Microscopic Dielectric and Gyration Tensors of Incommensurately Modulated Insulators

Abstract

Subject classification: 64.70.Rh; Crystal optical properties of insulating materials possessing incommensurately modulated phases are studied in the framework of a microscopic model. Quantum-mechanical expressions for the microscopic dielectric permittivity tensor are derived. It is shown that the contributions from the long-wavelength reciprocal lattice vectors with the lowest microscopic indices should be taken into account in the optical response of the incommensurate crystals. This justifies, from the standpoint of microscopic theory, a mesoscopic approach to the problem of light propagation in incommensurate crystals adopted in a number of earlier studies. The mesoscopic tensors associated with the first-order spatial dispersion are obtained and analyzed in detail. The optical gyration is revealed to be described by the dielectric tensor components linear in both the light wave vector and the mesoscopic incommensurate modulation wave vector. The latter contributions correspond to the gyration mechanism related to the mesoscopic inhomogeneity of the optical medium under study.

Spatial dispersion in incommensurately modulated insulators

“…We have proven that, for the case of crystalline media, the SD should be correctly described in terms of the Fourier components of an optical frequency dielectric permittivity dependent upon a single wavevector argument, the specific combination k + 1 2 h of the light wavevector and the generalized reciprocal lattice vectors. It is worth noting that, as far as the first-order SD is concerned, the above results, derived in a purely phenomenological way, agree with the microscopic theory [27] for the incommensurately modulated insulators, which predicts dipole-magnetodipole and dipole-quadrupole contributions to the dielectric tensor, linearly related to the mesoscopic modulation wavevector q.…”

“…It has been shown in [14] that the long-wavelength modulation with the wavevector q essentially affects a number of physical properties of the A 2 BX 4 crystals, thus justifying keeping the contributions from q while passing to the macroscopic parameters. Such an approach also agrees with the microscopic models which predict that the Fourier components εh i j decrease rapidly with increasing n 3 or m (see [2], chapter 4, and the proof for the IC systems [27,33]). Hence, we shall not discuss the known [13,15] procedure of macroscopic averaging of equation ( 23) but write down straightaway the mesoscopic CR for the case of a single long-wavelength periodicity (λ m = 2π/q) dominating in the structure of the IC phase:…”

“…where the ε i j are spatially independent components, and ε i j (ϕ + qr) and γ i jl (ϕ + qr) periodic functions of the argument ϕ + qr. It is worth noticing that formulae (30) and ( 31) agree well with the results [27] obtained in the framework of a microscopic theory. We shall use this CR for the approximate description of crystal optics of centrosymmetric IC phases in the planewave modulation region.…”

“…Furthermore, the wavevector dependence of the conductivity tensor derived in section 13 in [2] within a simple microscopic model for non-modulated crystals may indeed be expressed with a single argument 2k + h 0 , in accordance with our results 3 . The analysis of the results derived with the microscopic approach [27] confirms that the same should be true of the IC crystals.…”

Symmetry peculiarities of dielectric tensor in incommensurately modulated crystal phases

“…The additional reason for this is the analysis of the quantum-mechanical expression for the ε n i ,m ij (ω, k, ϕ) components derived in a way similar to that used in [14]. These results are reported elsewhere [24].…”