Nonlinear Electromagnetic Response Research Articles

Realization of an atomic quantum Hall system in four dimensions.

Modern condensed matter physics relies on the concept of topology to classify matter, from quantum Hall systems to topological insulators. Engineered systems, benefiting from synthetic dimensions, can potentially give access to topological states predicted in dimensions D > 3. We report the realization of an atomic quantum Hall system evolving in four dimensions (4D), with two spatial dimensions and two synthetic ones encoded in the large spin of dysprosium atoms. We measure the nontrivial topological index of the ground band through a full characterization of the nonlinear electromagnetic response and observe the associated anisotropic hyperedge modes. We also excite nonplanar cyclotron motion, in contrast to the planar orbits in D ≤ 3. Our work may enable the investigation of strongly correlated topological liquids in 4D, generalizing fractional quantum Hall states.

Charge Conservation beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids

Nonlinear electromagnetic response functions have reemerged as a crucial tool for studying quantum materials, due to recently appreciated connections between optical response functions, quantum geometry, and band topology. Most attention has been paid to responses to spatially uniform electric fields, relevant to low-energy optical experiments in conventional solid state materials. However, magnetic and magnetoelectric phenomena are naturally connected by responses to spatially varying electric fields due to Maxwell’s equations. Furthermore, in the emerging field of moiré materials, characteristic lattice scales are much longer, allowing spatial variation of optical electric fields to potentially have a measurable effect in experiments. In order to address these issues, we develop a formalism for computing linear and nonlinear responses to spatially inhomogeneous electromagnetic fields. Starting with the continuity equation, we derive an expression for the second-quantized current operator that is manifestly conserved and model independent. Crucially, our formalism makes no assumptions on the form of the microscopic Hamiltonian and so is applicable to model Hamiltonians derived from tight-binding or calculations. We then develop a diagrammatic Kubo formalism for computing the wave vector dependence of linear and nonlinear conductivities, using Ward identities to fix the value of the diamagnetic current order by order in the vector potential. We apply our formula to compute the magnitude of the Kerr effect at oblique incidence for a model of a moiré-Chern insulator and demonstrate the experimental relevance of spatially inhomogeneous fields in these systems. We further show how our formalism allows us to compute the (orbital) magnetic multipole moments and magnetic susceptibilities in insulators. Turning to nonlinear response, we use our formalism to compute the second-order transverse response to spatially varying transverse electric fields in our moiré-Chern insulator model, with an eye toward the next generation of experiments in these systems. Published by the American Physical Society 2024

Grounded source transient electromagnetic 3D forward modeling with the spectral-element method and its application in hydraulic fracturing monitoring

A long wire with large current source transient electromagnetic (TEM) monitoring, with a large detection depth, low cost, safety, and environmental protection, has unique advantages in the testing and identification of unconventional reservoir fluid and the evaluation of stimulated reservoir volume. So, the TEM 3D forward modeling method has become a research hotspot. Although the finite-element method (FEM) is a type of numerical algorithm that has been widely applied in three-dimensional (3D) electromagnetic field forward modeling, the efficiency and accuracy of FEM require further improvement in order to meet the demand of fast 3D inversion. By increasing the order of the basis function and adjusting the principle of mesh discretization, the precision of the mixed-order spectral-element (SEM) result will be increased. The backward Euler scheme is an unconditionally stable technique which can ignore the impact of the scale of the time step. To achieve a better description of the nonlinear electromagnetic (EM) response of the grounded source TEM method and to optimize the efficiency and accuracy/precision of the 3D TEM forward modeling method significantly, we proposed the use of 3D TEM forward modeling based on the mixed-order SEM and the backward Euler scheme, which can obtain more accurate EM results with fewer degrees of freedom. To check its accuracy and efficiency, the 1D and 3D layered models are applied to compare the SEM results with the semi-analytical and FEM solutions. In addition, we analyzed the accuracy and efficiency of the SEM method for different types of order basis functions. Finally, we calculated the long-wire source TEM response for a practical 3D earth model of a shale gas reservoir for fracturing monitoring and tested the feasibility of the TEM method in a hydraulic fracturing monitoring area to further demonstrate the flexibility of the SEM method.

Strong Kinetic-Inductance Kerr Nonlinearity with Titanium Nitride Nanowires

The kinetic inductance of charge carriers in disordered superconductors provides a broadband low-loss source of nonlinear electromagnetic response. This work investigates TiN nanowires as an alternative to Josephson junctions for applications involving elevated temperatures, higher frequencies, and strong magnetic fields. An extreme nanowire geometry for TiN microwave resonators leads to current-density concentration and enhanced self-Kerr coefficient, yielding a nonlinearity-to-loss ratio as high as 21% and quality factor exceeding 10,000. Such devices may find application in quantum frequency conversion of microwave photons, and with improvement might attain strong quantum nonlinearity.

Topological gap labeling with third Chern numbers in three-dimensional quasicrystals

We study the topological gap labeling of general 3D quasicrystals and we find that every gap in the spectrum is characterized by a set of the third Chern numbers. We show that a quasi-periodic structure has multiple Brillouin zones defined by redundant wavevectors, and the number of states below a gap is quantized as an integer linear combination of volumes of these Brillouin zones. The associated quantum numbers to characterize energy gaps can be expressed as third Chern numbers by considering a formal relationship between an adiabatic charge pumping under cyclic deformation of the quasi-periodic potential and a topological nonlinear electromagnetic response in 6D insulators.

Multi-Fidelity Model-Based Size Optimization of Electric Machines

The multi-modal problem and high computational cost represent challenges in the optimization of electric machines owing to their highly nonlinear electromagnetic response. To overcome these challenges, this paper proposes a multi-fidelity model-based sequential optimization method in which both low- and high-fidelity models are employed in two phases. In phase 1, the reluctance network (RN) is adopted as the low-fidelity model and mainly contributes to alleviating the abovementioned challenges. To overcome the low accuracy of the RN, the optimal design is obtained using a finite element model (FEM) in phase 2. The multi-start strategy and gradient-based algorithm are utilized instead of a heuristic algorithm in all phases to avoid excessive calculations. This multi-fidelity model concept presents a novelty compared to previous research that focused only on algorithm development. The effectiveness of the proposed method is validated with two examples, consisting of the TEAM workshop problem 25 and the torque ripple minimization of an interior permanent magnet synchronous motor. The optimal designs and computational time resulting from the proposed method are compared with those of the conventional method, where only a FEM is used during optimization. The results show that the proposed method is remarkable in finding superior optimal designs, while ignoring unimportant local optima. Additionally, it can save up to 90% of the computational time required by the conventional method.

Topology and geometry under the nonlinear electromagnetic spotlight.

For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their wavefunctions. A key challenge is to identify and implement experiments that probe or control these quantum properties. In this Review, we describe recent progress in this direction, focusing on nonlinear electromagnetic responses that arise directly from quantum geometry and topology. We give an overview of the field by discussing theoretical ideas, experiments and the materials that drive them. We conclude by discussing how these techniques can be combined with device architectures to uncover, probe and ultimately control quantum phases with emergent topological and correlated properties.

Dynamic pair-breaking current, critical superfluid velocity, and nonlinear electromagnetic response of nonequilibrium superconductors

We report numerical calculations of a dynamic pairbreaking current density $J_d$ and a critical superfluid velocity $v_d$ in a nonequilibrium superconductor carrying a uniform, large-amplitude ac current density $J(t)=J_a\sin\Omega t$ with $\Omega$ well below the gap frequency $\Omega\ll \Delta_0/\hbar$. The dependencies $J_d(\Omega,T)$ and $v_d(\Omega,T)$ near the critical temperature $T_c$ were calculated from either the full time-dependent nonequilibrium equations for a dirty s-wave superconductor and the time-dependent Ginzburg-Landau (TDGL) equations for a gapped superconductor, taking into account the GL relaxation time of the order parameter $\tau_{GL}$ and the inelastic electron-phonon relaxation time of quasiparticles $\tau_E$. We show that both approaches give similar frequency dependencies of $J_d(\Omega)$ and $v_d(\Omega)$ which gradually increase from their static pairbreaking GL values $J_c$ and $v_c$ at $\Omega\tau_E\ll 1$ to $\sqrt{2}J_c$ and $\sqrt{2}v_c$ at $\Omega\tau_E\gg 1$. Here $J_d$, $v_d$ and a dynamic superheating field at which the Meissner state becomes unstable were calculated in two different regimes of a fixed ac current and a fixed ac superfluid velocity induced by the applied ac magnetic field $H=H_a\sin\Omega t$ in a thin superconducting filament or a type-II superconductor with a large GL parameter. We also calculated a nonlinear electromagnetic response of a nonequilibrium superconducting state, particularly a dynamic kinetic inductance and a dissipative quasiparticle conductivity, taking into account the oscillatory dynamics of superconducting condensate and the kinetics of quasiparticles driven by a strong ac current. It is shown that an ac current density produces multiple harmonics of the electric field, the amplitudes of the higher-order harmonics diminishing as $\tau_E$ increases.

Electron Tunneling and X-Ray Photoelectron Spectroscopy Studies of the Superconducting Properties of Nitrogen-Doped Niobium Resonator Cavities

We use scanning tunneling microscopy (STM) and spectroscopy (STS), and x-ray photoelectron spectroscopy (XPS) to investigate the effect of nitrogen doping on the surface electronic and chemical structures of cutouts from superconducting $\mathrm{Nb}$ radio-frequency cavities. The goal of this work is to get insights into the fundamental physics and materials mechanisms behind the striking decrease of the surface resistance with the radio-frequency magnetic field, which has been observed on $N$-doped $\mathrm{Nb}$ cavities. Our XPS measurements reveal significantly more oxidized $\mathrm{Nb}$ $3d$ states and a thinner metallic suboxide layer on the $N$-doped $\mathrm{Nb}$ surfaces, which is also confirmed by tunneling spectroscopy measurements. In turn, tunneling measurements performed on native surfaces as well as on $\mathrm{Ar}$-ion sputtered surfaces allow us to separate the effect of $N$ doping on the surface-oxide layer from that on the density of states in the bulk. Analysis of our tunneling spectra in the framework of a model of a proximity-coupled normal layer at the surface [A. Gurevich and T. Kubo, Phys. Rev. B 96, 184515 (2017)] is consistent with the hypothesis that $N$-doping ameliorates lateral inhomogeneities of superconducting properties on the surface and shrinks the metallic suboxide layer. For the $\mathrm{Ar}$ sputtered surfaces, we also find evidence that $N$ doping changes the contact resistance between the metallic suboxide and the bulk niobium toward an optimum value corresponding to a minimum surface resistance. The totality of our experimental data suggests that the $N$ doping provides an effective tuning of the density of states in such a way that it can result in a decrease of the surface resistance with the radio-frequency field, as predicted by calculations of the nonlinear low-frequency electromagnetic response of dirty superconductors. Furthermore, STM imaging of vortex cores shows a slightly reduced average superconducting gap and a shorter coherence length in the $N$-doped $\mathrm{Nb}$ samples as compared to typically prepared $\mathrm{Nb}$ samples, indicating a stronger impurity scattering caused by nitrogen doping in a moderately disordered material.

Sensitivity analysis of high‐frequency nonlinearity and DC ohmic characteristics of graphene in ammonia environment

Graphene has a large specific surface area and a high electron traction rate, so it can be widely used in gas-sensing devices. To analyze the gas-sensing properties of graphene, the non-linear electromagnetic field response (NLEFR) of graphene before and after ammonia adsorption is studied in this paper. Under DC bias, the change rate of output harmonic power of the multilayer graphene-sensing characteristic analysis device is 30% higher than that of DC resistance. The results of this work indicate that a new graphene-based sensor can be developed using its NLEFR.

R3c-type LnNiO3 (Ln = La, Ce, Nd, Pm, Gd, Tb, Dy, Ho, Er, Lu) half-metals with multiple Dirac cones: a potential class of advanced spintronic materials.

In the past three years, Dirac half-metals (DHMs) have attracted considerable attention and become a high-profile topic in spintronics becuase of their excellent physical properties such as 100% spin polarization and massless Dirac fermions. Two-dimensional DHMs proposed recently have not yet been experimentally synthesized and thus remain theoretical. As a result, their characteristics cannot be experimentally confirmed. In addition, many theoretically predicted Dirac materials have only a single cone, resulting in a nonlinear electromagnetic response with insufficient intensity and inadequate transport carrier efficiency near the Fermi level. Therefore, after several attempts, we have focused on a novel class of DHMs with multiple Dirac crossings to address the above limitations. In particular, we direct our attention to three-dimensional bulk materials. In this study, the discovery via first principles of an experimentally synthesized DHM LaNiO3 with many Dirac cones and complete spin polarization near the Fermi level is reported. It is also shown that the crystal structures of these materials are strongly correlated with their physical properties. The results indicate that many rhombohedral materials with the general formula LnNiO3 (Ln = La, Ce, Nd, Pm, Gd, Tb, Dy, Ho, Er, Lu) in the space group R 3 c are potential DHMs with multiple Dirac cones.

Nonlinear electromagnetic response and Higgs-mode excitation in BCS superconductors with impurities

We reveal that due to the presence of disorder oscillations of the order parameter amplitude called the Higgs mode can be effectively excited by the external electromagnetic radiation in usual BCS superconductors. This mechanism works for superconductors with both isotropic s-wave and anisotropic, such as d-wave, pairings. The non-linear response in the presence of impurities is captured by the quasiclassical formalism. We demonstrate that analytical solutions of the Eilenberger equation with impurity collision integral and external field drive coincide with the exact summation of ladder impurity diagrams. Using the developed formalism we show that resonant third-harmonic signal observed in recent experiments is naturally explained by the excitation of Higgs mode mediated by impurity scattering.

Nonlinear electromagnetic response of few-layer graphene: A nonperturbative description

Nonperturbative approach based on exact solution of Boltzmann kinetic equation in the relaxation time approximation is developed for the study of nonlinear response of electron-doped few-layer graphene to a high-frequency electromagnetic field. It is shown that nonperturbative approach can be applied to a two-dimensional conductor with an arbitrary isotropic spectrum of carries. The cases of ABC stacked three-layer and ABC staked four-layer graphene are considered. The low-energy electron spectrum of such graphenes is characterized by the third and the fourth power in the momentum dependence, correspondingly. The transmission, reflection and absorption coefficients are calculated. It is shown that the transmission coefficient T of three- and four-layer graphene decreases under increase in the intensity of the incident wave I by the asymptotic law 1/2 T I  and 2/3 T I  , respectively. It is found that three-layer and four-layer graphenes demonstrate power-induced reflectance, in contrast to power-induced transparency in monolayer graphene. It is found that in the four-layer graphene irradiated by a monochromatic wave the induced electrical current contains only the first and the third harmonics. The analytical expression for the efficiency of the third-harmonic generation GTGH (the ratio of the intensity of third-harmonic radiation to the intensity of the incident wave) of the four-layer graphene is obtained. It is shown that only at rather small incident wave intensity the efficiency GTGH is proportional to the second power of I and at large incident wave intensity the efficiency GTGH approaches the constant quantity. Saturation of the efficiency of the third-order harmonic generation is caused by the increase of the reflection. In contrast, the efficiency of the third-order harmonic generation of monolayer graphene depends nonmonotonically on the intensity of the incident wave. The maximum is reached at rather small intensity I аnd the efficiency in the maximum is of order of 10-4 that is two orders of magnitude smaller than of four-layer graphene.

Parity anomaly in the nonlinear response of nodal-line semimetals

Nodal-line semimetals are topological semimetals characterized by one-dimensional band-touching loops protected by the combined symmetry of inversion $\mathcal{P}$ and time-reversal $\mathcal{T}$ in absence of spin-orbit coupling. These nodal loops can be understood as a one-parameter family of Dirac points exhibiting the parity anomaly associated to $\mathcal{P}\mathcal{T}$ symmetry. We find that the parity anomaly also appears in the nonlinear optical response of these systems in an analogous way to the linear response transport. We analyze the presence of a tilting term in the Hamiltonian as an element that does not spoil $\mathcal{P}\mathcal{T}$ symmetry: while it is $\mathcal{P}\mathcal{T}$ symmetric, it breaks separately both $\mathcal{P}$ and $\mathcal{T}$ symmetries, allowing for the potential experimental observability of the linear and nonlinear Hall conductivities in appropriate nodal-line semimetals. We also propose effective actions for both the linear and nonlinear electromagnetic responses of tilted nodal-line semimetals. We find that the linear Hall-like response of tilted nodal-line semimetals is an axion response due to the parity anomaly, extending the class of systems that display such electromagnetic response.

Reevaluation of radiation reaction and consequences for light-matter interactions at the nanoscale.

In the context of electromagnetism and nonlinear optical interactions, damping is generally introduced as a phenomenological, viscous term that dissipates energy, proportional to the temporal derivative of the polarization. Here, we follow the radiation reaction method presented in [Phys. Lett. A157, 217 (1991)], which applies to non-relativistic electrons of finite size, to introduce an explicit reaction force in the Newtonian equation of motion, and derive a hydrodynamic equation that offers new insight on the influence of damping in generic plasmas, metal-based and/or dielectric structures. In these settings, we find new damping-dependent linear and nonlinear source terms that suggest the damping coefficient is proportional to the local charge density and nonlocal contributions that stem from the spatial derivative of the magnetic field. We discuss the conditions that could modify both linear and nonlinear electromagnetic responses.

Strong enhancement of third-harmonic generation in a double layer graphene system caused by electron-hole pairing

A manifestation of electron-hole pairing in nonlinear electromagnetic response of a double layer graphene system is studied. It is shown that the pairing causes the appearance of a number of peaks in the frequency dependence of the intensity of the third-harmonic generation (THG). The highest peak corresponds to , where ω is the incident wave frequency, and Δ is the order parameter of the electron-hole pairing. The absolute value of the THG intensity in the systems with electron-hole pairing is of several orders of magnitude greater than the THG intensity in the unpaired state. It is shown that huge enhancement of the THG intensity occurs both in the double monolayer and double bilayer graphene systems.

Artificial Nonlinearity Generated from Electromagnetic Coupling Metamolecule.

A purely artificial mechanism for optical nonlinearity is proposed based on a metamaterial route. The mechanism is derived from classical electromagnetic interaction in a metamolecule consisting of a cut-wire meta-atom nested within a split-ring meta-atom. Induced by the localized magnetic field in the split-ring meta-atom, the magnetic force drives an anharmonic oscillation of free electrons in the cut-wire meta-atom, generating an intrinsically nonlinear electromagnetic response. An explicit physical process of a second-order nonlinear behavior is adequately described, which is perfectly demonstrated with a series of numerical simulations. Instead of "borrowing" from natural nonlinear materials, this novel mechanism of optical nonlinearity is artificially dominated by the metamolecule geometry and possesses unprecedented design freedom, offering fascinating possibilities to the research and application of nonlinear optics.

Scaling laws for nonlinear electromagnetic responses of Dirac fermion

We theoretically propose that the Dirac fermion in two-dimensions shows the giant nonlinear responses to electromagnetic fields in terahertz region. A scaling form is obtained for the current and magnetization as functions of the normalized electromagnetic fields $E/E_\omega$ and $B/B_\omega$, where the characteristic electric (magnetic) field $E_\omega$ ($B_\omega$) depends on the frequency $\omega$ as $\hbar\omega^2/ev_F$ ($\hbar\omega^2/ev_F^2$), and is typically of the order of 80 V/cm ( 8 mT) in the terahertz region. Applications of the present theory to graphene and surface state of a topological insulator are discussed.

Quantum theory of the third-order nonlinear electrodynamic effects of graphene

The linear energy dispersion of graphene electrons leads to a strongly nonlinear electromagnetic response of this material. We develop a general quantum theory of the third-order nonlinear local dynamic conductivity of graphene $\sigma_{\alpha\beta\gamma\delta}(\omega_1,\omega_2,\omega_3)$, which describes its nonlinear response to a uniform electromagnetic radiation. The derived analytical formulas describe a large number of different nonlinear phenomena such as the third harmonic generation, the four wave mixing, the saturable absorption, the second harmonic generation stimulated by a dc electric current, etc., which may be used in different terahertz and optoelectronic devices.

Negative differential resistance and characteristic nonlinear electromagnetic response of a Topological Insulator.

Materials exhibiting negative differential resistance have important applications in technologies involving microwave generation, which range from motion sensing to radio astronomy. Despite their usefulness, there has been few physical mechanisms giving rise to materials with such properties, i.e. GaAs employed in the Gunn diode. In this work, we show that negative differential resistance also generically arise in Dirac ring systems, an example of which has been experimentally observed in the surface states of Topological Insulators. This novel realization of negative differential resistance is based on a completely different physical mechanism from that of the Gunn effect, relying on the characteristic non-monotonicity of the response curve that remains robust in the presence of nonzero temperature, chemical potential, mass gap and impurity scattering. As such, it opens up new possibilities for engineering applications, such as frequency upconversion devices which are highly sought for terahertz signal generation. Our results may be tested with thin films of Bi2Se3 Topological Insulators, and are expected to hold qualitatively even in the absence of a strictly linear Dirac dispersion, as will be the case in more generic samples of Bi2Se3 and other materials with topologically nontrivial Fermi sea regions.