We employ first-principles calculations in the formalism of standard and hybrid density functional theory to study the electronic and structural properties of wurtzite ${\text{Al}}_x{\text{Ga}}_{1-x}\text{N}$ alloys. We address the discrepancies observed in literature regarding essential electronic properties of these alloys and we investigate the dependence of these properties on the atomic ordering and composition. We show that the bowing parameter is significantly affected by the atomic ordering, ranging from zero to strong downward bowing. The effects of atomic ordering of the alloys on their band offset with respect to the pure phases are also investigated. Finally, using the effective band structure approach, we study the electronic band structure of the random alloys.

Quasi-one-dimensional systems demonstrate Van Hove singularities in the density of states ${\nu }_F$ and the resistivity $\rho$, occurring when the Fermi level $E$ crosses a bottom $E_N$ of some subband of transverse quantization. We demonstrate that the character of smearing of the singularities crucially depends on the concentration of impurities. There is a crossover concentration $n_c\propto \left|\lambda \right|,\lambda \ll 1$ being the dimensionless amplitude of scattering. For $n\gg n_c$, the singularities are simply rounded at $\varepsilon \equiv E-E_N\sim {\tau }^{-1}$—the Born scattering rate. For $n\ll n_c$, the single-impurity non-Born effects in scattering become essential despite $\lambda \ll 1$. The peak of the resistivity is asymmetrically split in a Fano-resonance manner (however, with a more complex structure). Namely, for $\varepsilon >0$, there is a broad maximum at $\varepsilon \propto {\lambda }^2$, while for $\varepsilon <0$, there is a deep minimum at $\left|\varepsilon \right|\propto n^2\ll {\lambda }^2$. The behavior of $\rho$ below the minimum depends on the sign of $\lambda$. In case of repulsion, $\rho$ monotonically grows with $\left|\varepsilon \right|$ and saturates for $\left|\varepsilon \right|\gg {\lambda }^2$. In case of attraction, $\rho$ has a sharp maximum at $\left|\varepsilon \right|\propto {\lambda }^2$. The latter feature is due to resonant scattering at quasistationary bound states that inevitably arise just below the bottom of each subband for any attracting impurity.

The energy spectrum for the problem of $8-Pmmn$ borophene's electronic carriers under normal incidence of electromagnetic waves is studied without the use of any perturbative technique. This allows us to study the effects of very strong fields. To obtain the spectrum and wave functions, the time-dependent Dirac equation is solved by using a frame moving with the space-time cone of the wave, i.e., by transforming the equation into an ordinary differential equation in terms of the wave phase, leading to an electron-wave quasiparticle. The limiting case of strong fields is thus analyzed. The resulting eigenfunctions obey a generalized Mathieu equation, i.e., of a classical parametric pendulum. The energy spectrum presents bands and a gap at the Fermi energy. The gaps are due to the space-time diffraction of electrons in phase with the electromagnetic field, i.e., electrons in borophene acquire an effective mass under strong electromagnetic radiation.

Using an equation of motion (EOM) approach, we calculate excitonic properties of monolayer transition metal dichalcogenides perturbed by an external magnetic field. We compare our findings to the widely used Wannier model for excitons in two-dimensional materials and to recent experimental results. We find good agreement between the calculated excitonic transition energies and the experimental results. In addition, we find that the exciton energies calculated using the EOM approach are slightly lower than the ones calculated using the Wannier model. Finally, we also show that the effect of the dielectric environment on the magnetoexciton transition energy is minimal due to counteracting changes in the exciton energy and the exchange self-energy correction.

Low optical absorptivity of graphene limits the quantum efficiency of graphene-based optoelectronic devices. We demonstrate a broadband enhancement of absorptivity in an architecture of graphene intercalation inside a simple-cubic woodpile photonic crystal. Significant light-trapping effect is achieved due to spectrally broad and dense resonances in the architecture, especially modes propagating nearly parallel to the interface between the photonic crystal and the background material. We demonstrate an overall absorptivity $\sim 10$ to 17 times larger than the free-standing bare graphene monolayer with bandwidth to central frequency ratio 0.3, and $\sim 5$ to 11 times larger with bandwidth to central frequency ratio 1.33. A distributed intercalation of three graphene monolayers proves a $\sim 70\%$ overall absorptivity with bandwidth to central frequency ratio 0.3.

We construct a topological spin-liquid (TSL) model on the kagome lattice, with $\mathrm{SU}\left(3\right)$ symmetry with the fundamental representation at each lattice site, based on projected entangled pair states (PEPS). Using the PEPS framework, we can adiabatically connect the model to a fixed-point model (analogous to the dimer model for resonating valence bond states) which we prove to be locally equivalent to a ${\mathbb{Z}}_3$ quantum double model. Numerical study of the interpolation reveals no sign of a phase transition or long-range order, characterizing the model conclusively as a gapped TSL. We further study the entanglement spectrum of the model and find that while it is gapped, it exhibits branches with vastly different velocities, with the slow branch matching the counting of a chiral $\mathrm{SU}{\left(3\right)}_1$ Conformal Field Theory, suggesting that it can be deformed to a model with chiral $\mathrm{SU}{\left(3\right)}_1$ entanglement spectrum.

The quantum Fisher information is of considerable interest not only for quantum metrology but also because it is a useful entanglement measure for finite temperature mixed states. In particular, it estimates the degree to which multipartite entanglement is present. Recent results have related the quantum Fisher information to experimentally measurable probes. While in principle possible, a direct evaluation of the quantum Fisher information at finite temperatures is technically challenging and here we show that a simple estimate can be obtained for materials where the single-mode approximation is valid. We focus on the $S=1$ antiferromagnetic Heisenberg model with uniaxial anisotropy. Quantum Monte Carlo techniques are used to determine low-temperature correlations from which the quantum Fisher information can be estimated within the single-mode approximation. The quantum Fisher information is compared to the quantum variance for the staggered magnetization operators in the transverse direction and inequalities between the quantum Fisher information, the quantum variance, and the full variance are discussed. Both the quantum and full variance as well as the quantum Fisher information are examined at finite temperatures above the isotropic point and at the quantum critical point for the Haldane-Néel transition. A finite size scaling study of the quantum Fisher information is performed at the quantum critical point and used to confirm the Ising nature of the Haldane-Néel transition.

We study equilibrium and nonequilibrium properties of electron-phonon systems described by the Hubbard-Holstein model using dynamical mean-field theory. In equilibrium, we benchmark the results for impurity solvers based on the one-crossing approximation and slave-rotor approximation against non-perturbative numerical renormalization group reference data. We also examine how well the low-energy properties of the electron-boson coupled systems can be reproduced by an effective static electron-electron interaction. The one-crossing and slave-rotor approximations are then used to simulate insulator-to-metal transitions induced by a sudden switch-on of the electron-phonon interaction. The slave-rotor results suggest the existence of a critical electron-phonon coupling above which the system is transiently trapped in a nonthermal metallic state with coherent quasiparticles. The same quench protocol in the one-crossing approximation results in a bad metallic state.

The change of a material's electrical resistance (R) in response to an external magnetic field (B) provides subtle information for the characterization of its electronic properties and has found applications in sensor and storage related technologies. In good metals, Boltzmann's theory predicts a quadratic growth in magnetoresistance (MR) at low B and saturation at high fields. On the other hand, a number of nonmagnetic materials with weak electronic correlation and low carrier concentration for metallicity, such as inhomogeneous conductors, semimetals, narrow gap semiconductors and topological insulators, and two dimensional electron gas, show positive, nonsaturating linear magnetoresistance (LMR). However, observation of LMR in single crystals of a good metal is rare. Here we present low-temperature, angle-dependent magnetotransport in single crystals of the antiferromagnetic metal, ${\mathrm{TmB}}_4$. We observe large, positive, and anisotropic MR(B), which can be tuned from quadratic to linear by changing the direction of the applied field. In view of the fact that isotropic, single crystalline metals with large Fermi surface (FS) are not expected to exhibit LMR, we attribute our observations to the anisotropic FS topology of ${\mathrm{TmB}}_4$. Furthermore, the linear MR is found to be temperature independent, suggestive of quantum mechanical origin.

We show that the Kondo screening in a correlated double-quantum-dot structure may be caused solely by the proximity of a superconductor which induces nonlocal pairing by Andreev reflection processes. This leads to an effective exchange interaction, which we estimate perturbatively, and we corroborate the analytical predictions by the numerical renormalization group calculations, using an effective model for the superconductor-proximized nanostructure. We determine the dependence of the relevant Kondo temperature on the coupling to the superconductor and predict a characteristic modification of conventional low-temperature transport behavior, which can be used to experimentally distinguish this phenomenon from other Kondo effects. The occurrence of nonlocal pairing exchange does not depend on the details of the proposed setup; therefore, it can also be relevant for the bulk materials, such as heavy-fermion compounds.

Defect calculations using the density and hybrid functionals in combination with the supercell approach are employed to characterize the electrical properties of a number of ZnO nanowires of various thicknesses doped with Bi atoms occupying surface sites. The variation of the differences between the total energies of charged and neutral supercells with the supercell size is studied, which led the authors to devise an extrapolation procedure to obtain reliable defect energetics in the dilute defect limit. The calculated defect formation energies indicate that although the substitution of Bi into Zn or O sites can take place spontaneously under suitable thermodynamic conditions, the substitution into Zn sites is generally more likely. The defect (charge-state) transition energies are computed and parameterized as a function of the nanowire thickness. It is revealed that the substitution of Bi into O (Zn) sites on the surface of ZnO nanowires yields deep acceptor (shallow donor) levels (except for extremely thin nanowires). It is therefore concluded that the incorporation of Bi into the surface of ZnO nanowires results in $n$-type doping.

It is well established that external electrostatic fields modify the electronic structure and optical response of materials. Modifications of the optical response of quasi-one-dimensional graphene nanoribbons (GNRs) depend strongly on the direction of the electrostatic field. While transverse fields primarily lift degeneracies in the band structure, longitudinal fields are responsible for considerable nonperturbative Franz-Keldysh effects. Also, electric fields break the inversion symmetry of GNRs and result in strong electric field-induced second harmonic generation. In this work, we study field-induced modifications of the linear and nonlinear optical response of narrow and wide semiconducting armchair GNRs (AGNRs). Both finite and infinite AGNRs with and without electrostatic fields are studied and length convergence is analyzed. Similarly, the width convergence of wide AGNRs to the two-dimensional graphene limit with and without longitudinal fields is investigated.

We explore the broadband excitation spectrum of bulk ${\mathrm{PtTe}}_2$ using electron energy-loss spectroscopy and density-functional theory. In addition to infrared modes related to intraband three-dimensional (3D) Dirac plasmon and interband transitions between the 3D Dirac bands, we observe modes at 3.9, 7.5, and 19.0 eV in the ultraviolet region. The comparison of the excitation spectrum with the calculated orbital-resolved density of states allows us to ascribe spectral features to transitions between specific electronic states. Additionally, we study the thickness dependence of the high-energy-loss peak in the ${\mathrm{PtTe}}_2$ thin films. We show that, unlike graphene, the high-energy EELS peak in ${\mathrm{PtTe}}_2$ thin film gets redshifted by $\sim 2.5$ eV with increasing thickness.

We investigate a two-way waveguide constructed by bringing close two identical magneto-optical photonic crystals which each supports a counterpropagating topological one-way edge state. We find a unique slow-light state that exhibits a very small group velocity $\left(n_g=529.2\right)$, a zero group-velocity dispersion, distortionless pulse transport, and ease to be magnetically tuned within a broad frequency range, simultaneously. We show that this unique group-dispersionless slow-light state originates from the strong coupling of the two counterpropagating topological states, which causes complete exchange and transfer of energy flow between them, induces a vortexlike close loop of energy transport channel around the source, leads to complete destructive interference in the far field, and finally results in a very slow propagation velocity of electromagnetic waves. These results indicate that deeply digging into the interaction between photonic topological states can help to open up an arena in topological physics and find great potential of applications such as optical buffer memories and enhanced light-matter interaction.

The atomic cluster expansion is developed as a complete descriptor of the local atomic environment, including multicomponent materials, and its relation to a number of other descriptors and potentials is discussed. The effort for evaluating the atomic cluster expansion is shown to scale linearly with the number of neighbors, irrespective of the order of the expansion. Application to small Cu clusters demonstrates smooth convergence of the atomic cluster expansion to meV accuracy. By introducing nonlinear functions of the atomic cluster expansion an interatomic potential is obtained that is comparable in accuracy to state-of-the-art machine learning potentials. Because of the efficient convergence of the atomic cluster expansion relevant subspaces can be sampled uniformly and exhaustively. This is demonstrated by testing against a large database of density functional theory calculations for copper.

We propose an analytical procedure to fully solve a two-level system coupled to phonons. Instead of using the common formulation in terms of linear and quadratic system-phonon couplings, we introduce different phonons depending on the system electronic level. We use this approach to recover known results for the linear-coupling limit in a simple way. More importantly, we derive results for the quadratic coupling induced by a phonon frequency change, a problem considered up to now as not analytically solvable.

We study the spin-1 excitation spectra of the flat-band ferromagnetic phases in interacting topological insulators. As a paradigm, we consider a quarter-filled square lattice Hubbard model whose free part is the $\pi$-flux state with topologically nontrivial and nearly flat electron bands, which can realize either the Chern or $Z_2$ Hubbard model. By using the numerical exact diagonalization method with a projection onto the nearly flat band, we obtain the ferromagnetic spin-1 excitation spectra for both the Chern and $Z_2$ Hubbard models, consisting of spin waves and Stoner continuum. The spectra exhibit quite distinct dispersions for both cases; in particular the spin wave is gapless for the Chern Hubbard model, while gapped for the $Z_2$ Hubbard model. Remarkably, in both cases, the nonflatness of the free electron bands introduces dips in the lower boundary of the Stoner continuum. It significantly renormalizes the energies of the spin waves around these dips downward and leads to roton-like spin excitations. We elaborate that it is the softening of the roton-like modes that destabilizes the ferromagnetic phase, and determine the parameter region where the ferromagnetic phase is stable.

We report an Fe $L$-edge resonant inelastic x-ray scattering (RIXS) study of the unusual superconductor $\beta$-FeSe. The high-energy resolution of this RIXS experiment ($\approx 55\mathrm{meV}$ FWHM) made it possible to resolve low-energy excitations of the Fe $3d$ manifold. These include a broad peak which shows dispersive trends between 100 and 200 meV along the $(\pi ,0)$ and $(\pi ,\pi )$ directions of the one-Fe square reciprocal lattice, and which can be attributed to paramagnon excitations. The multiband valence state of FeSe is among the most metallic in which such excitations have been discerned by soft x-ray RIXS.

We study the magnetic susceptibility of a two-dimensional cone of Majorana modes localized at the surface of a three-dimensional time-reversal invariant topological superconductor belonging to class DIII. A field parallel to the surface tilts the surface Majorana cone along the supercurrent direction. For fields larger than a critical threshold field $H^{*}$, $H>H^{*}$, a transition from a type I to a type II Dirac cone occurs and a finite current carried by the Majorana modes starts to flow, leading to an additional diamagnetic contribution to the surface magnetization. On a curved surface, interband transitions are promoted by the Majorana spin connection that couples to the external field, giving rise to a finite-frequency magnetic susceptibility.

Recently, a new family of iron-based superconductors called 12442 was discovered and the muon spin relaxation ($\mu \mathrm{SR}$) measurements on ${\mathrm{KCa}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$ and ${\mathrm{CsCa}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$ polycrystals, two members of the family, indicated that both have a nodal superconducting gap structure with $s+d$ pairing symmetry. Here we report the ultralow-temperature thermal conductivity measurements on ${\mathrm{CsCa}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$ single crystals ($T_c=29.3\mathrm{K}$). A negligible residual linear term ${\kappa }_0/T$ in zero field and the field dependence of ${\kappa }_0/T$ suggest multiple nodeless superconducting gaps in ${\mathrm{CsCa}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$. This gap structure is similar to ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ and moderately doped ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ but contrasts to the nodal gap structure indicated by the $\mu \mathrm{SR}$ measurements on ${\mathrm{CsCa}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$ polycrystals.