The Casimir Effect in Topological Matter

The normal Casimir-Lifshitz force for laterally moving graphene

We consider the system of two parallel sheets of graphene which are moving with relative parallel velocityv⃗and calculate the Casimir energy by using the scattering approach. We analyze in detail the normal (perpendicular to the planes) Casimir force for two systems-graphene/graphene and ideal metal/graphene. In the non-relativistic casev≪vF, the relative correction to the Casimir energy(Ev-E0)/E0is proportional to the (v/c)2(the maximum value is 0.0033 for the gapeless case andv=vF) for the first system, and it is zero up to the Fermi velocityv=vFfor system ideal metal/graphene.

Nonlinear actuation of micromechanical Casimir oscillators with topological insulator materials toward chaotic motion: Sensitivity on magnetization and dielectric properties

We have investigated the dynamical actuation of micro-electromechanical systems under the influence of attractive and repulsive Casimir forces between topological insulator plates as a function of their dielectric function and coating magnetization. The analysis of the Casimir force in the limit of strong and weak magnetization shows that the attractive force, which is produced for plate magnetizations in the same direction, is greater than the repulsive force that is produced for opposite magnetizations. However, both forces remain comparable for intermediate magnetizations. Moreover, for weak magnetization, the attractive force becomes stronger for an increasing dielectric function, while the opposite occurs for the repulsive force. On the other hand, increasing magnetization decreases the influence of the dielectric function on both the repulsive and attractive forces. Furthermore, for conservative systems, bifurcation and phase portrait analysis revealed that increasing magnetization decreases the regime of stable operation for devices with attractive forces, while their operation remains always stable under the presence of repulsive forces. Finally, for non-conservative periodically driven systems, the Melnikov function and Poincaré portrait analysis show that for magnetizations in the same direction leading to strong attractive Casimir forces, chaotic motion toward stiction is highly likely to occur preventing the long-term prediction of actuating dynamics. A remedy for this situation is obtained by the application of any magnetization in opposite directions between the interacting surfaces since the repulsive force makes it possible to prevent stiction.

Casimir forces out of thermal equilibrium near a superconducting transition

We present a comprehensive analysis of the out-of-equilibrium Casimir pressure between two high-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_c$$\end{document}Tc superconducting plates, each kept at a different temperature. Two interaction regimes can be distinguished. While the zero-point energy dominates in the near field, thermal effects become important at large interplate separations causing a drop in the force’s magnitude compared with the usual thermal-equilibrium case. Our detailed calculations highlight the competing role played by propagating and evanescent modes. Moreover, as one of the plates undergoes the superconducting transition, we predict an abrupt change in the force for any plate distance, which has not been previously observed in other systems. The sensitivity of the dielectric function of the high-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_c$$\end{document}Tc superconductors makes them ideal systems for a possible direct measurement of the out-of-equilibrium Casimir pressure.