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The strong coupling between electromagnetic field and lattice oscillation in piezoelectric materials gives rise to phonon polariton excitations. Such quasiparticles open up new directions in modulating the ubiquitous Casimir force. Here by utilizing the generalized Born-Huang hydrodynamics model, three types of phonons in piezoelectrics are studied: longitudinal optical phonon, transverse optical phonon and phonon polariton. The phonon-electromagnetic coupling results in a complex set of Fresnel reflection matrices which prevents the utilization of the standard Lifshitz approach for calculating Casimir forces in the imaginary frequency domain. Our calculations are based on an approach within real frequency and finite temperatures, through which various regimes of the Casimir interaction are examined. Our study shows that piezoelectrics emerge as a set of materials where this ubiquitous force can be controlled via phonon properties for the first time. The Casimir interaction appears as a suitable means to distinguish between different types of surface phonon polaritons associated with different structural piezoelectric polytypes., Comment: 8 pages, 4 figures, supplementary information with 10 pages, 4 figures; submitted

We calculate the Casimir-Lifshitz force (CLF) between a metallic sphere and a graphene-coated SiO$_2$ plane and compare our finding with the experiment and theory by M. Liu \emph{et al.}, PRL {\bf 126}, 206802 (2021), where a non-local and lossless model for the graphene conductivity (GC) has been used and shown to be compatible with the experimental results. Recently, that conductivity model has been shown to be not correctly regularized [arXiv:2403.02279], to predict nonphysical results in the non-local regime, and being correct only in its local limit, where its expression is identical to the local Kubo conductivity model (once also losses are introduced). To compare the experimental results with the correctly regularized Kubo theory and to clarify the effective role played by the graphene non-locality and losses in that experiment, we calculated the CLF using three different models for the GC: the correct general non-local Kubo model, the local Kubo model, and the non-regularized and lossless model used by M. Liu \emph{et al.}. For the parameters of the experiment, the predictions for the Casimir-Lifshitz force using the three models are practically identical, implying that, for the experiment, both non-local and lossy effects in the GC are negligible. This explains why the GC model used in M. Liu \emph{et al.} provides results in agreement with the experiment. We find that the experiment cannot distinguish between the Drude and Plasma prescriptions. Our findings are relevant for present and future comparisons with experimental measurement of the Casimir-Lifshitz force involving graphene structures. Indeed, we show that an extremely simple local Kubo model, explicitly depending on Dirac mass, chemical potential, losses and temperature, is largely enough for a totally comprehensive comparison with typical experimental configurations., Comment: 17 pages, 15 figures

The Casimir interaction and torque are related phenomena originating from the exchange of electromagnetic excitations between objects. While the Casimir force exists between any types of objects, the materials or geometrical anisotropy drives the emergence of the Casimir torque. Here both phenomena are studied theoretically between dielectric films with immersed parallel single wall carbon nanotubes in the dilute limit with their chirality and collective electronic and optical response properties taken into account. It is found that the Casimir interaction is dominated by thermal fluctuations at sub-micron separations, while the torque is primarily determined by quantum mechanical effects. This peculiar quantum vs. thermal separation is attributed to the strong influence of reduced dimensionality and inherent anisotropy of the materials. Our study suggests that nanostructured anisotropic materials can serve as novel platforms to uncover new functionalities in ubiquitous Casimir phenomena., Comment: 9 pages, 4 figures, submitted to Phys. Rev. B

We study within the framework of the Lifshitz theory the long-range Casimir force for in-plane isotropic and anisotropic free-standing transdimensional material slabs. In the former case, we show that the confinement-induced nonlocality not only weakens the attraction of ultrathin slabs but also changes the distance dependence of the material-dependent correction to the Casimir force to go as $\sim\!1/\!\sqrt{l}$ contrary to the $\sim\!1/l$ dependence of that of the local Lifshitz force. In the latter case, we use closely packed array of parallel aligned single-wall carbon nanotubes in a dielectric layer of finite thickness to demonstrate strong orientational anisotropy and crossover behavior for the inter-slab attractive force in addition to its reduction with decreasing slab thickness. We give physical insight as to why such a pair of ultrathin slabs prefers to stick together in the perpendicularly oriented manner, rather than in the parallel relative orientation as one would customarily expect., Comment: 20 pages, 4 figures, 52 references

Van der Waals interactions are ubiquitous and they play an important role for the stability of materials. Current understanding of this type of coupling is based on linear response theory, while optical nonlinearities are rarely considered in this context. Many materials, however, exhibit strong optical nonlinear response, which prompts further evaluation of dispersive forces beyond linear response. Here we present a $\textit{Discrete Coupled Nonlinear Dipole}$ approach that takes into account linear and nonlinear properties of all dipolar nanoparticles in a given system. This method is based on a Hamiltonian for nonlinear dipoles, which we apply in different systems uncovering a complex interplay of distance, anisotropy, polarizibilities, and hyperpolarizabilities in the vdW energy. This investigation broadens our basic understanding of dispersive interactions, especially in the context of nonlinear materials., Comment: 7 pages, 3 figures; submitted; a part of this work has been presented at APS March Meeting 2023 (N17.00010)

We study the heat transfer between N coupled quantum resonators with applied synthetic electric and magnetic fields realized by changing the resonators parameters by external drivings. To this end we develop two general methods, based on the quantum optical master equation and on the Langevin equation for $N$ coupled oscillators where all quantum oscillators can have their own heat baths. The synthetic electric and magnetic fields are generated by a dynamical modulation of the oscillator resonance with a given phase. Using Floquet theory we solve the dynamical equations with both methods which allow us to determine the heat flux spectra and the transferred power. With apply these methods to study the specific case of a linear tight-binding chain of four quantum coupled resonators. We find that in that case, in addition to a non-reciprocal heat flux spectrum already predicted in previous investigations, the synthetic fields induce here non-reciprocity in the total heat flux hence realizing a net heat flux rectification.

Twisted bilayered graphenes at magic angles are systems housing long ranged periodicity of Moir\'e pattern together with short ranged periodicity associated with the individual graphenes. Such materials are a fertile ground for novel states largely driven by electronic correlations. Here we find that the ubiquitous Casimir force can serve as a platform for macroscopic manifestations of the quantum effects stemming from the magic angle bilayered graphenes properties and their phases determined by electronic correlations. By utilizing comprehensive calculations for the electronic and optical response, we find that Casimir torque can probe anisotropy from the Drude conductivities in nematic states, while repulsion in the Casimir force can help identify topologically nontrivial phases in magic angle twisted bilayered graphenes., Comment: 9 pages, 6 figures (main), 7 pages, 7 figures (supplementary); provisionally accepted for publication in 2D Materials

The van der Waals (vdW) interaction plays a prominent role between neutral objects at separations where short ranged chemical forces are negligible. This type of dispersive coupling is determined by the interplay between geometry and response properties of the materials making up the objects. Here, we investigate the vdW interaction between 1D, 2D, and 3D standard and Dirac materials within the Random Phase Approximation, which takes into account collective excitations originating from the electronic Coulomb potential. A comprehensive understanding of characteristic functionalities and scaling laws are obtained for systems with parabolic energy dispersion (standard materials) and crossing linear bands (Dirac materials). By comparing the quantum mechanical and thermal limits the onset of thermal fluctuations in the vdW interaction is discussed showing that thermal effects are significantly pronounced at smaller scales in reduced dimensions., Comment: 8 pages (main), 6 pages (supplementary information), 5 figures. Published on Journal of Physics: Materials

We study quantum friction and Casimir forces with a full-relativistic formalism for atoms modelled as Unruh-DeWitt detectors in the presence of arbitrary macroscopic objects. We consider the general case of atoms with arbitrary relativistic trajectories in arbitrary quantum states (including coherent superpositions) close to objects that impose arbitrary boundary conditions. Particularizing for conducting plates, we show that, for relative velocities close to the speed of light, the quantum friction diverges while the Casimir force is almost independent of the velocity. Since we include the effect of the finite size of the detector and the finite interaction time, we also obtain quantum friction when the detector is isolated but follows a non-inertial trajectory., Comment: 27 pages (includes 10 pages of appendices), 12 Figures. RevTeX 4.1

In this note we discuss the invariance under general changes of reference frame of all the physical predictions of particle detector models in quantum field theory in general and, in particular, of those used in quantum optics to model atoms interacting with light. We find explicitly how the light-matter interaction Hamiltonians change under general coordinate transformations, and analyze the subtleties of the Hamiltonians commonly used to describe the light-matter interaction when relativistic motion is taken into account., Comment: 11 pages. ReVteX 4.1. V2: Updated to match published version

The Casimir force is a universal interaction induced by electromagnetic quantum fluctuations between any types of objects. The expansion of the graphene family by adding silicene, germanene, and stanene, 2D allotropes of Si, Ge, and Sn, lands itself as a platform to probe Dirac-like physics in honeycomb staggered systems in such a ubiquitous interaction. We discover Casimir force phase transitions between these staggered 2D materials induced by the complex interplay between Dirac physics, spin-orbit coupling, and externally applied fields. In particular, we find that the interaction energy experiences different power law distance decays, magnitudes, and dependences on characteristic physical constants. Furthermore, due to the topological properties of these materials, repulsive and quantized Casimir interactions become possible., Comment: 12 pages, 9 Figures (4 pages and 5 figures in the Supporting Information). Discussion about thermal corrections to the Casimir force was included. Updated figures in the manuscript and supplementary information

Interactions induced by electromagnetic fluctuations, such as van der Waals and Casimir forces, are of universal nature present at any length scale between any types of systems with finite dimensions. Such interactions are important not only for the fundamental science of materials behavior, but also for the design and improvement of micro- and nano-structured devices. In the past decade, many new materials have become available, which has stimulated the need of understanding their dispersive interactions. The field of van der Waals and Casimir forces has experienced an impetus in terms of developing novel theoretical and computational methods to provide new insights in related phenomena. The understanding of such forces has far reaching consequences as it bridges concepts in materials, atomic and molecular physics, condensed matter physics, high energy physics, chemistry and biology. In this review, we summarize major breakthroughs and emphasize the common origin of van der Waals and Casimir interactions. We examine progress related to novel ab initio modeling approaches and their application in various systems, interactions in materials with Dirac-like spectra, force manipulations through nontrivial boundary conditions, and applications of van der Waals forces in organic and biological matter. The outlook of the review is to give the scientific community a materials perspective of van der Waals and Casimir phenomena and stimulate the development of experimental techniques and applications., Comment: 54 pages, 18 figures, 400+ references. Review article

We compute the radiative heat transfer between two sheets of 2D Dirac materials, including topological Chern insulators and graphene, within the framework of the local approximation for the optical response of these materials. In this approximation, which neglects spatial dispersion, we derive both numerically and analytically the short-distance asymptotic of the near-field heat transfer in these systems, and show that it scales as the inverse of the distance between the two sheets. Finally, we discuss the limitations to the validity of this scaling law imposed by spatial dispersion in 2D Dirac materials., Comment: 15 pages, 4 figures. Updated version including corrected analysis of the far-field regime

We demonstrate how to control the spectra and current flow of Dirac electrons in both a graphene sheet and a topological insulator by applying either two linearly polarized laser fields with frequencies $\omega$ and $2\omega$ or a monochromatic (one-frequency) laser field together with a spatially periodic static potential(graphene/TI superlattice). Using the Floquet theory and the resonance approximation, we show that a Dirac point in the electron spectrum can be split into several Dirac points whose relative location in momentum space can be efficiently manipulated by changing the characteristics of the laser fields. In addition, the laser-field controlled Dirac fermion band structure -- Dirac fermion time-Floquet crystal -- allows the manipulation of the electron currents in graphene and topological insulators. Furthermore, the generation of dc currents of desirable intensity in a chosen direction occurs when applying the bi-harmonic laser field which can provide a straightforward experimental test of the predicted phenomena., Comment: 9 pages, 7 figures, version that will appear in Phys. Rev. B

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)$_2$Te$_3$, that were recently discovered to be Chern insulators with quantized Hall conductivity., Comment: 11 pages, 3 figures, updated discussion and references

This thesis consists on two separate parts. In the first part, we discuss about the nature of the Casimir effect as the response of a fluctuant medium to the breakdown of the translation symmetry because the presence of intrusions in that medium. To do so, we present a dynamical approximation of Casimir effect, which generalizes Casimir effect studies to out of equilibrium steady states. The equilibrium known case is recovered as a particular case, including the case of electromagnetic (EM) Casimir effect generated because of quantum fluctuations. This formalism also allows us to define (and calculate) the variance of Casimir forces. In the second part of this thesis, by the use of a Multiscattering formalism, we study the nature of the multibody Casimir effect. We demonstrate that the Casimir force and energy between two spheres in presence of a plate (perfect metal objects all of them) is non-monotonous with the distance between spheres and between sphere and plate. We derive the Pairwise Summation Approximation (PSA) of the EM field from this multiscattering formalism for generalized dielectrics, including magnetic responses and Topological Insulators as an example of magnetoelectric couplings. We also study the nonmonotonous behavior of the entropy with the temperature for a system of two perfect metal spheres and describes the Casimir energy between non-parallel cylinders, a geometry not studied until now to our knownledge., Comment: Ph.D. Thesis, 10 chapters, 231 pages and 33 figures. University Complutense of Madrid, Spain, 28th October 2011

Recently, a method based on stochastic quantization has been proposed to compute the Casimir force and its fluctuations in arbitrary geometries. It relies on the spectral decomposition of the Laplacian operator in the given geometry. Both quantum and thermal fluctuations are considered. Here we use such method to compute the Casimir force on the plates of a finite piston of arbitrary cross section. Asymptotic expressions valid at low and high temperatures and short and long distances are obtained. The case of a piston with triangular cross section is analysed in detail. The regularization of the divergent stress tensor is described., Comment: 10 pages and 4 figures. Accepted for publication in the Proceedings of the tenth conference on Quantum Field Theory under the influence of external conditions - QFEXT'11

We calculate the Casimir energy and entropy for two perfect metal spheres in the large and short separation limit. We obtain nonmonotonic behavior of the Helmholtz free energy with separation and temperature, leading to parameter ranges with negative entropy, and also nonmonotonic behavior of the entropy with temperature and with the separation between the spheres. The appearance of this anomalous behavior of the entropy is discussed as well as its thermodynamic consequences., Comment: 10 pages and 8 figures. Accepted for publication in the Proceedings of the tenth conference on Quantum Field Theory under the influence of external conditions - QFEXT'11

The Casimir interaction between one-dimensional metallic objects (cylinders, wires) displays unconventional features. Here we study the orientation dependence of this interaction by computing the Casimir energy between two inclined cylinders over a wide range of separations. We consider Dirichlet, Neumann and perfect metal boundary conditions, both at zero temperature and in the classical high temperature limit. For all types of boundary conditions, we find that at large distances the interaction decays slowly with distance, similarly to the case of parallel cylinders, and at small distances scales as the interaction of two spheres (but with different numerical coefficients). Our numerical results at intermediate distances agree with our analytic predictions at small and large separations. Experimental implications are discussed., Comment: 9 pages, 5 figures

In this paper we show how the stochastic quantization method developed by Parisi and Wu can be used to obtain Casimir forces. Both quantum and thermal fluctuations are taken into account by a Langevin equation for the field. The method allows the Casimir force to be obtained directly, derived from the stress tensor instead of the free energy. It only requires the spectral decomposition of the Laplacian operator in the given geometry. The formalism provides also an expression for the fluctuations of the force. As an application we compute the Casimir force on the plates of a finite piston of arbitrary cross section. Fluctuations of the force are also directly obtained, and it is shown that, in the piston case, the variance of the force is twice the force squared., Comment: Submitted to EPL

The Pairwise Summation Approximation (PSA) of Casimir energy is applied to a system of two dielectrics with magnetoelectric coupling. In particular, the case of Topological Insulators (TI) is studied in detail. Depending on the the optical response of the TI, we obtain a stable equilibrium distance, atraction for all distances, or repulsion for all distances at zero temperature. This equilibrium distance disappears in the high temperature limit. These results are independent on the geometry of the TI, but are only valid in the diluted approximation., Comment: 6 pages, 4 figures

We calculate the Casimir energy and entropy for two spheres described by the perfect metal model, plasma model, and Drude model in the large separation limit. We obtain nonmonotonic behavior of the Helmholtz free energy with separation and temperature for the perfect metal and plasma models, leading to parameter ranges with negative entropy, and also nonmonotonic behavior of the entropy with temperature and the separation between the spheres. This nonmonotonic behavior has not been found for Drude model. The appearance of this anomalous behavior of the entropy is discussed as well as its thermodynamic consequences., Comment: 9 pages, 7 figures