A detailed analysis of the optical response of a system accommodating several coupled modes is needed for the complete understanding of the strong coupling effect. In this paper, we report on the analysis of scattering cross-section spectra of Au antennas on a ${\mathrm{SiO}}_2$ layer on a Si substrate in the IR region. A classical model of coupled oscillators is used for determining the resonant energies, damping rates, and coupling strengths of four phonon polariton modes in the ${\mathrm{SiO}}_2$ layer coupled to a localized surface plasmon mode in a Au antenna. The calculated Hopfield mixing coefficients then show the contribution of the individual uncoupled modes to the hybrid modes of the coupled system.

Spinel oxides are well-known functional materials but rarely show superconductivity. Recently, emergent superconductivity was discovered in ${\mathrm{MgTi}}_2{\mathrm{O}}_4$, which is attributed to the increase of electron doping and the suppression of orbital order. Here, we utilized Ti $L$-edge resonant inelastic x-ray scattering to study the orbital excitations in superconducting (SC) and insulating ${\mathrm{MgTi}}_2{\mathrm{O}}_4$ films. We find that the spectral weight of orbital excitations is enhanced and the energy of $t_{2g}$ intraband excitation is softened in the SC film compared to the insulating one, suggesting higher electron doping and a suppressed orbital order gap in the SC sample. These observations were further supported by our multiplet calculations using the minimal two-site model. Our results provide spectroscopic evidence for the competition between orbital order and superconductivity in ${\mathrm{MgTi}}_2{\mathrm{O}}_4$ and shed light on searching for novel superconductors in spinel oxides.

We present a numerically exact study of a polaron with quadratic coupling to the oscillator displacement, or $X^2$ polaron, using two alternative methodological developments. Our results cover both antiadiabatic and adiabatic regimes and the entire range of electron-phonon coupling $g_2$, from the system's stability threshold at attractive $g_2=-1$ to arbitrary strong repulsion at $g_2\gg 1$. The key properties of $X^2$ polarons prove dramatically different from their linear counterparts. They (i) are insensitive even to large quadratic coupling except in the antiadiabatic limit near the threshold of instability at attraction, (ii) depend only on the adiabatic ratio but are insensitive to the electron dispersion and dimension of space, and (iii) feature weak lattice deformations even at the instability point. Our results are of direct relevance to the properties of electrons at low densities in polar materials, including recent proposals for their superconducting states.

Equiatomic NiCoCr solid solutions have been shown by recent experiments and atomistic simulations to display exceptional mechanical properties that have been suggested to be linked to nanostructural short-range order (SRO) features that may arise from thermal treatments, such as annealing or/and aging. Here we use hybrid Monte Carlo–molecular dynamics simulations to gain further insights of thermal effects on the SRO formation as well as the edge dislocation plasticity mechanisms of equiatomic NiCoCr face-centered cubic solid solution. For that purpose, we utilize two well-known NiCoCr interatomic potentials, one of which displays well-documented SRO, believed to be linked to experimental evidence and labeled as the Li-Sheng-Ma potential, while the other (Farkas-Caro) does not. We use these two potentials to discern short-range ordering (from inherent randomness in random solid solutions) and understand how SROs influence dislocation depinning dynamics in various thermal annealing scenarios. In this context, we used robust, scale-dependent metrics to infer a characteristic SRO size in the Li-Sheng-Ma case by probing local concentration fluctuations which otherwise indicate uncorrelated patterns in the Farkas-Caro case in a close agreement with random alloys. Our Voronoi-based analysis shows meaningful variations of local misfit properties owing to the presence of SROs. Using relevant order parameters, we also report on the drastic increase of chemical ordering within the stacking fault region. More importantly, we find that the Li-Sheng-Ma potential leads to excellent edge dislocation depinning strength with low stacking fault width. Our findings indicate an enhanced roughening mechanism due to the SROs-misfit synergy that leads to significant improvements in dislocation glide resistance. We argue that the improvements in alloy strength have their atomistic origins in the interplay between nanoscopic SROs and atomic-level misfit properties.

By combining molecular statics simulations and continuum mechanics-based modeling, we show in this paper that the torsion of a $\langle 001\rangle$ single-crystal copper nanowire with a circular cross section gives rise to a warp, i.e., to a displacement field along the wire axis that renders the cross section nonplanar. This behavior, which is in apparent contradiction with what is predicted by continuum mechanics for an isotropic cylinder, can be well explained if we take into account the elastic response of the wire lateral surface. The latter is characterized by the anisotropy of the surface elastic constants and, more specifically in the case of torsion, by the surface shear constant $C_{44}^S$ whose strength as a function of the local orientation of the lateral surface is estimated independently from atomistic calculations on slabs presenting different vicinal surfaces. The solution of the torsion problem is then obtained by adopting a semi-inverse method in the framework of the finite strain theory in linear elasticity with Gurtin-Murdoch boundary conditions linking surface stress and bulk stress. It is shown that such an approach is well suited to explain quantitatively the warp obtained in our atomistic simulations and to prove the preponderant role played by the surface elastic constant $C_{44}^S$.

We report a theory of optical generation and detection of the propagating spin waves in antiferromagnetic materials relevant for ultrafast pump-probe experiments. We derive and solve the equations of motion for antiferromagnetic spins in response to the light-induced effective magnetic field in the linear regime. Different forms of the excitation and the properties of the generated spin waves are analyzed. We theoretically show the selective detection of the spin waves by the magneto-optical Kerr effect. The developed formalism is readily applicable to inform future experiments on antiferromagnetic optomagnonics.

Ultrafast laser-induced heating of ferrimagnetic iron garnet in an external magnetic field triggers magnetization precessional dynamics with a large amplitude. The dynamics is studied as a function of magnetic field, laser fluence, and sample temperature. Exploring the three-dimensional space of these parameters experimentally and computationally, we identify the conditions for which the amplitude of the precession is the largest and even achieves values sufficient for magnetic recording. We found that the range of external magnetic fields and temperatures, which corresponds to the magnetic recording, is rather narrow. Modeling the dynamics, using magnetization as a macroscopic parameter, reveals that this range of parameters is defined by the optimal height of the potential barrier separating two stable states. The barrier needs to be low enough to allow the switching but not so low that the stability of the states is lost.

The recent observed anomalous Hall effect in magic angle twisted bilayer graphene (TBG) aligned to hexagonal boron nitride (hBN) and unconventional ferroelectricity in Bernal bilayer graphene sandwiched by hBN present a platform to tune the correlated properties in graphene systems. In these graphene-based moiré superlattices, the aligned hBN substrate plays an important role. In this paper, we analyze the effects of hBN substrate on the band structure of the TBG. By means of an atomistic tight-binding model we calculate the electronic properties of TBG suspended and encapsulated with hBN. Interestingly, we found that the physical properties of TBG are extremely sensitive to the presence of hBN and they may be completely different if TBG is suspended or encapsulated. We quantify these differences by analyzing their electronic properties and band topology. We found that the narrow bandwidth, band gap, and local density of states are significantly modified by the aligned hBN substrates. Interestingly, these electronic properties can be used as a signature of the alignment in experiment. Moreover, the TBG/hBN superlattices in the presence or absence of the twofold rotation symmetry respond differently to the external electric field. For the TBG suspended in the hBN, application of an electric field results in the charge unevenly distributed between graphene layers, which can be used to tune the strength of the valley Hall effect or the anomalous Hall effect. Such rich topological phase diagram in these systems may be useful for experiments.

${\mathrm{EuTe}}_4$ is a van der Waals material exhibiting a charge density wave (CDW) with a large thermal hysteresis in the resistivity and CDW gap. In this paper, we systematically study the electronic structure and transport properties of ${\mathrm{EuTe}}_4$ using high-resolution angle-resolved photoemission spectroscopy (ARPES), magnetoresistance (MR) measurements, and scanning tunneling microscopy (STM). We observe a CDW gap of $\sim 200\mathrm{meV}$ at low temperatures that persists up to 400 K, suggesting that the CDW transition occurs at a much higher temperature. The ARPES intensity near the Fermi level shows large thermal hysteretic behavior, consistent with the resistivity measurement. The hysteresis in the resistivity measurement does not change under a magnetic field up to 7 T, excluding the thermal magnetic hysteretic effect. Instead, the surface topography measured with STM shows surface domains with different CDW trimerization directions, which may be important for the thermal hysteretic behavior. Interestingly, we reveal a large negative MR at low temperatures that can be associated with the canting of magnetically ordered Eu spins. Our results shed light on the understanding of magnetic, transport, and electronic properties of ${\mathrm{EuTe}}_4$.

In recent years, it has been shown that Berry curvature monopoles and dipoles play essential roles in the anomalous Hall and the nonlinear Hall effects, respectively. In this work, we demonstrate that Berry curvature multipoles (the higher moments of Berry curvatures at the Fermi energy) can induce higher-order nonlinear anomalous Hall (NLAH) effects. Specifically, an AC Hall voltage perpendicular to the current direction emerges, where the frequency is an integer multiple of the frequency of the applied current. Importantly, by analyzing the symmetry properties of all the 3D and 2D magnetic point groups, we note that the quadrupole, hexapole, and even higher Berry curvature moments can cause the leading-order frequency multiplication in certain materials. To provide concrete examples, we point out that the third-order NLAH voltage can be the leading-order Hall response in certain antiferromagnets due to Berry curvature quadrupoles, and the fourth-order NLAH voltage can be the leading response in the surface states of topological insulators induced by Berry curvature hexapoles. Our results are established by symmetry analysis, effective Hamiltonian, and first-principles calculations. Other materials which support the higher-order NLAH effect are further proposed, including 2D antiferromagnets and ferromagnets, Weyl semimetals, and twisted bilayer graphene near the quantum anomalous Hall phase.

We study spin configurations of classical magnetic impurities placed close to the edge of a two-dimensional topological superconductor both analytically and numerically. First, we demonstrate that the spin of a single magnetic impurity close to the edge of a topological superconductor tends to align along the edge. The strong easy-axis spin anisotropy behind this effect originates from the interaction between the impurity and the gapless helical Majorana edge states. We then compute the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities placed close to the edge. We show that, in the limit of large interimpurity distances, the RKKY interaction between the two impurities is mainly mediated by the Majorana edge states and leads to a ferromagnetic alignment of both spins along the edge. This effect could be used to detect helical Majorana edge states.

Nonlinear optical (NLO) effect plays a crucial role to engineer optical angular frequency and symmetry of electronic system. Metallic transition-metal dichalcogenides are one of two-dimensional (2D) materials, which have no inversion symmetry for odd-number layers. In particular, odd-number-layered ${\mathrm{NbSe}}_2$ has spin splitting owing to Ising-type spin-orbit coupling. In this paper, we numerically calculate the NLO charge and spin conductivities of ${\mathrm{NbSe}}_2$ based on an effective tight-binding model for several different optical effects, i.e., symmetry manipulation by bicircular light (BCL) and bulk photovoltaic effect (shift and injection currents). Under irradiation of BCL which can control the symmetry of electronic system, the current can be generated even in even-number-layered ${\mathrm{NbSe}}_2$. Also, we find that shift current can be generated for odd-number-layered ${\mathrm{NbSe}}_2$, which is robust against electronic scattering, i.e., topological current. The direction of generated shift current can be switched by altering polarization of light. Our results will serve to design opto-spintronics devices based on 2D materials to manipulate the charge and spin currents and their directions by controlling the polarization of incident light which recasts the symmetry of electronic systems.

We investigate a spin-$\frac{1}{2}$ fermion chain minimally coupled to a ${\mathbb{Z}}_2$ gauge field. In the sector of the gauge generator ${\widehat{G}}_j=-1$, the model reduces to the Hubbard model with repulsive on-site interaction coupled to a ${\mathbb{Z}}_2$ gauge field. We uncover how electric fields affect low-energy excitations by both analytical and numerical methods. In the half-filling case, despite electric fields, the system is still a Mott insulator, just like the Hubbard model. For hole-doped systems, holes are confined under nonzero electric fields, resulting in a hole-pair bound state. Furthermore, this bound state also significantly affects the superconductivity, which manifests itself in the emergence of attractive interactions between bond-singlet Cooper pairs. Specifically, numerical results reveal that the dimension of the dominant superconducting order parameter becomes smaller when increasing the electric field, signaling an enhancement of the superconducting instability induced by lattice fermion confinement. The superconducting order can even be the dominant order of the system for suitable doping and large applied electric field. The confinement also induces a $\pi$ momentum for the dominant superconducting order parameter leading to a quasi-long-range pair density wave order. Our results provide insights for understanding unconventional superconductivity in ${\mathbb{Z}}_2$ lattice gauge theories and might be experimentally addressed in quantum simulators.

The interplay between strong correlations and nontrivial topology in twisted moiré systems can give rise to a rich landscape of ordered states that intertwine the spin, valley, and charge degrees of freedom. In this paper, we investigate the properties of a system that displays long-range valley-polarized nematic order. Besides breaking the threefold rotational symmetry of the triangular moiré superlattice, this type of order also breaks twofold rotational and time-reversal symmetries, which leads to interesting properties. First, we develop a phenomenological model to describe the onset of this ordered state in twisted moiré systems, and to explore its signatures in their thermodynamic and electronic properties. Its main manifestation is that it triggers the emergence of in-plane orbital magnetic moments oriented along high-symmetry lattice directions. We also investigate the properties of the valley-polarized nematic state at zero temperature. Due to the existence of a dangerously irrelevant coupling $\lambda$ in the six-state clock model that describes the putative valley-polarized nematic quantum critical point, the ordered state displays a pseudo-Goldstone mode. Using a two-patch model, we compute the fermionic self-energy to show that down to very low energies, the Yukawa-like coupling between the pseudo-Goldstone mode and the electronic degrees of freedom promotes the emergence of non-Fermi liquid behavior. Below a crossover energy scale ${\mathrm{\Omega }}^{*}\sim {\lambda }^{3/2}$, however, Fermi liquid behavior is recovered. Finally, we discuss the applicability of these results to other nontrivial nematic states, such as the spin-polarized nematic phase.

Weyl semimetals (WSMs) with paired Weyl points in momentum space have attracted much attention in the past decade, and materials for this phase and the exotic Fermi arcs at their surface have been realized, in which the topology can be found in a finite momentum interval. Here we suggest a four-band model for WSM with two Weyl points in the $k_z$ axis, yet with totally different Fermi arcs at the surfaces. It exhibits a large anomalous Hall conductivity in the bulk, and large density of state on their surface. We analytically and numerically demonstrate the topological properties of this model from the dispersion, $k_z$-dependent Chern number, Fermi arc states, and dual topological phase. Furthermore, we investigate the effects of the magnetic field on the unusual Fermi arcs and find two emergent Fermi surfaces. Their combination can lead to diverse Lifshitz phase transitions when the thickness of the slab is decreased. The change of Fermi surfaces can be detected by the quantum oscillation, in which the contributions from a different number of closed Fermi surfaces can lead to different magnetotransport behaviors. We expect this model can stimulate the search for its realization in condensed matter physics and quantum simulating platforms.

Two-dimensional gapped semi-Dirac (GSD) materials are systems with a finite band gap that whose carriers behave relativistically in one direction and Schrödinger-like in the other. In the present paper, we show that besides the two well-known energy band features (curvature and chirality), the band-gap parameter also plays a crucial role in the index and magnetic-field dependence of the Landau levels (LLs) in a GSD system. We take monolayer phosphorene as a GSD representative example to explicitly provide physical insights into the role of this parameter in determining the index and magnetic-field dependence of LLs. We derive an effective one-dimensional Schrödinger equation for charge carriers in the presence of a perpendicular magnetic field and argue that the form of its effective potential is sensitive to a dimensionless band gap that is tunable by structural parameters. The theoretical magnitude of this effective gap and its interplay with oval shape $k$-space cyclotron orbits resolve the seemingly contradiction in determining the type of the quantum Hall effect in pristine monolayer phosphorene. Our results confirm that the dependence of LLs on the magnetic field in this GSD material is as for conventional two-dimensional semiconductor electron gases up to the very high field. Using the strain-induced band gap reduction, we show that the field dependence of the LLs continuously evolves into $B^{2/3}$ behavior, which holds for a gapless semi-Dirac system. The highlighted role of the band-gap parameter may affect the consequences of the band anisotropy in the physical properties of a GSD material, including magnetotransport, optical conductivity, dielectric function, and thermoelectric performance.

We study Majorana zero modes bound to giant vortices in topological superconductors or topological insulator/normal superconductor heterostructures. By expanding in inverse powers of a large winding number $n$, we find an analytic solution for asymptotically all $n$ zero modes required by the index theorem. Contrary to the existing estimates, the solution is not pinned to the vortex boundary and is composed of the warped lowest Landau level states. While the dynamics which shapes the zero modes is a subtle interference of the magnetic effects and Andreev reflection, the solution is very robust and is determined by a single parameter, the vortex radius. The resulting local density of states has a number of features which give remarkable signatures for an experimental observation of the Majorana fermions in two dimensions.