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This paper presents a theoretical framework for exploring the optical properties of layered materials. The derived analytical formulas for reflectance and transmittance spectra incorporate vertical valence-state transitions and appropriate boundary conditions for finite-width bulk materials, integrated with the generalized tight-binding model to account for intrinsic interactions and external fields. The study reveals distinct structures in the spectra of multilayer graphene for different stacking layers at low energies (∼0.2–0.8 eV), attributed to interband transitions at the K point. Furthermore, the high-energy part (≳5 eV) highlights thickness-dependent plasmon effects characterized by unique resonance frequencies in the optical spectra. These features depend on the dimensionality, interlayer coupling, and electronic structure of the material. This work provides a deeper understanding of the optical properties of layered structures, facilitating their exploration and characterization for diverse applications. [ABSTRACT FROM AUTHOR]

In this expository article, we present a systematic formal derivation of the Kubo formula for the linear-response current due to a time-harmonic electric field applied to non-interacting, spinless charged particles in a finite volume in the quantum setting. We model dissipation in a transparent way by assuming a sequence of scattering events occurring at random-time intervals modeled by a Poisson distribution. By taking the large-volume limit, we derive special cases of the formula for free electrons, continuum and tight-binding periodic systems, and the nearest-neighbor tight-binding model of graphene. We present the analogous formalism with dissipation to derive the Drude conductivity of classical free particles. [ABSTRACT FROM AUTHOR]

We describe the low‐temperature optical conductivity as a function of frequency for a quantum‐mechanical system of electrons that hop along a polymer chain. To this end, we invoke the Su–Schrieffer–Heeger tight‐binding Hamiltonian for noninteracting spinless electrons on a one‐dimensional (1D) lattice. Our goal is to show via asymptotics how the interband conductivity of this system behaves as the smallest energy bandgap tends to close. Our analytical approach includes: (i) the Kubo‐type formulation for the optical conductivity with a nonzero damping due to microscopic collisions, (ii) reduction of this formulation to a 1D momentum integral over the Brillouin zone, and (iii) evaluation of this integral in terms of elementary functions via the three‐dimensional Mellin transform with respect to key physical parameters and subsequent inversion in a region of the respective complex space. Our approach reveals an intimate connection of the behavior of the conductivity to particular singularities of its Mellin transform. The analytical results are found in good agreement with direct numerical computations. [ABSTRACT FROM AUTHOR]

Y-shaped Kekulé bond textures in a honeycomb lattice on a graphene-copper superlattice have recently been experimentally revealed. In this paper, the effects of such a bond modulation on the transport coefficients of Kekulé-patterned graphene are investigated in the presence of a perpendicular magnetic field. Analytical expressions are derived for the Hall and longitudinal conductivities using the Kubo formula. It is found that the Y-shaped Kekulé bond texture lifts the valley degeneracy of all Landau levels except that of the zero mode, leading to additional plateaus in the Hall conductivity accompanied by a split of the corresponding peaks in the longitudinal conductivity. Consequently, the Hall conductivity is quantized as ± ne 2/ h for n = 2, 4, 6, 8, 10, …, excluding some plateaus that disappear due to the complete overlap of the Landau levels of different cones. These results also suggest that DC Hall conductivity measurements will allow us to determine the Kekulé bond texture amplitude. [ABSTRACT FROM AUTHOR]

The performance of a multi-layered parallel plate waveguide, supported by graphene plates, is evaluated here. The graphene layers were biased with both magnetic and electric fields. The graphene plates weremodelled as an anisotropic surface derived from the Kubo formula. Maxwell's equations were solved for these waveguides; and it is shown when both magnetic and electric biases were applied to the graphene, hybrid modes propagated inside the waveguides. The intensity of each TM and TE mode could be adjusted with an applied external field bias. This study of wave confinement has shown that, by varying the bias, full control can be exerted over the wave's propagation within a waveguide; whereby, increasing the bias causes added phase changes over the propagation length, while increasing the waveguide's attenuation. It must be emphasized that the presented procedure is also applicable to other guiding structures that have boundary with isotropic or anisotropic conductivities. [ABSTRACT FROM AUTHOR]

We first review the problem of a rigorous justification of Kubo's formula for transport coefficients in gapped extended Hamiltonian quantum systems at zero temperature. In particular, the theoretical understanding of the quantum Hall effect rests on the validity of Kubo's formula for such systems, a connection that we review briefly as well. We then highlight an approach to linear response theory based on non-equilibrium almost-stationary states (NEASS) and on a corresponding adiabatic theorem for such systems that was recently proposed and worked out by one of us in [51] for interacting fermionic systems on finite lattices. In the second part of our paper, we show how to lift the results of [51] to infinite systems by taking a thermodynamic limit. [ABSTRACT FROM AUTHOR]

We investigate the physical properties of silicene with both staggered sublattice potential and magnetization by using Kubo formalism, the latter arises from the magnetic proximity effect by depositing Fe atoms to silicene or depositing silicene on an appropriate ferromagnetic insulator. Based on the low-energy continuum model of the system where inversion symmetry is broken, we show that the system exhibits spin half metal state when staggered sublattice potential is in the same magnitude with mean and staggered magnetization. Besides, Hall conductivity and magnetic moment are all valley dependent, so we investigate the valley Hall effect of the system further by considering magnetization exclusively. This means carriers in different valleys turning into opposite directions transverse to an in-plane electric field. At last, we prove these results by investigating Berry curvature that characterizing Hall transport, which is also valley dependent. These effects can be used to generate valley-polarized currents solely by magnetization, forming the basis for the valley-based electronics applications. [ABSTRACT FROM AUTHOR]

Based on Kubo's linear response formalism, temperature dependence of the spin-Hall conductivity of a two-dimensional impure (magnetic and nonmagnetic impurities) Rashba electron gas in the presence of electron-electron and electron-phonon interactions is analyzed theoretically. We will show that the temperature dependence of the spin-Hall conductivity is determined by the relaxation rates due to these interactions. At low temperature, the elastic lifetimes ( $$\tau _\mathrm{n}$$ and $$\tau _\mathrm{m} )$$ are determined by magnetic and nonmagnetic impurity concentrations which are independent of the temperature, while the inelastic lifetimes ( $$\tau _\mathrm{ee}$$ and $$\tau _\mathrm{ep} )$$ related to the electron-electron and electron-phonon interactions, decrease when the temperature increases. We will also show that since the spin-Hall conductivity is sensitive to temperature, we can distinguish the intrinsic and extrinsic contributions. [ABSTRACT FROM AUTHOR]

Increasing attention on plasmonics materials has been paid due to their exciting physical behaviors and potential applications. Here, we present the application of the Kubo formula by providing a description of the underlying mechanisms to realize the effective permittivity. We obtain plasma frequency and linear relation of frequencies with the effective permittivity. We have proposed an improved method to retrieve the effective parameters (index of refraction, impedance, permittivity, and permeability) of metamaterials from transmission and reflection data. Extents far above the calculated relations are very good match with effective permittivity-related environment, including nanospheres of some metals and a samples of the high refractive index dielectric material. [ABSTRACT FROM AUTHOR]

We calculate the conductivity of a clean graphene sheet at finite temperatures starting from the tight-binding model. We obtain a finite value for the dc-conductivity at zero temperature. For finite temperature, the spontaneous electron-hole creation, responsible for the finite conductivity at zero temperature, is washed out and the dc-conductivity yields zero. Our results are in agreement with calculations based on the field-theoretical model for graphene. [ABSTRACT FROM AUTHOR]

This note is a continuation of our recent paper [V. Jakšić Y. Ogata, and C.-A. Pillet, The Green-Kubo formula and Onsager reciprocity relations in quantum statistical mechanics. Commun. Math. Phys. in press.] where we have proven the Green-Kubo formula and the Onsager reciprocity relations for heat fluxes in thermally driven quantum open systems. In this note we extend the derivation of the Green-Kubo formula to heat and charge fluxes and discuss some other generalizations of the model and results of [V. Jakšić Y. Ogata and C.-A. Pillet, The Green-Kubo formula and Onsager reciprocity relations in quantum statistical mechanics. Commun. Math. Phys. in press.]. [ABSTRACT FROM AUTHOR]

Structural defects are inherent in solids at a finite temperature, because they diminish free energies by growing entropy. The arrangement of these defects may display long-range orders, as occurring in quasicrystals, whose hidden structural symmetry could greatly modify the transport of excitations. Moreover, the presence of such defects breaks the translational symmetry and collapses the reciprocal lattice, which has been a standard technique in solid-state physics. An alternative to address such a structural disorder is the real space theory. Nonetheless, solving 1023 coupled Schrödinger equations requires unavailable yottabytes (YB) of memory just for recording the atomic positions. In contrast, the real-space renormalization method (RSRM) uses an iterative procedure with a small number of effective sites in each step, and exponentially lessens the degrees of freedom, but keeps their participation in the final results. In this article, we review aperiodic atomic arrangements with hierarchical symmetry investigated by means of RSRM, as well as their consequences in measurable physical properties, such as electrical and thermal conductivities. [ABSTRACT FROM AUTHOR]