Optical response of two-dimensional systems: Insights from classical electromagnetism to 
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Mazzei, Stefano; Giorgetti, C.

doi:10.1103/physrevb.106.035431

Cited by 2 publications

(20 citation statements)

References 45 publications

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“…For the out-ofplane component, where the Adler and Wiser formula should in principle be valid, we showed that the difficulty in defining the thickness of matter and calculating a reliable value for the average of the induced electric field leads to a continuous shift of the absorption resonance. This behavior is similar to the effective-medium theory between matter and vacuum [11,13], but it occurs in the region that seems to define the interfaces, and the Adler-Wiser formula clearly gives wrong spectra [18,22]. Nevertheless, we also showed that the different in-plane and out-of-plane macroscopic dielectric functions calculated with the same value for the thickness of matter gave the same reflectance and transmittance spectra [18,22].…”

Section: Introductionsupporting

confidence: 78%

“…This behavior is similar to the effective-medium theory between matter and vacuum [11,13], but it occurs in the region that seems to define the interfaces, and the Adler-Wiser formula clearly gives wrong spectra [18,22]. Nevertheless, we also showed that the different in-plane and out-of-plane macroscopic dielectric functions calculated with the same value for the thickness of matter gave the same reflectance and transmittance spectra [18,22]. This means that the response function calculated within TD-DFT, which is a longitudinal formalism, still contains the electronic properties at the origin of the optical response, which is in essence a transverse phenomenon.…”

Section: Introductionmentioning

confidence: 51%

“…In Ref. [18], we solved the Dyson equation to obtain the response function to the external potential χ . For 3D crystals, it is directly related to the macroscopic average of the inverse dielectric matrix ε −1 00 (q; ω) = 1 + 4π |q| 2 χ 00 (q; ω), which is expected to give the plasmon, and the use of the Adler and Wiser formula [19][20][21] ε M (ω) = lim q→0 1/ε −1 00 (q; ω) allows for the calculation of the absorption spectrum in the optical limit.…”

Section: Introductionmentioning

confidence: 99%

“…Nevertheless, beyond the scaling effect, the role of the interfaces will be shown to be crucial, and since they are characterized by an abrupt change of the electronic density, we will work within the random phase approximation (RPA) to focus on the LFEs. We will use the Selected-G formalism with the slab potential [13,16], as well as a mixed-space approach [13,18], where the in-plane directions are treated in reciprocal space, and the direction perpendicular to the slab is described in real space, in order to tackle the question of the definition of the interfaces. This leads us to provide a criterion to define the thickness of a quasi-2D object, and to question the relation between the longitudinal-longitudinal and transverse-transverse contractions of the dielectric tensor for the out-of-plane direction of a 2D object.…”

Section: Introductionmentioning

confidence: 99%

“…This leads us to provide a criterion to define the thickness of a quasi-2D object, and to question the relation between the longitudinal-longitudinal and transverse-transverse contractions of the dielectric tensor for the out-of-plane direction of a 2D object. We will still use a silicon slab as a model system, since the absorption and plasmon resonance are separated of more that 10 eV, which allows for a clear distinction [18,22].…”

Section: Introductionmentioning

confidence: 99%

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Optical properties of quasi-two-dimensional objects from time-dependent density functional theory: Longitudinal versus transverse dielectric functions

Mazzei

Giorgetti

2023

Phys. Rev. B

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Comprehension of the electronic properties of nano-objects is a key to defining dedicated properties, which can be adjusted by changing their size. Beyond confinement effects, the presence of interfaces, i.e., places where there is an abrupt change of electronic density, should also play a role. Time-dependent density functional theory (TD-DFT) is a state-of-the-art ab initio formalism in which this effect is accounted for through the so-called local field effects. In an earlier paper [S. Mazzei and C. Giorgetti, Phys. Rev. B 106, 035431 (2022)], we showed that the framework inherited from three-dimensional crystals could not provide reliable absorption spectra. In the present paper, we propose to calculate the macroscopic average of the dielectric tensor of a quasi-twodimensional (2D) object from the response function of the density to the total macroscopic potential in order to avoid use of the so-called Adler and Wiser formula. We evidence that the inclusion of interfaces in the thickness of the slab causes the response function for the out-of-plane component to move sharply from the bulk absorption resonance to the plasmon one. This shows that the longitudinal-longitudinal contraction of the dielectric tensor is no longer equal to the transverse-transverse one in a quasi-2D object for out-of-plane perturbation. Nevertheless, we also show that the macroscopic average of the dielectric tensor of an ultrathin slab calculated within the longitudinal formalism of TD-DFT depicts the properties of the transverse reflectance and transmittance spectra of a thin slab.

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Section: Introductionsupporting

confidence: 78%

Section: Introductionmentioning

confidence: 51%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Optical properties of quasi-two-dimensional objects from time-dependent density functional theory: Longitudinal versus transverse dielectric functions

Mazzei

Giorgetti

2023

Phys. Rev. B

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Transitions in Xenes between excitonic, topological and trivial insulator phases: Influence of screening, band dispersion and external electric field

et al. 2023

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Using a variational approach, the binding energies E_bEb of the lowest bound excitons in Xenes under varying electric field are investigated. The internal exciton motion is described both by Dirac electron dispersion and in effective-mass approximation, while the screened electron-hole attraction is modeled by a Rytova-Keldysh potential with a 2D electronic polarizability \alpha_{2D}α2D. The most important parameters as spin-orbit-induced gap E_gEg, Fermi velocity v_FvF and \alpha_{2D}α2D are taken from ab initio density functional theory calculations. In addition, \alpha_{2D}α2D is approximated in two different ways. The relation of E_bEb and E_gEg is ruled by the screening. The existence of an excitonic insulator phase with E_b>E_gEb>Eg sensitively depends on the chosen \alpha_{2D}α2D. The values of E_gEg and \alpha_{2D}α2D are strongly modified by a vertical external electric bias UU, which defines a transition from the topological into a trivial insulator at U=E_g/2U=Eg/2, with the exception of plumbene. Within the Dirac approximation, but also within the effective mass description of the kinetic energy, the treatment of screening dominates the appearance or non-appearance of an excitonic insulator phase. Gating does not change the results: the prediction done at zero electric field is confirmed when a vertical electric field is applied. Finally, Many-Body perturbation theory approaches based on the Green’s function method, applied to stanene, confirm the absence of an excitonic insulator phase, thus validating our results obtained by ab initio modeling of \alpha_{2D}α2D.

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Optical response of two-dimensional systems: Insights from classical electromagnetism to ab initio calculations

Cited by 2 publications

References 45 publications

Optical properties of quasi-two-dimensional objects from time-dependent density functional theory: Longitudinal versus transverse dielectric functions

Optical properties of quasi-two-dimensional objects from time-dependent density functional theory: Longitudinal versus transverse dielectric functions

Transitions in Xenes between excitonic, topological and trivial insulator phases: Influence of screening, band dispersion and external electric field

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