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In this work, we develop a symmetry-based classification of Chern phases in honeycomb photonic crystals, considering arbitrary nonreciprocal couplings compatible with energy conservation. Our analysis focuses on crystals formed through nonreciprocal perturbations of photonic graphene. These perturbations, which can have arbitrary spatial variations, are generally described by scalar and vector fields. Using a tight-binding model, we consider the most general nonreciprocal interactions, including gyromagnetic, pseudo-Tellegen, and moving medium responses, and examine how the corresponding nonreciprocal fields influence the crystal's topology. Our findings reveal that nonreciprocal interactions alone are insufficient to induce a topologically nontrivial phase. Instead, a nontrivial p6m component in the nonreciprocal fields is required to open a bandgap and achieve a non-zero Chern number. These results provide a symmetry-based roadmap for engineering photonic topological phases via nonreciprocal perturbations of photonic graphene, offering practical guidelines for designing topological phases in graphene-like photonic crystals., Comment: 47 pages, 8 figures

In this work, we develop an analytical framework to understand quantum friction across distinct stability regimes, providing approximate expressions for frictional forces both in the deep stable regime and near the critical threshold of instability. Our primary finding is analytical proof that, near the instability threshold, the quantum friction force diverges logarithmically. This result, verified through numerical simulations, sheds light on the behavior of frictional instabilities as the system approaches criticality. Our findings offer new insights into the role of instabilities, critical divergence and temperature in frictional dynamics across quantum and classical regimes.

Recent studies have shown that non-equilibrium optical systems under static electric fields offer a pathway to realize chiral gain, where the non-Hermitian response of a material is controlled by the spin angular momentum of the wave. In this work, we uncover the topological nature of chiral gain and demonstrate how a static electric bias induces topological bandgaps that support unidirectional edge states at the material boundaries. Curiously, in our system, these topological edge states consistently exhibit dissipative properties. We further show that, by operating outside the topological gap, the chiral gain can be leveraged to engineer boundary-confined lasing modes with orbital angular momentum, locked to the orientation of the applied electric field. Our results open new possibilities for loss-compensated photonic waveguides, enabling advanced functionalities such as unidirectional, lossless edge-wave propagation and the generation of structured light with intrinsic orbital angular momentum.

Conventional Chern insulators are two-dimensional periodic structures that support unidirectional edge states at the boundary, while the wave propagation in the bulk regions is forbidden. The number of unidirectional edge states is governed by the gap Chern number, a topological invariant that depends on the global properties of the system over the entire wavevector space. This concept can also be extended to systems with a continuous translational symmetry provided they satisfy a regularization condition for large wavenumbers. Here, we discuss how the spatial dispersion, notably the high-spatial frequency behavior of the material response, critically influences the topological properties, and consequently, the net number of unidirectional edge states. In particular, we show that seemingly small perturbations of a local magnetized plasma can lead to distinct Chern phases and, consequently, markedly different edge state dispersions., Comment: 37 pages, 5 figures

Conventional optical materials are characterized by either a dissipative response, which results in polarization-independent absorption, or by a gain response that leads to wave amplification. In this study, we explore the potential of a peculiar class of materials with chiral-gain properties, where gain selectively amplifies waves of one polarization handedness, while dissipation suppresses the opposite handedness. We uncover a novel phenomenon, gain-momentum locking, at the boundary of these chiral-gain materials, where surface plasmons are uniquely amplified or attenuated based on their direction of propagation. This effect, driven by the interplay between spin-momentum locking and polarization-sensitive non-Hermitian responses, enables precise control over unidirectional wave propagation. Our findings open the door to photonic devices with unprecedented capabilities, such as lossless unidirectional edge-wave propagation and the generation of light with intrinsic orbital angular momentum., Comment: 25 pages, 5 figures

We study plasmonic time crystals, which constitute an extension of the dielectric-based photonic time crystals to plasmonic media. A salient feature of plasmonic time crystals is their ability to support amplification of both longitudinal and transverse modes. In particular, we show that such systems support collective resonances of longitudinal modes, independently of the wave vector $k$. These resonances originate from the interaction between the positive and negative frequency branches of the plasmonic dispersion relation of the unmodulated system, and from the divergence of the density of states near the plasma frequency $\omega_p$. The strongest resonance occurs at a modulation frequency of $\Omega = 2 \omega_p$, associated with a direct inter-band transition. Higher-order resonances are associated with related mechanisms but at lower modulation frequencies. We demonstrate these resonances for various periodic modulation profiles, and also provide a generic perturbative formula for resonance widths in the limit of weak modulation amplitude, in the absence of losses. Our findings offer insights into using time-modulated plasmonic media to enhance optical gain., Comment: main text (7pp, 2 figures) + supplementary material (7pp + 4 figures)

Here, we investigate the effective response of three-dimensional spacetime crystals formed by spherical scatterers under a travelling-wave modulation. We develop an analytical formalism to homogenize the spacetime crystals that extends the renowned Clausius-Mossotti formula to time-varying platforms. Our formalism shows that travelling-wave spacetime crystals can be used to engineer a wide range of classes of nonreciprocal bianisotropic couplings in the long wavelength limit. In particular, our theory reveals the possibility of realizing a purely isotropic Tellegen response in crystals formed by interlaced sub-lattices of scatterers subjected to different modulation velocities. Furthermore, we introduce a class of generalized Minkowskian crystals that displays invariance under arbitrary Lorentz boosts aligned with a fixed spatial direction. We prove that such systems are formed by pseudo-uniaxial materials with the principal axis aligned parallel to the modulation velocity. The electromagnetic response of such generalized Minkowskian crystals is indistinguishable from that of moving photonic crystals.

Here, we present an exploratory study of the potential applications of electrically biased materials that possess a nonreciprocal and non-Hermitian electromagnetic response analogous to the electronic response of field-effect transistors. The most distinctive feature of such materials is their chiral-gain, meaning that their response can be active or dissipative depending on the handedness of the wave polarization. Here, we show how the chiral-gain can be harnessed to develop novel electromagnetic devices with unique properties such as chiral lasers, polarization-dependent mirrors, and coherent-perfect-absorber lasers. Furthermore, it is demonstrated that materials with chiral-gain can bypass a reciprocity constraint that typically limits the external coupling strength, thus facilitating the excitation of cavities with extremely large quality factors., Comment: 39 pages, 10 figures

We investigate the frictional force arising from quantum fluctuations when two dissipative metallic plates are set in a shear motion. While early studies showed that the electromagnetic fields in the quantum friction setup reach nonequilibrium steady states, yielding a time-independent force, other works have demonstrated the failure to attain steady states, leading to instability and time-varying friction under sufficiently low-loss conditions. Here, we develop a fully quantum-mechanical theory without perturbative approximations and unveil the transition from stable to unstable regimes of the quantum friction setup. Due to the relative motion of the plates, their electromagnetic response may be active in some conditions, resulting in optical gain. We prove that the standard fluctuation-dissipation leads to inconsistent results when applied to our system, and, in particular, it predicts a vanishing frictional force. Using a modified fluctuation-dissipation relation tailored for gain media, we calculate the frictional force in terms of the system Green's function, thereby recovering early works on quantum friction. Remarkably, we also find that the frictional force diverges to infinity as the relative velocity of the plates approaches a threshold. This threshold is determined by the damping strength and the distance between the metal surfaces. Beyond this critical velocity, the system exhibits instability, akin to the behaviour of a laser cavity, where no steady state exists. In such a scenario, the frictional force escalates exponentially. Our findings pave the way for experimental exploration of the frictional force in proximity to this critical regime., Comment: Accepted for publication in Physical Review Research

Photonic systems with time-varying modulations have attracted considerable attention as they allow for the design of non-reciprocal devices without the need for an external magnetic bias. Unlike time-invariant systems, such modulations couple modes with different frequencies. Here, we discuss how this coupling and particle-hole symmetry may lead to the resonant interaction of positive and negative frequency oscillators. To illustrate this idea, we analyze a dispersive spacetime crystal described by a Drude-Lorentz model with a travelingwave modulation. Our findings demonstrate that the interaction between positive and negative frequency bands can induce parametric instabilities under certain conditions, stemming from the interplay between dispersion and spacetime modulations. In particular, we find that material dispersion creates the conditions for the formation of instabilities for arbitrarily small modulations speeds in the absence of dissipative channels., Comment: 15 pages, 4 figures

Here, we present an in-depth theoretical analysis of the linear electrooptic effect in low-symmetry three-dimensional (3D) conductive materials with large Berry curvature dipoles. Our study identifies two distinct kinetic contributions to the linear electrooptic effect: a gyrotropic Hermitian (conservative) piece and a non-Hermitian term that can originate optical gain. We concentrate on the study of 3D materials belonging to the 32 ($D_3$) point group subject to a static electric bias along the trigonal axis. Our investigation shows that doped trigonal tellurium has promising properties, with its gyrotropic electrooptic response offering the potential for realizing electrically-biased electromagnetic isolators and inducing significant optical dichroism. Most notably, it is demonstrated that under sufficiently large static electric bias, tellurium's non-Hermitian electrooptic response may lead to optical gain. Using first-principles calculations, it is shown that n-doped tellurium is particularly promising, as it can host significantly larger Berry curvature dipoles than the more common p-doped tellurium., Comment: 38 pages, 9 figures

Materials with Berry curvature dipoles (BDs) support a non-Hermitian electro-optic (EO) effect that is investigated here for lasing at terahertz (THz) frequencies. Such a system is here conceived as a stack of low-symmetry 2D materials. We show that a cavity made of such a material supports a nonreciprocal growing mode with elliptical polarization that generates an unstable resonance leading to self-sustained oscillations. Notably, we demonstrate that the chiral nature of the gain derived from the Berry dipole allows for the manipulation of the laser light's handedness by a simple reversal of the electric field bias.

Time-variant systems have recently garnered considerable attention due to their unique potentials in manipulating electromagnetic waves. Here, we introduce a novel class of topological systems that rely on spacetime crystals with a traveling-wave modulation that emulates certain aspects of physical motion. Challenging intuition, our findings reveal that, even though such systems rely on a linear momentum bias, it is feasible to engineer an internal angular momentum and non-trivial topological phases by leveraging the symmetry of its structural elements. Furthermore, we establish that the proposed platforms exhibit a gauge degree of freedom associated with the arbitrariness in the choice of the coordinate transformation that eliminates the time dependence of the Hamiltonian that describes the system. The topology is intricately governed by a synthetic magnetic potential whose field lines can be controlled by manipulating material anisotropy. Remarkably, we demonstrate that the proposed spacetime crystals host an unconventional class of scattering-immune edge states. The oscillation frequency of the edge states adapts continuously along the propagation path, shaped by the geometric attributes of the path itself., Comment: 37 pages, 9 figures

We present a theoretical study of the interaction between an atom characterized by a degenerate ground state and a reciprocal environment, such as a semiconductor nanoparticle, without the presence of external bias. Our analysis reveals that the combined influence of the electron's intrinsic spin magnetic moment on the environment and the chiral atomic dipolar transitions may lead to either the spontaneous breaking of time-reversal symmetry or the emergence of time-crystal-like states with remarkably long relaxation times. The different behavior is ruled by the handedness of the precession motion of the atom's spin vector, which is induced by virtual chiral-dipolar transitions. Specifically, when the relative orientation of the precession angular velocity and the electron spin vector is as in a spinning top, the system manifests time-crystal-like states. Conversely, with the opposite relative orientation, the system experiences spontaneous symmetry breaking of time-reversal symmetry. Our findings introduce a novel mechanism for the spontaneous breaking of time-reversal symmetry in atomic systems, and unveil an exciting opportunity to engineer a nonreciprocal response at the nanoscale, exclusively driven by the quantum vacuum fluctuations., Comment: 62 pages

We introduce a homogenization approach to characterize the dynamical response of a generic dispersive spacetime crystal in the long-wavelength limit. The theory is applied to dispersive spacetime platforms with a travelling-wave modulation. It is shown that for long wavelengths the effective response may be described by a frequency dependent permittivity. Due to the active nature of spacetime systems, the permittivity is not bound by the same constraints as in standard time-invariant metamaterials. In particular, we find that dispersive spacetime crystals can exhibit rather peculiar physics, such as an anomalous (non-Foster) permittivity dispersion with a negative stored energy density, alternate between gain and loss regimes, and present multiple resonances in the quasistatic regime. Furthermore, it is verified with numerical simulations that the effective theory captures faithfully the exact dispersion of the first few photonic bands., Comment: "in press" at Physical Review B, 43 pages, 8 figures

We theoretically investigate the role of chiral-transitions in the quantum friction force that acts on a two-level atom that moves with relative velocity v parallel to a planar metallic surface. We find that the friction force has a component that is sensitive to the handedness of the atomic transition dipole moment. In the particular, we show that the friction force due to a particular atomic transition can be enhanced by a dipole moment with a certain handedness, and almost suppressed by the dipole moment with the opposite handedness. Curiously, the handedness of the transition dipole moment that boosts the ground-state friction force is the opposite of what is classically expected from the spin-momentum locking. We explain this discrepancy in terms of the interaction between positive and negative frequency oscillators.

In this work, we develop a homogenization model to determine the effective response of a metallic nanowire array embedded in an electric gyrotropic material. We study the interaction of electromagnetic waves with the metamaterial and demonstrate that the nanowire array can greatly enhance the nonreciprocal response of the gyrotropic substrate. In particular, the metamaterial can either absorb the incoming energy almost entirely or reflect it with little loss, depending on the sign of the incidence angle. We explore the implications of our findings in the context of Kirchhoff's law of thermal radiation. Our results demonstrate that the wire array can boost the difference between the emissivity and absorptivity in a broad spectrum of frequencies and incidence angles as compared to an unstructured gyrotropic substrate. These findings suggest potential applications for the nonreciprocal wire medium in thermal management, radiative cooling, and others., Comment: 34 pages, 11 figures

Over the past decade, there has been a great interest in topological effects, with concepts originally developed in the context of electron transport in condensed matter platforms now being extended to optical systems. While topological properties in electronic systems are often linked to the quantization of electric conductivity observed in the integer quantum Hall effect, a direct analogue in optics remains elusive. In this study, we bridge this gap by demonstrating that the response of the Poynting vector (which may be regarded as a "photon current") to the mechanical acceleration of a medium provides a precise photonic analogue of the electric conductivity. In particular, it is shown that the photonic conductivity determines the energy irreversibly transferred from a periodic mechanical driving of the medium to the electromagnetic field. Furthermore, it is demonstrated that for nonreciprocal systems enclosed in a cavity, the constant acceleration of the system induces a flow of photons along a direction perpendicular to the acceleration, analogous to the Hall effect but for light. The spectral density of the photonic conductivity is quantized in the band gaps of the bulk region with the conductivity quantum determined by the gap Chern number., Comment: 46 pages

This paper presents an analytical framework for the study of scattering and diffraction phenomena in spacetime-modulated metallic gratings. Using a Lorentz transformation, it is shown that a particular class of spacetime-modulated gratings behave effectively as moving media. We take advantage of this property to derive a closed analytical solution for the wave scattering problem. In particular, using our formalism it is possible to avoid spacetime Floquet-Bloch expansions, as the solution of the problem in the original laboratory frame (grating parameters are periodic in space and time) is directly linked to a co-moving frame where the metallic grating is time-invariant (grating parameters are periodic only in space). In this way, we identify a fundamental connection between moving metallic gratings and spacetime-modulated metamaterials, and exploit this link to study the nonreciprocal response of the structure. Some limitations and difficulties of the alternative nonrelativistic Galilean approach are discussed and the benefits of the Lorentz approach are highlighted. Finally, some analytical results are presented in order to validate the formalism. The results include scenarios involving TM(p) and TE(s) normal and oblique incidence, even beyond the onset of the diffraction regime. Furthermore, we show how the synthetic Fresnel drag can tailor the Goos-H\"anchen effect and create a specular point shifted towards the direction of the synthetic motion, independent of the sign of the incidence angle., Comment: Published in Physical Review Applied, 20, 014063, 2023

Here, we show that isorefractive spacetime crystals with a travelling-wave modulation may mimic rigorously the response of moving material systems. While generic spacetime crystals are characterized by a bi-anisotropic coupling in the co-moving frame, isorefractive crystals have a response that is observer independent, which leads to isotropic constitutive relations free of bianisotropy. We show how to take advantage of this property in the calculation of the band diagrams of isorefractive spacetime crystals in the laboratory frame and in the study of the synthetic Fresnel drag. Furthermore, we discuss the impact of considering either a Galilean or a Lorentz transformation in the homogenization of spacetime crystals, showing that the effective response is independent of the considered transformation.

Photonic platforms invariant under parity ($\mathcal{P}$), time-reversal ($\mathcal{T}$), and duality ($\mathcal{D}$) can support topological phases analogous to those found in time-reversal invariant ${\mathbb{Z}_2}$ electronic systems with conserved spin. Here, we demonstrate the resilience of the underlying spin Chern phases against non-Hermitian effects, notably material dissipation. We identify that non-Hermitian, $\mathcal{P}\mathcal{D}$-symmetric, and reciprocal photonic insulators fall into two topologically distinct classes. Our analysis focuses on the topology of a $\mathcal{P}\mathcal{D}$-symmetric and reciprocal parallel-plate waveguide (PPW). We discover a critical loss level in the plates that marks a topological phase transition. The Hamiltonian of the $\mathcal{P}\mathcal{T}\mathcal{D}$-symmetric system is found to consist of an infinite direct sum of Kane-Mele type Hamiltonians with a common band gap. This structure leads to the topological charge of the waveguide being an ill-defined sum of integers due to the particle-hole symmetry. Each component of this series corresponds to a spin-polarized edge state. Our findings present a unique instance of a topological photonic system that can host an infinite number of edge states in its band gap.

Here, we investigate the nonreciprocal propagation and amplification of surface plasmons in drift-current biased graphene, using both Galilean and relativistic-type Doppler shift transformations of the graphene's conductivity. Consistent with previous studies, both conductivity models predict strongly nonreciprocal propagation of surface plasmons due to the drag effect caused by the drifting electrons. In particular, the Galilean Doppler shift model leads to stronger spectral asymmetries in the plasmon dispersion with regimes of unidirectional propagation. Remarkably, it is shown that both conductivity models predict regimes of nonreciprocal plasmon amplification in a wide angular sector of in-plane directions when the drift-current biased graphene sheet is coupled to a plasmonic substrate (namely, SiC), with the plasmon amplification rate being substantially higher for the relativistic Doppler shift model., Comment: 29 pages, 10 figures

Here, we show that spacetime modulations provide an exciting route to realize complex nonreciprocal couplings, and in particular the elusive axion response. We develop an analytical formalism to homogenize anisotropic spacetime crystals in the long wavelength limit. It is found that spacetime crystals with suitable glide-rotation symmetry can have a giant axion-type response, several orders of magnitude larger than in natural materials. The nonreciprocal axion response may have interesting applications in optics, for example in electromagnetic isolation, and in addition may enable exciting new forms of light-wave interactions.

Topological photonics has recently emerged as a very general framework for the design of unidirectional edge waveguides immune to back-scattering and deformations, as well as other platforms that feature extreme nonreciprocal wave phenomena. While the topological classification of time invariant crystals has been widely discussed in the literature, the study of spacetime crystals formed by time-variant materials remains largely unexplored. Here, we extend the methods of topological band theory to photonic crystals formed by inclusions that are subject to a spacetime rotating-wave modulation that imitates a physical rotating motion. By resorting to an approximate nonhomogeneous effective description of the electromagnetic response of the inclusions, it is shown that they possess a bianisotropic response that breaks the time-reversal symmetry and may give rise to non-trivial topologies. In particular, we propose an implementation of the Haldane model in a spacetime modulated photonic crystal., Comment: 29 pages, 6 figures

Topological photonics provides a powerful framework to describe and understand many nontrivial wave phenomena in complex electromagnetic platforms. The topological index of a physical system is an abstract global property that depends on the family of operators that describes the propagation of Bloch waves. Here, we highlight that there is a profound geometrical connection between topological physics and the topological theory of mathematical surfaces. We show that topological band theory can be understood as a generalization of the topological theory of surfaces and that the genus of a surface can be regarded as a Chern number of a suitable operator defined over the surface. We point out some nontrivial implications of topology in the context of radiation problems and discuss why for physical problems the topological index is often associated with a bulk-edge correspondence., Comment: 24 pages

Dispersion forces between neutral material bodies are due to fluctuations of the polarization of the bodies. For bodies in equilibrium these forces are often referred to as Casimir-Lifshitz forces. For bodies in relative motion, in addition to the Casimir-Lifshitz force, a lateral frictional force ("quantum friction", in the zero temperature limit) comes into play. The widely accepted theory of the fluctuation induced forces is based on the "fluctuational electrodynamics" , when the Maxwell equations are supplemented by random current sources responsible for the fluctuations of the medium polarization. The first part of our paper touches on some conceptual issues of the theory, such as the dissipation-less limit and the link between Rytov's approach and quantum electrodynamics. We point out the problems with the dissipation-less plasma model (with its unphysical double pole at zero frequency) which still appears in the literature. The second part of the paper is devoted to "quantum friction", in a broad sense, and it contains some novel material. In particular, it is pointed out that in weakly dissipative systems the friction force may not be a stationary process. It is shown, using an "exact" (nonpertubative) quantum treatment that under appropriate conditions, an instability can occur when the kinetic energy (due to the relative motion between the bodies) is transformed into coherent radiation, exponentially growing in intensity (the instability gets eventually limited by non-linear effects). We also discuss a setup when the two bodies are at rest but a constant electric current is flowing in one of the bodies. One may say that only the electron component of one body is dragged with respect to the other body, unlike the usual setup when the two bodies are in relative motion. Clearly there are differences in the frictional forces between the two setups., Comment: 19 pages, latex

Semiconductor transistors are essential elements of electronic circuits as they enable, for example, the isolation or amplification of voltage signals. While conventional transistors are point-type (lumped-element) devices, it may be highly interesting to realize a distributed transistor-type optical response in a bulk material. Here, we show that low-symmetry two-dimensional metallic systems may be the ideal solution to implement such a distributed-transistor response. To this end, using the semiclassical Boltzmann equation approach, we characterize the optical conductivity of a two-dimensional material under a static electric bias. It is found that similar to the nonlinear Hall effect, the electron transport depends on the Berry curvature dipole. Our analysis reveals that the electro-optic effect modifies the optical conductivity of the material, breaking the electromagnetic reciprocity and yielding a dynamical response that imitates that of a transistor but in a distributed volume. Furthermore, the effective conductivity tensor can be non-Hermitian, opening the possibility of optical gain. To maximize the non-Hermitian response, we explore the specific case of strained twisted bilayer graphene. Our analysis reveals that the optical gain for incident light transmitted through the biased system depends on the light polarization, and can be quite large, especially for multilayer configurations.

Here, inspired by the operation of conventional semiconductor transistors, we introduce a novel class of bulk materials with nonreciprocal and non-Hermitian electromagnetic response. Our analysis shows that material nonlinearities combined with a static electric bias may lead to a linearized permittivity tensor that lacks the Hermitian and transpose symmetries. Remarkably, the material can either dissipate or generate energy, depending on the relative phase of the electric field components. We introduce a simple design for an electromagnetic isolator based on an idealized "MOSFET-metamaterial" and show that its performance can in principle surpass conventional Faraday isolators due to the material gain. Furthermore, it is suggested that analogous material responses may be engineered in natural media in nonequilibrium situations. Our solution determines an entirely novel paradigm to break the electromagnetic reciprocity in a bulk nonlinear material using a static electric bias.