Layered Electron Gas Model Research Articles

Dielectric properties of graphene/ MoS2 heterostructures from ab initio calculations and electron energy-loss experiments

High-energy electronic excitations of graphene and ${\mathrm{MoS}}_{2}$ heterostructures are investigated by momentum-resolved electron energy-loss spectroscopy in the range of 1 to 35 eV. The interplay of excitations on different sheets is understood in terms of long-range Coulomb interactions and is simulated using a combination of ab initio and dielectric model calculations. In particular, the layered electron-gas model is extended to thick layers by including the spatial dependence of the dielectric response in the direction perpendicular to the sheets. We apply this model to the case of graphene/${\mathrm{MoS}}_{2}$/graphene heterostructures and discuss the possibility of extracting the dielectric properties of an encapsulated monolayer from measurements of the entire stack.

Plasmon bands in multilayer graphene

High-energy collective electronic excitations (plasmons) in freestanding multilayer graphene are studied by momentum-resolved electron energy-loss spectroscopy (EELS). For normal incidence, only the high-energy plasmon band is excited and we measure a blueshift of the π -plasmon dispersion with increasing thickness. The observed transition between two-dimensional and three-dimensional behavior is explained using a layeredelectron-gas (LEG) model. We propose a method to measure all individual plasmon bands by tilting the sample with respect to the electron beam. As a proof of concept, EELS experiments for three-layer graphene are compared with predictions from the LEG model.

High-energy plasmon spectroscopy of freestanding multilayer graphene

We present several applications of the layered electron gas model to electron energy loss spectroscopy of free-standing films consisting of $N$ graphene layers in a scanning transmission electron microscope. Using a two-fluid model for the single-layer polarizability, we discuss the evolution of high-energy plasmon spectra with $N$, and find good agreement with the recent experimental data for both multi-layer graphene with $N<10$, and thick slabs of graphite. Such applications of these analytical models help shed light on several features observed in the plasmon spectra of those structures, including the role of plasmon dispersion, dynamic interference in excitations of various plasmon eigenmodes, as well as the relevance of the bulk plasmon bands, rather than surface plasmons, in classifying the plasmon peaks.

Effective Potential and Superconductivity in Copper OxideSuperconductors

The layered electron gas (LEG) model has been used to calculate theeffective potential (using three types of 2D polarizability which arebased on tight binding approximation, random phase approximation andmarginal Fermi liquid approxiation) for cuprate superconductors whichconsist of one and two Cu–O layers per unit cell, respectively.The calculated effective potential has then been averaged over wavevector and a comparative study of effective potentials is made. It isnoticed that the calculated effective potentials usingpolarizabilities based on tight binding approximation and marginalFermi liquid approximation give comparatively better descriptions ofcuprate superconductors. The possible use of our calculated effectivepotential to compute TC for superconductors hasbeen suggested. It is found that the net attractive effectivepotential can be obtained within the LEG model for q (a–b plane component of the wave vector)smaller than one-tenth of the Fermi wave vector.

Study of Low Temperature Specific Heat in La-Ba/Sr-CuO Superconductors

The low temperature specific heat of La 1.85 Ba 0.15 CuO 4 and La 1.8 Sr 0.2 CuO 4 superconductors has been investigated based on the free electron, layered electron gas model of quasi-two-dimensional (2D) layers of CuO 2 along the a-b plane. The interaction potential properly incorporates the effect of electron-electron, electron-phonon and electron-plasmon interactions. The lattice contribution to the specific heat is well estimated from the electron-phonon part of the interaction potential. The results on the behaviour of the specific heat (C) with temperature (T) for both systems are similar to those observed in previous experiments. It is noticed that the specific heat contribution from the Debye model is significant at low temperatures (5 K ≤ T ≤ T c ) while the Einstein model affords the specific heat at higher temperatures (T ≥ T c ). The estimated lattice specific heat, when subtracted from the experimental data, results in a finite value of the electronic specific heat coefficient (γ). Non-zero values of γ indicate the electronic origin intrinsic to these superconductors. A linear temperature dependence of ΔC (= C exp - C latt )/T in the range 20 K ≤ T ≤ 45 K is depicted. Furthermore, the density of states at the Fermi level is also estimated. The results derived are consistent with the reported data. The implications of the above analysis are discussed.

Effect of doping concentration on normal state resistivity of La2 −x (Ba, Sr) x CuO4 superconductors

Based on free electron layered electron gas model of quasi two dimensional CuO2 layers in La(Ba/Sr)CuO superconductors a model potentialV(q) is developed earlier with the electron-electron and electron-phonon interactions. The model approach facilitates the dielectric functions and the dispersion relations of 2D acoustic phonon and plasmon modes. We have then worked out the coupling strength (γ) linking electrons to the 2D acoustic phonon mode (ħω_) from the residue at the pole ofV(q). Furthermore, the scattering time (τ e−ph) during electron-phonon interaction (EPI) for this simplified system is also estimated. The contribution to the normal state in plane resistivity due to EPI is then evaluated. Finally, the variations ofτ andρ is studied with the doping concentration (x) and temperature (T) and the results obtained by us show reasonably good agreement with the available experimental data.

Soft acoustic plasmons in cuprate superconductors

The layered electron gas model is applied to the study of plasmons in the normal state of cuprate superconductors consisting of one and two CuO conducting layers per unit cell. It is found that the well-behaved plasmon modes can exist for a restricted range of wave-vectors. We further notice that soft acoustic plasma modes may not exist in these materials because of high value of damping parameter, resulting from the strong electron-impurity scattering. The calculated plasma energies of well-behaved modes appear to be too high to be useful for pairing within a BCS framework.

Plasmons below Tc in cuprate superconductors

We used the layered electron gas model to perform a theoretical study of frequency and line shape for plasmons below T c in cuprate superconductors, in the frequency range h ̵ ω≤2Δ≤ qv F< k B T< k B T c, where q, Δ, v F, k B and T are the component of the wave vector in the a- b-plane, the binding energy of a Cooper pair, Fermi velocity, Boltzmann constant and the temperature, respectively. The polarizability for a two-dimensional plane, which corresponds to a conducting Cu-O plane, is calculated for the above-mentioned ω-range. The calculated polarizability is then used to calculate the imaginary part of the inverse dielectric response function, which gives rise to the frequency and line shape of plasmons. The calculated plasmon frequencies and the line shapes are found to be of similar nature to that of a three-dimensional electron gas below T c.

Plasmons in cuprate superconductors.

The customary way of determining the complex dielectric constant from the measured reflectance spectra suffers from large uncertainties because of the extrapolations required for the Kramers-Kronig transformation. To avoid these, a method is introduced in which reflectance and ellipsometric data on single crystals and epitaxial films are combined. Utilizing this approach, the spectral functions of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ (Y-Ba-Cu-O) and ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$ (Bi-Sr-Ca-Cu-O) are determined with substantially improved accuracy. This enables the unambiguous identification of optic plasmons at 1.4 eV in Y-Ba-Cu-O and at 1.1 eV in Bi-Sr-Ca-Cu-O. No other low-lying optic plasmons are detected, which likely rules out most plasmon-mediated superconductivity models. Next, the bare plasma frequency is found to be \ensuremath{\Elzxh}${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$=3.2\ifmmode\pm\else\textpm\fi{}0.3 eV in Y-Ba-Cu-O and \ensuremath{\Elzxh}${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$=2.4\ifmmode\pm\else\textpm\fi{}0.3 eV in Bi-Sr-Ca-Cu-O. These values support ascribing the strong infrared absorption to charge carriers which, however, are not free-electron-like, but rather show characteristic polaronic behavior. Finally, in both Y-Ba-Cu-O and Bi-Sr-Ca-Cu-O, it is found that Im(-1/\ensuremath{\epsilon})=\ensuremath{\beta}${\mathrm{\ensuremath{\omega}}}^{2}$ for small \ensuremath{\omega}, and this law is conjectured to be universal for all layered cuprate superconductors. It is again not Drude-like; it may be compatible with the layered electron-gas model. The latter implies existence of a broad band of acoustic plasmon branches.

Moment sum rules for a layered electron gas

We have evaluated the first few frequency moments of the dissipation spectra for longitudinal and transverse excitations in a layered electron gas model, consisting of a periodic stack of two-dimensional electron gases. Short-range interplanar correlations yield a specific contribution to the first moment of the current-current dissipation spectra whenever the wave vector has a finite perpendicular component. The result is interpreted as evidence for additional excitations lying above the well-known acoustic plasmon in this model system.

Plasma oscillations of layered electron gases in semiconductor heterostructures

The plasma oscillations of layered electron systems in modulation doped GaAs–(AlGa)As heterostructures were investigated by inelastic light scattering. These experiments are the first to probe the dispersion of the plasma frequency in multiple semiconductor heterostructures. The measured dispersions are linear in the in‐plane component of wave vector. These results confirm predictions of the layered electron gas model.