We compute the magnetocrystalline anisotropy energy within two-dimensional Rashba models. For a ferromagnetic free-electron Rashba model, the magnetic anisotropy is exactly zero regardless of the strength of the Rashba coupling, unless only the lowest band is occupied. For this latter case, the model predicts in-plane anisotropy. For a more realistic Rashba model with finite band width, the magnetic anisotropy evolves from in-plane to perpendicular and back to in-plane as bands are progressively filled. This evolution agrees with first-principles calculations on the interfacial anisotropy, suggesting that the Rashba model captures energetics leading to anisotropy originating from the interface provided that the model takes account of the finite Brillouin zone. The results show that the electron density modulation by doping or an external voltage is more important for voltage-controlled magnetic anisotropy than the modulation of the Rashba parameter.

We present numerical studies of the dynamics of vortices in the Ginzburg-Landau model using equations derived from the gradient flow of the free energy. Our equations are equivalent to the time dependent Ginzburg-Landau equations. We have modeled the dynamics of multiple $n$-vortex configurations starting far from equilibrium. We find generically that there are two time scales for equilibration: a short time scale related to the formation time for a single $n$ vortex, and a longer time scale that characterizes vortex-vortex interactions.

Using the Landau-Zener-Stückelberg-Majorana-type (LZSM) semiclassical approach, we study both graphene and a thin film of a Weyl semimetal subjected to a strong ac electromagnetic field. The spectrum of quasienergies in the Weyl semimetal turns out to be similar to that of a graphene sheet. It has been predicted qualitatively that the transport properties of strongly irradiated graphene oscillate as a function of the radiation intensity [S. V. Syzranov et al., Phys. Rev. B 88, 241112 (2013)]. Here we obtain rigorous quantitative results for a driven linear conductance of graphene and a thin film of a Weyl semimetal. The exact quantitative structure of oscillations exhibits two contributions. The first one is a manifestation of the Ramsauer-Townsend effect, while the second contribution is a consequence of the LZSM interference defining the spectrum of quasienergies.

We show that for two-band systems nonsymmorphic symmetries may enforce the existence of band crossings in the bulk, which realize Fermi surfaces of reduced dimensionality. We find that these unavoidable crossings originate from the momentum dependence of the nonsymmorphic symmetry, which puts strong restrictions on the global structure of the band configurations. Three different types of nonsymmorphic symmetries are considered: (i) a unitary nonsymmorphic symmetry, (ii) a nonsymmorphic magnetic symmetry, and (iii) a nonsymmorphic symmetry combined with inversion. For nonsymmorphic symmetries of the latter two types, the band crossings are located at high-symmetry points of the Brillouin zone, with their exact positions being determined by the algebra of the symmetry operators. To characterize these band degeneracies we introduce a global topological charge and show that it is of ${\mathbb{Z}}_2$ type, which is in contrast to the local topological charge of Fermi points in, say, Weyl semimetals. To illustrate these concepts, we discuss the $\pi$-flux state as well as the Su-Schrieffer-Heeger model at its critical point and show that these two models fit nicely into our general framework of nonsymmorphic two-band systems.

Raman scattering on phonons in GaN with wurtzite structure ($\alpha$-GaN) is used to determine the coefficients of second-harmonic generation (SHG) and the linear electro-optic effect (LEO) in the region of optical transparency for excitations below the band gap. For wurtzite-type crystals, the symmetry requires that three SHG coefficients $d_{31}, d_{33}$, and $d_{24}$ and three LEO coefficients $r_{31}, r_{33}$, and $r_{42}$ be considered. In this work, the dependence of these SHG and LEO coefficients on the Raman scattering intensities of the polar transverse optical (TO) and longitudinal optical (LO) phonon modes in wurtzite-type crystals and their corresponding Faust-Henry coefficients is derived. In the case of GaN, the obtained SHG coefficients are $\left|d_{31}\right|$ = 2.46 pm/V, $\left|d_{33}\right|$ = 3.97 pm/V, and $\left|d_{24}\right|$ = 2.48 pm/V, which agree well with results measured by other methods. Also, all three LEO coefficients of GaN have been determined: $\left|r_{13}^S\right|$ = 0.72 pm/V, $\left|r_{33}^S\right|$ = 1.31 pm/V, and $\left|r_{42}^S\right|$ = 0.38 pm/V. Contrary to previous reports, our results indicate an important contribution of the ionic lattice displacements to the linear electro-optic effect. The ratios of the three SHG coefficients or the three LEO coefficients, which correspond to different nonlinear susceptibility tensor elements, depend on the relative intensities of the polar TO and LO phonon modes connected with different Raman tensor elements.

The interaction between coherent polaritons and incoherent excitons plays an important role in polariton physics. Using resonant pump-probe spectroscopy with selective excitation of single polariton branches, we investigate the different dephasing mechanisms responsible for generating a long-lived exciton reservoir. As expected, pumping the upper polariton results in a strong dephasing process that leads to the generation of a long lived reservoir. Unexpectedly, we observe an efficient reservoir creation while exciting only the lower polariton branch when the detuning is increased towards positive detuning. We propose a simple theoretical model, the polaritonic Bloch equations, to describe the dynamics of the system.

Time evolution of long-range spatial coherence in a freely decaying cavity-polariton condensate excited resonantly in a high-$Q$ GaAs microcavity is found to be qualitatively different from that in nonresonantly excited condensates. The first-order spatial correlation function $g^{\left(1\right)}(r_1,r_2)$ in response to resonant 1.5 ps pump pulses at normal incidence leaving the exciton reservoir empty is found to be nearly independent of the excitation density. $g^{\left(1\right)}$ exceeds 0.7 within the excited spot and decreases very slowly in the decaying and expanding condensate. It remains above 0.5 until the polariton blue shift $\alpha |{\psi }^2|$ gets comparable to the characteristic amplitude of the disorder potential $\delta E_{LP}$. The disorder is found to reveal itself at $\alpha |{\psi }^2|\lesssim \delta E_{LP}$ in fast and short-range phase fluctuations as well as vortex formation. They lead to oscillations in $g^{\left(1\right)}\left(t\right)$, but have little effect on the overall coherence, which is well reproduced in the framework of the Gross-Pitaevskii equations.

First-principles calculations were carried out to explore the possible coupling between spin-polarized electronic states and ferroelectric polarization in monolayers of transition-metal dichalcogenides $M{X}_2$ ($M=\mathrm{Mo},\mathrm{W};X=\mathrm{S},\mathrm{Se},\mathrm{Te})$ with distorted octahedrally coordinated $1T$ structures. For $d^2$ metal ions, two competing metal clustering effects can take place, where metal ions are arranged in trimers or zigzag chains. Among these, the former structural distortion comes along with an improper ferroelectric phase which persists in the monolayer limit. Switchable Rashba-like spin-polarization features are predicted in the trimerized polytype, which can be permanently tuned by acting on its ferroelectric properties. The polar trimerized structure is found to be stable for $1T-{\mathrm{MoS}}_2$ only, while the nonpolar polytype with zigzag metal clustering is predicted to stabilize for other transition-metal dichalcogenides with $d^2$ metal ions.

Magnesium hydroxide $\left[\mathrm{Mg}{\left(\mathrm{OH}\right)}_2\right]$ has a layered brucitelike structure in its bulk form and was recently isolated as a new member of two-dimensional monolayer materials. We investigated the electronic and optical properties of monolayer crystals of $\mathrm{Mg}{\left(\mathrm{OH}\right)}_2$ and ${\mathrm{WS}}_2$ and their possible heterobilayer structure by means of first-principles calculations. It was found that both monolayers of $\mathrm{Mg}{\left(\mathrm{OH}\right)}_2$ and ${\mathrm{WS}}_2$ are direct-gap semiconductors and these two monolayers form a typical van der Waals heterostructure with a weak interlayer interaction and a type-II band alignment with a staggered gap that spatially separates electrons and holes. We also showed that an out-of-plane electric field induces a transition from a staggered to a straddling-type heterojunction. Moreover, by solving the Bethe-Salpeter equation on top of single-shot ${\mathrm{G}}_0{\mathrm{W}}_0$ calculations, we show that the low-energy spectrum of the heterobilayer is dominated by the intralyer excitons of the ${\mathrm{WS}}_2$ monolayer. Because of the staggered interfacial gap and the field-tunable energy-band structure, the $\mathrm{Mg}{\left(\mathrm{OH}\right)}_2-{\mathrm{WS}}_2$ heterobilayer can become an important candidate for various optoelectronic device applications in nanoscale.

Recently, the two-dimensional (2D) semiconductors arsenene and antimonene, with band gaps larger than 2.0 eV, have attracted tremendous interest, especially for potential applications in optoelectronic devices with a photoresponse in the blue and UV range. Motivated by this exciting discovery, types of highly stable wide-band-gap 2D nitride semiconductors were theoretically designed. We propose single-layer $1T-X{\mathrm{N}}_2$ ($X=\mathrm{S}$, Se, and Te) via first-principles simulations. We compute $1T-X{\mathrm{N}}_2$ ($X=\mathrm{S}$, Se, and Te) with indirect band gaps of 2.825, 2.351, and 2.336 eV, respectively. By applying biaxial strain, they are able to induce the transition from a wide-band-gap semiconductor to a metal, and the range of absorption spectra of $1T-X{\mathrm{N}}_2$ ($X=\mathrm{S}$, Se, and Te) obviously extend from the ultraviolet region to the blue-purple light region. With an underlying graphene, we find that $1T-X{\mathrm{N}}_2$ can completely shield the light absorption of graphene in the range of 1–1.6 eV. Our research paves the way for optoelectronic devices working under blue or UV light, and mechanical sensors based on these 2D crystals.

Using angle-resolved photoemission spectroscopy (ARPES), we study the effect of the so-called herringbone reconstruction of Au(111) on the dispersion of the free-electron-like surface state. While earlier ARPES investigations have only reported a minor interplay of the surface state dispersion and the underlying reconstruction, we show that the uniaxial lattice distortion and the thereby changed reciprocal lattice for the first atomic layer lead to distinct surface state dispersions around the first-order reciprocal lattice points of the three domains, creating a constant energy surface resembling a trefoil knot. The findings resolve the long-standing discrepancy between, on one hand, the reconstruction-induced surface state modifications reported in scanning tunneling microscopy and first principles calculations and, on the other hand, their conspicuous absence in photoemission.

Pyrochlore iridates and pyrochlore ices are two families of materials where novel quantum phenomena are intertwined with strong spin-orbit coupling, substantial electron correlation, and geometrical frustration. Motivated by the puzzling experiments on two pyrochlore systems ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ and ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, we study the proximate Ising orders and the quantum phase transition out of quantum spin ice U(1) quantum spin liquid (QSL). We apply the electromagnetic duality of the compact quantum electrodynamics to analyze the condensation of the “magnetic monopoles” in the U(1) QSL. The monopole condensation naturally and necessarily leads to the Ising orders that generically break the lattice translation symmetry. We demonstrate that the antiferromagnetic Ising order with the ordering wave vector $\mathbf{Q}=2\pi \left(001\right)$ is proximate to the U(1) QSL while the ferromagnetic Ising state with $\mathbf{Q}=\left(000\right)$ is not proximate to the U(1) QSL. This implies that if there exists a direct transition from the U(1) QSL to the ferromagnetic Ising order, the transition must be strongly first order. We apply the monopole condensation to explain the magnetic orders and the transitions in ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ and ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$.

We introduce a real-space technique able to extend the standard Hopfield approach commonly used in quantum polaritonics to the case of inhomogeneous lossless materials interacting with the electromagnetic field. We derive the creation and annihilation polaritonic operators for the system normal modes as linear, space-dependent superpositions of the microscopic light and matter fields. We prove their completeness and invert the Hopfield transformation expressing the microscopic fields as functions of the polaritonic operators. As an example, we apply our approach to the case of a planar interface between vacuum and a polar dielectric, showing how we can consistently treat both propagative and surface modes, and express their nonlinear interactions, arising from phonon anharmonicity, as polaritonic scattering terms. We also show that our theory, including the proof of completeness, can be naturally extended to the case of dissipative materials.

We present a model Hamiltonian approach to evaluate the effect of adsorption on magnetic anisotropy of an iron-phthalocyanine (FePc) molecule. We describe the electronic ground state as a mixed configuration consisting of the ${}^{3}E$ and ${}^{3}B_2$ states under the $C_{4v}$ symmetry, which well reproduces the magnetic properties measured for the bulk FePc. We focus on the deformation of each $3d$ orbital and the modification of the ligand-field splitting by hybridization with the substrate electronic states. As an interesting example, we evaluate the $d$-orbital deformation in FePc on Au(111) from the density functional theory calculations, and demonstrate that the respective $d$-orbital deformation and the modification of the ligand-field splitting affect magnetic anisotropy through change of the mixed nature in the ground state. In addition, we propose that inelastic electron tunneling spectroscopy with a cryogenic scanning tunneling microscope is a promising tool to verify the mixed configuration by measuring the low-energy excited states and evolutions to external magnetic fields.

Monolayer epitaxial graphene grown on 6H-SiC(0001) was recently investigated by grazing-incidence fast-atom diffraction and analyzed with an ab initio electronic density calculation and with exact atomic diffraction methods. With these results as a reference, the hard-corrugated-wall model (HCW) is used as a complementary analytic approach to link binary potentials to the observed atomic corrugation. The main result is that the HCW model reproduces the macroscopic corrugation of the moiré pattern on a quantitative level, suggesting that soft-wall corrections may be neglected for macroscopic superstructures, allowing straightforward analysis in terms of a one-dimensional corrugation function.

We explore the role of flexoelectric effect in functional properties of nanoscale ferroelectric films with mixed electronic-ionic conductivity. Using a coupled Ginzburg-Landau model, we calculate spontaneous polarization, effective piezoresponse, elastic strain and compliance, carrier concentration, and piezoconductance as a function of thickness and applied pressure. In the absence of flexoelectric coupling, the studied physical quantities manifest well-explored size-induced phase transitions, including transition to paraelectric phase below critical thickness. Similarly, in the absence of external pressure flexoelectric coupling affects properties of these films only weakly. However, the combined effect of flexoelectric coupling and external pressure induces polarizations at the film surfaces, which cause the electric built-in field that destroys the thickness-induced phase transition to paraelectric phase and induces the electretlike state with irreversible spontaneous polarization below critical thickness. Interestingly, the built-in field leads to noticeable increase of the average strain and elastic compliance in this thickness range. We further illustrate that the changes of the electron concentration by several orders of magnitude under positive or negative pressures can lead to the occurrence of high- or low-conductivity states, i.e., the nonvolatile piezoresistive switching, in which the swing can be controlled by the film thickness and flexoelectric coupling. The obtained theoretical results can be of fundamental interest for ferroic systems, and can provide a theoretical model for explanation of a set of recent experimental results on resistive switching and transient polar states in these systems.

The design and synthesis of three-dimensional denser carbons are one of the hot issues in condensed matter physics because of their fascinating properties. Here we identify by ab initio calculations several tetragonal and monoclinic polymorphs of carbon that adopt the $t32, t{32}^{*}, m32$, and $m{32}^{*}$ structures in $P\overline{4}{2}_{1}c, P{4}_3{2}_{1}2, P{2}_1/c$, and $C2$ symmetry, respectively. These carbon polymorphs have large 32-atom unit cells in all-$s{p}^3$ bonding networks comprising five- and six-membered rings that are dynamically stable, as verified by a phonon mode analysis. Electronic band structure calculations show that they are insulators with band gaps in the range of 5.19–5.41 eV, close to the calculated band gap of 5.34 eV for diamond. Remarkably, these carbon phases possess an extremely high atom number density exceeding that of diamond. The present results establish different types of carbon phases and offer insights into their outstanding structural and electronic properties.

The magnetic system of the ${\mathrm{Mn}}_{1-x}{\mathrm{Fe}}_x\mathrm{Ge}$ solid solution is ordered in a spiral spin structure in the whole concentration range of $x\in [0÷1]$. The close inspection of the small-angle neutron-scattering data reveals the quantum phase transition from the long-range ordered to short-range ordered helical structure upon increase of Fe concentration at $x\in [0.25÷0.4]$. The short-range order (SRO) of the helical structure is identified as a Lorentzian contribution, while long-range order is associated with the Gaussian contribution into the scattering profile function. The scenario of the quantum phase transition with $x$ as a driving parameter is similar to the thermal phase transition in pure MnGe. The quantum nature of the SRO is proved by the temperature-independent correlation length of the helical structure at low- and intermediate-temperature ranges with remarkable decrease above certain temperature $T_Q$. We suggest the $x$-dependent modification of the effective Ruderman-Kittel-Kasuya-Yosida exchange interaction within the Heisenberg model of magnetism to explain the quantum critical regime in ${\mathrm{Mn}}_{1-x}{\mathrm{Fe}}_x\mathrm{Ge}$.

Based on first-principles calculations and tight-binding model analysis, we propose that black phosphorus (BP) can host a three-dimensional topological node-line semimetal state under pressure when spin-orbit coupling (SOC) is ignored. A closed topological node line exists in the first Brillouin zone (BZ) near the Fermi energy, which is protected by the coexistence of time-reversal and spatial inversion symmetry with band inversion driven by pressure. Drumheadlike surface states have been obtained on the beard (100) surface. Due to the weak intrinsic SOC of a phosphorus atom, a band gap less than 10 meV is opened along the node line in the presence of SOC, and the surface states are almost unaffected by SOC.