Tunable Casimir repulsion with three-dimensional topological insulators

Superlattices of Gadolinium and Bismuth Based Thallium Dichalcogenides as Potential Magnetic Topological Insulators

Using relativistic spin-polarized density functional theory calculations we investigate magnetism, electronic structure and topology of the ternary thallium gadolinium dichalcogenides TlGdZ2 (Z= Se and Te) as well as superlattices on their basis. We find TlGdZ2 to have an antiferromagnetic exchange coupling both within and between the Gd layers, which leads to frustration and a complex magnetic structure. The electronic structure calculations reveal both TlGdSe2 and TlGdTe2 to be topologically trivial semiconductors. However, as we show further, a three-dimensional (3D) magnetic topological insulator (TI) state can potentially be achieved by constructing superlattices of the TlGdZ2/(TlBiZ2)n type, in which structural units of TlGdZ2 are alternated with those of the isomorphic TlBiZ2 compounds, known to be non-magnetic 3D TIs. Our results suggest a new approach for achieving 3D magnetic TI phases in such superlattices which is applicable to a large family of thallium rare-earth dichalcogenides and is expected to yield a fertile and tunable playground for exotic topological physics.

Topological signatures in the entanglement of a topological insulator-quantum dot hybrid

In the present work, we consider a hybrid plexciton composed of a semiconductor quantum dot interacting with a topological insulator nanoparticle subject to an external magnetic field. Due to the topological magnetoelectricity of the nanoparticle, long-living plasmonic surface modes are induced, which are quantized and coupled with the quantum dot through its polarization operator. We consider the hybrid as an open quantum system, such that environment effects are accounted by the master equation in the Born-Markov approximation. Then, we apply the Peres' positive partial transpose criterion to quantify the entanglement of the hybrid. We show that this entanglement is a direct signature of the [Formula: see text] invariant of topological insulators.

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.

Modulation of Casimir Force between Graphene-Covered Hyperbolic Materials

A flexible method for modulating the Casimir force is proposed by combining graphene and hyperbolic materials (HMs). The proposed structure employs two candidates other than graphene. One is hexagonal boron nitride (hBN), a natural HM. The other is porous silicon carbide (SiC), which can be treated as an artificial HM by the effective medium theory. The Casimir force between graphene-covered hBN (porous SiC) bulks is presented at zero temperature. The results show that covering HM with graphene increases the Casimir force monotonically. Furthermore, the force can be modulated by varying the Fermi level, especially at large separation distances. The reflection coefficients are thoroughly investigated, and the enhancement is attributed to the interaction of surface plasmons (SPs) supported by graphene and hyperbolic phonon polaritons (HPhPs) supported by HMs. Moreover, the Casimir force can be controlled by the filling factor of porous SiC. The Casimir force can thus be modulated flexibly by designing desired artificial HMs and tuning the Fermi level. The proposed models have promising applications in practical detection and technological fields.

Topology-tuned light scattering around Fano resonances by a core-shell cylinder

The topological magnetoelectric (TME) effect is a novel optical response from topological insulators. This effect shows that magnetic (electric) polarization can be induced by an applied electric (magnetic) field, and it is characterized by the fine structure constant. However, the TME effect is generally very weak and still a challenge to be observed in the experiment. In this paper, we showed that the far-field scattering of a core-shell topological cylinder can be tuned by the TME effect which was enhanced at the surface of plasmonic core around Fano resonance. The interference of broad dipolar mode and narrow quadrupole mode is changed with the topological magnetoelectric polarizability. We demonstrated the reversal of optical responses associated with the TME effect in both far-field and near field. Our results may offer an alternative way to observe the TME effect in topological insulators.

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.

The Casimir Effect in Topological Matter

We give an overview of the work done during the past ten years on the Casimir interaction in electronic topological materials, our focus being solids, which possess surface or bulk electronic band structures with nontrivial topologies, which can be evinced through optical properties that are characterizable in terms of nonzero topological invariants. The examples we review are three-dimensional magnetic topological insulators, two-dimensional Chern insulators, graphene monolayers exhibiting the relativistic quantum Hall effect, and time reversal symmetry-broken Weyl semimetals, which are fascinating systems in the context of Casimir physics. Firstly, this is for the reason that they possess electromagnetic properties characterizable by axial vectors (because of time reversal symmetry breaking), and, depending on the mutual orientation of a pair of such axial vectors, two systems can experience a repulsive Casimir–Lifshitz force, even though they may be dielectrically identical. Secondly, the repulsion thus generated is potentially robust against weak disorder, as such repulsion is associated with the Hall conductivity that is topologically protected in the zero-frequency limit. Finally, the far-field low-temperature behavior of the Casimir force of such systems can provide signatures of topological quantization.

Nonlinear Actuation of Casimir Oscillators toward Chaos: Comparison of Topological Insulators and Metals

In the current study, we explore the sensitivity of the actuation dynamics of electromechanical systems on novel materials, e.g., Bi2Se3, which is a well-known 3D Topological Insulator (TI), and compare their response to metallic conductors, e.g., Au, that are currently used in devices. Bifurcation and phase portraits analysis in conservative systems suggest that the strong difference between the conduction states of Bi2Se3 and Au yields sufficiently weaker Casimir force to enhance stable operation. Furthermore, for nonconservative driven systems, the Melnikov function and Poincare portrait analysis probed the occurrence of chaotic behavior leading to increased risk for stiction. It was found that the presence of the TI enhanced stable operation against chaotic behavior over a significantly wider range of operation conditions in comparison to typical metallic conductors. Therefore, the use of TIs can allow sufficient surface conductance to apply electrostatic compensation of residual contact potentials and, at the same time, to yield sufficiently weak Casimir forces favoring long-term stable actuation dynamics against chaotic behavior.

Perspective on Some Recent and Future Developments in Casimir Interactions

Here, we present a critical review of recent developments in Casimir physics motivated by discoveries of novel materials. Specifically, topologically nontrivial properties of the graphene family, Chern and topological insulators, and Weyl semimetals have diverse manifestations in the distance dependence, presence of fundamental constants, magnitude, and sign of the Casimir interaction. Limited studies of the role of nonlinear optical properties in the interaction are also reviewed. We show that, since many new materials have greatly enhanced the nonlinear optical response, new efficient pathways for investigation of the characteristic regimes of the Casimir force need to be explored, which are expected to lead to new discoveries. Recent progress in the dynamical Casimir effect is also reviewed and we argue that nonlinear media can open up new directions in this field as well.

Chiral-Anomaly-Driven Casimir-Lifshitz Torque between Weyl Semimetals

We propose a new mechanism to generate the Casimir-Lifshitz torque between Weyl semimetals arising from the chiral anomaly. For short distances ranging from a nanometer to a few tens of nanometers, chiral anomaly is manifested via a Casimir-Lifshitz torque ∼sin(θ) with θ being the twisting angle. As the distance between Weyl semimetals increases from a submicrometer to a few micrometers, chiral-anomaly-driven Casimir-Lifshitz torque between Weyl semimetals is remarkably large, which is comparable with that of conventional birefringent materials.

Casimir torque and force in anisotropic saturated ferrite three-layer structure

Based on the scattering formalism and transfer matrix method, we calculate the Casimir energy in multilayer system containing general anisotropic media and apply the result to the anisotropic saturated ferrite three-layer structure. We investigate the stable equilibrium resulting from repulsive Casimir force in the three-layer anisotropic ferrite structure, focusing on the control of the equilibrium position by means of the external magnetic field, which might provide possibility for Casimir actuation under external manipulation. Furthermore, we propose a Casimir torque switch where the torque acting on the intermediate layer can be switched on and off by tuning the relative orientation between the external magnetic fields applied on the outer ferrite layers. The relation between the feature of torque-off/torque-on state and the weak/strong anisotropy of the ferrite is studied. These findings suggest potential application of Casimir torque in, e.g., cooling the rotation of a thin slab in micromachining process via external magnetic field.

Resonant Photovoltaic Effect in Doped Magnetic Semiconductors

The rectified nonlinear response of a clean, time-reversal symmetric, undoped semiconductor to an ac electric field includes a well known intrinsic shift current. We show that when Kramers degeneracy is broken, a distinct second order rectified response appears due to Bloch state anomalous velocities in a system with an oscillating Fermi surface. This effect, which we refer to as the resonant photovoltaic effect, produces a resonant galvanic current peak at the interband absorption threshold in doped semiconductors or semimetals with approximate particle-hole symmetry. We evaluate the resonant photovoltaic effect for a model of the surface states of a magnetized topological insulator.

Enhancement of long-distance Casimir-Polder interaction between an excited atom and a cavity made of metamaterials

Within the framework of macroscopic quantum electrodynamics, we investigate both the radiation force and the potential of Casimir-Polder type acting on an excited cold two-level atom in a cavity made of left-handed materials and topological insulators. As the time-reversal symmetry is broken on the surface of the topological insulators, the spontaneous emission of the atom placed near the focus point(s) exhibits anisotropic properties. While the potential wells are normally shallow for topological trivial dielectric, they may be amplified in the presence of topological magnetoelectric effect. We find that when there exists only one focus point in the cavity, it is possible to boost the forces or the potential wells by up to one order of magnitude. Meanwhile, the lifetime of the atom could be prolonged owing to the focus effect of the left-handed materials, where the emitted photons can trace back to the atom and reabsorbed by itself. Our results indicate the possibility in forming long-lived potential wells, which may have potential applications in trapping and guiding cold atoms far away from the surface.

Stable Casimir equilibria and quantum trapping

The Casimir interaction between two parallel metal plates in close proximity is usually thought of as an attractive interaction. By coating one object with a low-refractive index thin film, we show that the Casimir interaction between two objects of the same material can be reversed at short distances and preserved at long distances so that two objects can remain without contact at a specific distance. With such a stable Casimir equilibrium, we experimentally demonstrate passive Casimir trapping of an object in the vicinity of another at the nanometer scale, without requiring any external energy input. This stable Casimir equilibrium and quantum trapping can be used as a platform for a variety of applications such as contact-free nanomachines, ultrasensitive force sensors, and nanoscale manipulations.

Fluctuation-Induced Torque on a Topological Insulator out of Thermal Equilibrium

Topological insulators with the time reversal symmetry broken exhibit strong magnetoelectric and magneto-optic effects. While these effects are well understood in or near equilibrium, nonequilibrium physics is richer yet less explored. We consider a topological insulator thin film, weakly coupled to a ferromagnet, out of thermal equilibrium with a cold environment (quantum electrodynamics vacuum). We show that the heat flow to the environment is strongly circularly polarized, thus carrying away angular momentum and exerting a purely fluctuation-driven torque on the topological insulator film. Utilizing the Keldysh framework, we investigate the universal nonequilibrium response of the TI to the temperature difference with the environment. Finally, we argue that experimental observation of this effect is within reach.

Repulsive Casimir force between hyperbolic metamaterials

The Casimir force between electric and magnetic hyperbolic metamaterial slabs is investigated. Due to hyperbolic dispersion, the electromagnetic features of these metamaterials along the optical axis are different from those perpendicular to the optical axis; consequently, these features contribute differently to the Casimir effect. The repulsive Casimir force is formed between electric and magnetic hyperbolic metamaterial slabs; moreover, hyperbolic dispersion can enhance the repulsive effect. However, by utilizing the extremely anisotropic behavior of hyperbolic metamaterials and changing the separation distance between the two slabs, the restoring Casimir force emerges. Additionally, by considering the dispersion of both the permittivity and the permeability of hyperbolic metamaterials, the Casimir force reaches several equilibrium points at different separation distances. Furthermore, the Casimir force at room temperature is discussed. Although the temperature can weaken the effect of the restoring Casimir force, stable equilibria may remain upon choosing suitable filling factors. This work shows that hyperbolic metamaterials have potential applications in micro- and nanoelectromechanical systems, especially for maintaining stability and overcoming adhesion problems.

Chaotic behavior in Casimir oscillators: A case study for phase-change materials

Casimir forces between material surfaces at close proximity of less than 200 nm can lead to increased chaotic behavior of actuating devices depending on the strength of the Casimir interaction. We investigate these phenomena for phase-change materials in torsional oscillators, where the amorphous to crystalline phase transitions lead to transitions between high and low Casimir force and torque states, respectively, without material compositions. For a conservative system bifurcation curve and Poincare maps analysis show the absence of chaotic behavior but with the crystalline phase (high force-torque state) favoring more unstable behavior and stiction. However, for a nonconservative system chaotic behavior can take place introducing significant risk for stiction, which is again more pronounced for the crystalline phase. The latter illustrates the more general scenario that stronger Casimir forces and torques increase the possibility for chaotic behavior. The latter is making it impossible to predict whether stiction or stable actuation will occur on a long-term basis, and it is setting limitations in the design of micronano devices operating at short-range nanoscale separations.

Casimir free energy of dielectric films: classical limit, low-temperature behavior and control

The Casimir free energy of dielectric films, both free-standing in vacuum and deposited on metallic or dielectric plates, is investigated. It is shown that the values of the free energy depend considerably on whether the calculation approach used neglects or takes into account the dc conductivity of film material. We demonstrate that there are material-dependent and universal classical limits in the former and latter cases, respectively. The analytic behavior of the Casimir free energy and entropy for a free-standing dielectric film at low temperature is found. According to our results, the Casimir entropy goes to zero when the temperature vanishes if the calculation approach with neglected dc conductivity of a film is employed. If the dc conductivity is taken into account, the Casimir entropy takes the positive value at zero temperature, depending on the parameters of a film, i.e. the Nernst heat theorem is violated. By considering the Casimir free energy of SiO₂ and Al₂O₃ films deposited on a Au plate in the framework of two calculation approaches, we argue that physically correct values are obtained by disregarding the role of dc conductivity. A comparison with the well known results for the configuration of two parallel plates is made. Finally, we compute the Casimir free energy of SiO₂, Al₂O₃ and Ge films deposited on high-resistivity Si plates of different thicknesses and demonstrate that it can be positive, negative and equal to zero. The effect of illumination of a Si plate with laser light is considered. Possible applications of the obtained results to thin films used in microelectronics are discussed.

Quantized chiral anomaly materials cloak

Chiral anomaly materials (CAM, e.g., axion insulator, topological insulator and some of Weyl semimetal) are new states of quantum matter. Anomalous Hall effect can occur in CAM, the anomalous Hall effect is closely related to the topological magneto-electric effect, i.e., when an electric field is applied to CAM, not only the electric field is induced, but also the magnetic field, vice versa. According to those properties, we design an electric cloak with quantized CAM and conductor, and a magnetic cloak with quantized CAM and superconductor. Simulation and calculation results show that the electric cloak can cloak applied electric field and induce magnetic field, and the magnetic cloak can cloak applied magnetic field and induce electric field. When applied electric field is generated by a point charge, the monopole can be obtained.

Strong Thermal and Electrostatic Manipulation of the Casimir Force in Graphene Multilayers

We show that graphene-dielectric multilayers give rise to an unusual tunability of the Casimir-Lifshitz forces and allow to easily realize completely different regimes within the same structure. Concerning thermal effects, graphene-dielectric multilayers take advantage of the anomalous features predicted for isolated suspended graphene sheets, even though they are considerably affected by the presence of the dielectric substrate. They can also achieve the anomalous nonmonotonic thermal metallic behavior by increasing the graphene sheets density and their Fermi level. In addition to a strong thermal modulation occurring at short separations, in a region where the force is orders of magnitude larger than the one occurring at large distances, the force can be also adjusted by varying the number of graphene layers as well as their Fermi levels, allowing for relevant force amplifications which can be tuned, very rapidly and in situ, by simply applying an electric potential. Our predictions can be relevant for both Casimir experiments and micro- or nanoelectromechanical systems and in new devices for technological applications.

Determination of the quantized topological magneto-electric effect in topological insulators from Rayleigh scattering

Topological insulators (TIs) exhibit many exotic properties. In particular, a topological magneto-electric (TME) effect, quantized in units of the fine structure constant, exists in TIs. Here, we theoretically study the scattering properties of electromagnetic waves by TI circular cylinders particularly in the Rayleigh scattering limit. Compared with ordinary dielectric cylinders, the scattering by TI cylinders shows many unusual features due to the TME effect. Two proposals are suggested to determine the TME effect of TIs simply by measuring the electric-field components of scattered waves in the far field at one or two scattering angles. Our results could also offer a way to measure the fine structure constant.

Repulsive Casimir effect with Chern insulators

We theoretically predict that the Casimir force in vacuum between two Chern insulator plates can be repulsive (attractive) at long distances whenever the sign of the Chern numbers characterizing the two plates are opposite (equal). A unique feature of this system is that the sign of the force can be tuned simply by turning over one of the plates or alternatively by electrostatic doping. We calculate and take into account the full optical response of the plates and argue that such repulsion is a general phenomena for these systems as it relies on the quantized zero frequency Hall conductivity. We show that achieving repulsion is possible with thin films of Cr-doped (Bi,Sb)2Te3, that were recently discovered to be Chern insulators with quantized Hall conductivity.

Theoretical ingredients of a Casimir analog computer

We derive a correspondence between the contour integration of the Casimir stress tensor in the complex-frequency plane and the electromagnetic response of a physical dissipative medium in a finite real-frequency bandwidth. The consequences of this correspondence are at least threefold: First, the correspondence makes it easier to understand Casimir systems from the perspective of conventional classical electromagnetism, based on real-frequency responses, in contrast to the standard imaginary-frequency point of view based on Wick rotations. Second, it forms the starting point of finite-difference time-domain numerical techniques for calculation of Casimir forces in arbitrary geometries. Finally, this correspondence is also key to a technique for computing quantum Casimir forces at micrometer scales using antenna measurements at tabletop (e.g., centimeter) scales, forming a type of analog computer for the Casimir force. Superficially, relationships between the Casimir force and the classical electromagnetic Green's function are well known, so one might expect that any experimental measurement of the Green's function would suffice to calculate the Casimir force. However, we show that the standard forms of this relationship lead to infeasible experiments involving infinite bandwidth or exponentially growing fields, and a fundamentally different formulation is therefore required.