Excitonic effects in the Casimir force

Our purpose in this work is to evaluate the spatial dispersion contribution to the Casimir force in an intrinsic semiconductor planar cavity where exciton resonances are considered in the dielectric response of the mirrors.In the long-wavelength limit much of the theory for the Casimir force calculation was done using classical electrodynamics based on the description of the mirrors response in terms of a local dielectric function. This local description proved extremely successful in many situations due to the fact that, at large separations between the mirrors, only the long-wavelength fields are relevant.In a translationally invariant system where the excitation in a given ?position depends also on a neighbourhood, the relation between displacement and electric field: (1)identifies the spatial dispersion effect with a wave-vector dependent dielectric response. Comparisons between Casimir forces in an intrinsic semiconductor planar cavity computed with local dielectric and non-local dielectric function in the framework of eq.(1), have recently proved to produce a Casimir force variation within current experimental precision [1].However, this description immediately leads to difficulties due to the intrinsic nonlocality of finite media resulting from the lack of translational invariance.In this case a more general relation holds between displacement and electric field, that in mixed coordinates is given by: (2)giving the correct consideration of surface potential effects [2].In the present work we will evaluate the spatial dispersion contribution to the Casimir force in a planar intrinsic semiconductor cavity in the framework of eq.(2), close to the interband transition energies, that are dominated by the Wannier exciton dynamics [2]. The calculation will be performed by an exciton envelope function [2] that is well suited for describing the center-of-mass dynamics [3]. The Casimir force is computed as a function of slabs and cavity thicknesses for two classes of intrinsic semiconductors: III-V (GaAs) and II-VI (CdS) and calculation are performed for heavy and light hole contributions. Finally, the Casimir force for weak and strong (polaritons) radiation-matter interactions are also briefly discussed.References[1] A.D.Hernandez de la Luz, et al., Sol. St. Comm. 132, 623 (2004).[2] A.D'Andrea and R. Del Sole, Phys. Rev. B 29, 4782 (1984)[3] D.Schiumarini, N.Tomassini, L.Pilozzi, A.D'Andrea, Phys.Rev.B 82, 075303 (2010)