics are focused on. A spinless-fermion model in a one-dimensional chain coupled with local phonons is analyzed numerically. The infinite time-evolving block decimation algorithm is adopted as a reliable numerical method for one-dimensional quantum many-body systems. Numerical results for the photoinduced CO melting dynamics without phonons are well interpreted by the soliton…
We analyze optical conductivity with the goal to demonstrate experimental manifestation of a new state of matter, the so-called fermion condensate. Fermion condensates are realized in quantum spin liquids, exhibiting typical behavior of heavy fermion metals. Measurements of the low-frequency optical conductivity collected on the geometrically frustrated insulator herbertsmithite provide important experimental evidence of the nature of its quantum spin liquid composed of spinons. To analyze recent measurements of the herbertsmithite optical conductivity at different temperatures, we employ a mo…
We calculate theoretically the optical conductivity in the bilayer graphene by considering Kubo-Green-Matsubara formalism. Different regimes of the interlayer coupling parameter have been considered in the paper. We show that the excitonic effects substantially affect the optical conductivity spectrum at the high-frequency regime when considering the full interaction bandwidth, leading to a total suppression of the usual Drude intraband optical transition channels and by creating a new type of optical gap. We discuss the role of the interlayer coupling parameter and the Fermi level on the cond…
