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Register a new userMaxwell Eigenmode approach to the Casimir-Lifshitz Torque
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More than forty years ago, Barash published a calculation of the full retarded Casimir-Lifshitz torque for planar birefringent media with arbitrary degrees of anisotropy. An independent theoretical confirmation has been lacking since. We report a systematic and transparent derivation of the torque between two media with both electric and magnetic birefringence. Our approach, based on an eigenmode decomposition of Maxwells equations, generalizes Barashs result for electrically birefringent materials, and can be generalized to a wide range of anisotropic materials and finite thickness effects.
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We model a cholesteric liquid crystal as a planar uniaxial multilayer system, where the orientation of each layer differs slightly from that of the adjacent one. This allows us to analytically simplify the otherwise acutely complicated calculation of the Casimir-Lifshitz torque. Numerical results differ appreciably from the case of nematic liquid crystals, which can be treated like bloc birefringent media. In particular, we find that the torque deviates considerably from its usual sinusoidal behavior as a function of the misalignment angle. In the case of a birefringent crystal faced with a cholesteric liquid one, the Casimir-Lifshitz torque decreases more slowly as a function of distance than in the nematic case. In the case of two cholesteric liquid crystals, either in the homochiral or in the heterochiral configuration, the angular dependence changes qualitatively as a function of distance. In all considered cases, finite pitch length effects are most pronounced at distances of about 10 nm.
Usual Gaussian beams are particular scalar solutions to the paraxial Helmholtz equation, which neglect the vector nature of light. In order to overcome this inconvenience, Simon et al. (J. Opt. Soc. Am. A 1986, 3, 536-540) found a paraxial solution to Maxwells equation in vacuum, which includes polarization in a natural way, though still preserving the spatial Gaussianity of the beams. In this regard, it seems that these solutions, known as Gauss-Maxwell beams, are particularly appropriate and a natural tool in optical problems dealing with Gaussian beams acted or manipulated by polarizers. In this work, inspired in the Bohmian picture of quantum mechanics, a hydrodynamic-type extension of such a formulation is provided and discussed, complementing the notion of electromagnetic field with that of (electromagnetic) flow or streamline. In this regard, the method proposed has the advantage that the rays obtained from it render a bona fide description of the spatial distribution of electromagnetic energy, since they are in compliance with the local space changes undergone by the time-averaged Poynting vector. This feature confers the approach a potential interest in the analysis and description of single-photon experiments, because of the direct connection between these rays and the average flow exhibited by swarms of identical photons (regardless of the particular motion, if any, that these entities might have), at least in the case of Gaussian input beams. In order to illustrate the approach, here it is applied to two common scenarios, namely the diffraction undergone by a single Gauss-Maxwell beam and the interference produced by a coherent superposition of two of such beams.
We study the Casimir torque between two metallic one-dimensional gratings rotated by an angle $theta$ with respect to each other. We find that, for infinitely extended gratings, the Casimir energy is anomalously discontinuous at $theta=0$, due to a critical zero-order geometric transition between a 2D- and a 1D-periodic system. This transition is a peculiarity of the grating geometry and does not exist for intrinsically anisotropic materials. As a remarkable practical consequence, for finite-size gratings, the torque per area can reach extremely large values, increasing without bounds with the size of the system. We show that for finite gratings with only 10 period repetitions, the maximum torque is already 60 times larger than the one predicted in the case of infinite gratings. These findings pave the way to the design of a contactless quantum vacuum torsional spring, with possible relevance to micro- and nano-mechanical devices.
We show in this paper that the technologically relevant field-like spin-orbit torque shows resilience against the geometrical effect of electron backscattering. As device grows smaller in sizes, the effect of geometry on physical properties like spin torque, and hence switching current could place a physical limit on the continued shrinkage of such device -- a necessary trend of all memory devices (MRAM). The geometrical effect of curves has been shown to impact quantum transport and topological transition of Dirac and topological systems. In our work, we have ruled out the potential threat of line-curves degrading the effectiveness of spin-orbit torque switching. In other words, spin-orbit torque switching will be resilient against the influence of curves that line the circumferences of defects in the events of electron backscattering, which commonly happen in the channel of modern electronic devices.
We analyze the structure of the surface states and Fermi arcs of Weyl semimetals as a function of the boundary conditions parameterizing the Hamiltonian self-adjoint extensions of a minimal model with two Weyl points. These boundary conditions determine both the pseudospin polarization of the system on the surface and the shape of the associated Fermi arcs. We analytically derive the expectation values of the density profile of the surface current, we evaluate the anomalous Hall conductivity as a function of temperature and chemical potential and we discuss the surface current correlation functions and their contribution to the thermal noise. Based on a lattice variant of the model, we numerically study the surface states at zero temperature and we show that their polarization and, consequently, their transport properties, can be varied by suitable Zeeman terms localized on the surface. We also provide an estimate of the bulk conductance of the system based on the Landauer-Buttiker approach. Finally, we analyze the surface anomalous thermal Hall conductivity and we show that the boundary properties lead to a correction of the expected universal thermal Hall conductivity, thus violating the Wiedemann-Franz law.
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