We studied $\mathrm{TbT}{\mathrm{e}}_3$ using scanning tunneling microscopy (STM) in the temperature range of 298–355 K. Our measurements detect a unidirectional charge density wave (CDW) state in the surface Te layer with a wave vector consistent with that of the bulk ${\mathit{q}}_{\mathrm{CDW}}=0.30\pm 0.01{\mathit{c}}^{*}$. However, unlike previous STM measurements, and differing from measurements probing the bulk, we detect two perpendicular orientations for the unidirectional CDW with no directional preference for the in-plane crystal axes ($a$ or $c$ axis) and no noticeable difference in wave vector magnitude. In addition, we find regions in which the bidirectional CDW states coexist. We propose that observation of two unidirectional CDW states indicates a decoupling of the surface Te layer from the rare-earth block layer below, and that strain variations in the Te surface layer drive the local CDW direction to the specific unidirectional or, in rare occurrences, bidirectional CDW orders observed. This indicates that similar driving mechanisms for CDW formation in the bulk, where anisotropic lattice strain energy is important, are at play at the surface. Furthermore, the wave vectors for the bidirectional order we observe differ from those theoretically predicted for checkerboard order competing with stripe order in a Fermi-surface nesting scenario, suggesting that factors beyond Fermi-surface nesting drive CDW order in $\mathrm{TbT}{\mathrm{e}}_3$. Finally, our temperature-dependent measurements provide evidence for localized CDW formation above the bulk transition temperature $T_{\mathrm{CDW}}$.

We discuss the emergence of bound states in the low-energy spectrum of the string-net Hamiltonian in the presence of a string tension. In the ladder geometry, we show that a single bound state arises either for a finite tension or in the zero-tension limit depending on the theory considered. In the latter case, we perturbatively compute the binding energy as a function of the total quantum dimension. We also address this issue in the honeycomb lattice where the number of bound states in the topological phase depends on the total quantum dimension. Finally, the internal structure of these bound states is analyzed in the zero-tension limit.

The role of exchange defects on the band structure of ${\mathrm{ZnGeN}}_2$ is investigated. Exchange defects are defined through the exchange of cations Zn and Ge starting from the ideal $Pna{2}_1$ crystal structure, which obeys the local octet rule. Each such exchange creates several nitrogen-centered tetrahedra which violate the local octet rule, although overall charge neutrality is preserved. We study several distributions of exchange defects, some with all antisites making up the exchange defect close to each other and with increasing numbers of exchange defects, and others where the two types of antisites ${\mathrm{Zn}}_{\mathrm{Ge}}$ and ${\mathrm{Ge}}_{\mathrm{Zn}}$ are kept separated from each other. We also compare the results for these models with a fully random distribution of Zn and Ge on the cation sites. We show that for a single-nearest-neighbor exchange defect, the band gap is narrowed by about 0.5 eV due to two effects: (1) the ${\mathrm{Zn}}_{\mathrm{Ge}}$ antisites form filled acceptor states just above and merging with the valence-band maximum (VBM) of perfect crystal ${\mathrm{ZnGeN}}_2$ and (2) the ${\mathrm{Ge}}_{\mathrm{Zn}}$ antisites form a resonance in the conduction band which lowers the conduction-band minimum (CBM). When more exchange defects are created, these acceptor states broaden into bands which can lower the gap further. When tetrahedra occur surrounded completely by four Zn atoms, states even deeper in the gap are found localized all near these tetrahedra, forming a separate intermediate band. Finally, for phase-segregated ${\mathrm{Zn}}_{\mathrm{Ge}}$ and ${\mathrm{Ge}}_{\mathrm{Zn}}$, the gap is significantly more reduced, but no separate band is found to occur. The ${\mathrm{Zn}}_{\mathrm{Ge}}$ acceptorlike states now form a percolating defect band which is significantly wider and hence reaches deeper into the gap. In all cases, the wave functions near the top of the new VBM remain, to some extent, localized near the ${\mathrm{Zn}}_{\mathrm{Ge}}$ sites. For a fully random case, the gap is even more severely reduced by almost 3 eV. The total energy of the system increases with the number of octet-rule-violating tetrahedra and the energy cost per exchange defect of order 2 eV is quite high.

We propose a scheme for engineering compressed spatial states in a two-dimensional parabolic potential with a spin-orbit coupling by selective spin measurements. This sequence of measurements results in a coordinate-dependent density matrix with probability maxima achieved at a set of lines or at a two-dimensional lattice. The resultant probability density depends on the spin-orbit coupling and the potential parameters and allows one to obtain a broad class of localized pure states on demand. The proposed scheme can be realized in spin-orbit-coupled Bose-Einstein condensates.

We present a self-consistent local mean-field analysis of core-shell nanoparticles with ferromagnetic materials but with antiferromagnetic interface exchange coupling. The importance of this type of structure for a variety of applications, including biomedical applications and magnetic recording, has been emphasized in recent studies of core-shell nanoparticles of iron and manganese oxides. We develop theoretical results for a different combination of materials that also have antiferromagnetic coupling, namely nanoparticles composed of Fe and Gd, and show how the magnetic properties depend on temperature and applied field. We examine results for the case where Gd is the core material and Fe is the shell and vice versa, as well as the results for an Fe/Gd alloy. We find that the size of the core (typically 4–5 nm in diameter) and shell (typically < 2 nm wide) and the combined size of the nanoparticle all affect the magnetic behavior of the system. As the temperature is varied, the particles go through multiple phases, including one where the core magnetic moment is aligned with an external field, one where the shell magnetic moment is aligned with an external field, and one where the core and shell magnetic moments are in a canted state (occurring for fields larger than 2 kOe). In addition, we calculate the net magnetic moment versus temperature for the various structures and show that the compensation temperature (where the net magnetic moments of the Fe and Gd nearly cancel) depends on all the material parameters—the core radius, the shell radius, and the magnetic field. We also examine the thermal stability of these structures and show that the nanoparticles can effectively be ferromagnetic at both low and high temperatures and show superparamagnetic-like behavior in the 200–300 K range.

We present a systematic study of the ac susceptibility of the chiral magnet ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x\mathrm{Si}$ with $x=0.30$ covering four orders of magnitude in frequencies from 0.1 Hz to 1 kHz, with particular emphasis to the pronounced history dependence. Characteristic relaxation times ranging from a few milliseconds to tens of seconds are observed around the skyrmion lattice A phase, the helical-to-conical transition and in a region above $T_C$. The distribution of relaxation frequencies around the A phase is broad, asymmetric, and originates from multiple coexisting relaxation processes. The pronounced dependence of the magnetic phase diagram on the magnetic history and cooling rates as well as the asymmetric frequency dependence and slow dynamics suggest more complicated physical phenomena in ${\mathrm{Fe}}_{0.7}{\mathrm{Co}}_{0.3}\mathrm{Si}$ than in other chiral magnets.

We performed an angle-resolved photoemission spectroscopy study of ${\mathrm{BaMn}}_2{\mathrm{As}}_2$ and ${\mathrm{BaMn}}_2{\mathrm{Sb}}_2$, which are isostructural to the parent compound ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ of the 122 family of ferropnictide superconductors. We show the existence of a strongly $k_z$-dependent band gap with a minimum at the Brillouin zone center, in agreement with their semiconducting properties. Despite the half filling of the electronic $3d$ shell, we show that the band structure in these materials is almost not renormalized from the Kohn-Sham bands of density functional theory. Our photon-energy-dependent study provides evidence for Mn-pnictide hybridization, which may play a role in tuning the electronic correlations in these compounds.

In this paper we calculate the nonlinear susceptibility and the resonant Raman cross section for the paramagnetic phase of the ferromagnetic quantum Ising model in one dimension. In this region the spectrum of the Ising model has a gap $m$. The Raman cross section has a strong singularity when the energy of the outgoing photon is at the spectral gap ${\omega }_f\approx m$ and a square root threshold when the frequency difference between the incident and outgoing photons ${\omega }_i-{\omega }_f\approx 2m$. The latter feature reflects the fermionic nature of the Ising model excitations.

A transport study of two-dimensional (2D) holes confined to wide GaAs quantum wells provides a glimpse of a subtle competition between different many-body phases at a Landau level filling $\nu =3/2$ in tilted magnetic fields. At large tilt angles ($\theta$), an anisotropic, stripe (or nematic) phase replaces the isotropic compressible Fermi sea at $\nu =3/2$ if the quantum well has a symmetric charge distribution. When the charge distribution is made asymmetric, instead of the stripe phase, an even-denominator fractional quantum state appears at $\nu =3/2$ in a range of large $\theta$, and reverts back to a compressible state at even higher $\theta$. We attribute this remarkable evolution to the significant mixing of the excited and ground-state Landau levels of 2D hole systems in tilted fields.

The quantum anomalous Hall effect is induced by substitution of a certain portion $x$ of Bi atoms in a BiTe-based insulating parent compound by magnetic ions (Cr or V). We find the density of in-gap states $N\left(E\right)$ emerging as a result of statistical fluctuations of the composition $x$ in the vicinity of the transition point where the average gap ${\overline{E}}_g$ passes through zero. A local gap follows the fluctuations of $x$. Using the instanton approach, we show that, near the gap edges, the tails are exponential $lnN\left(E\right)\propto -({\overline{E}}_g-|E\left|\right)$ and the tail states are due to small local gap reduction. Our main finding is that, even when the smearing magnitude exceeds the gap width, there exists a semihard gap around zero energy, where $lnN\left(E\right)\propto -\frac{{\overline{E}}_g}{\left|E\right|}ln\left(\frac{{\overline{E}}_g}{\left|E\right|}\right)$. The states responsible for $N\left(E\right)$ originate from local gap reversals within narrow rings. The consequence of the semihard gap is the Arrhenius, rather than variable-range hopping, temperature dependence of the diagonal conductivity at low temperatures.

The thermal properties of monolayers of group-VA elements (P, As, Sb) with graphenelike buckled and black phosphorenelike puckered honeycomb structures are investigated systematically by theoretical calculations based on the phonon Peierls-Boltzmann equation. These structures are found to be thermodynamically stable with no appreciable negative frequencies in the phonon dispersion spectra. Generally, the thermal conductivity decreases as the atomic number increases. Anisotropy of relaxation time and thermal conductivity between armchair and zigzag directions is observed in the puckered structure but absent in the buckled structure. By analyzing the phase space of the thermal resistive three-phonon-scattering process, it is found that the acoustic-optical phonon gaps presented in the buckled structures have significant effects on thermal conductivity, not only affecting relative contribution from each process but also leading to a slight difference in the temperature dependence for buckled phosphorene. Our findings indicate a useful route for tuning the thermal conductivity of structurally similar materials by phonon engineering.

The detection and identification of impurities and other point defects in materials is a challenging task. Signatures for point defects are typically obtained using spectroscopies without spatial resolution. Here we demonstrate the power of valence electron-energy-loss spectroscopy (VEELS) in an aberration-corrected scanning transmission-electron microscope (STEM) to provide energy-resolved and atomically resolved maps of electronic excitations of individual impurities which, combined with theoretical simulations, yield unique signatures of distinct bonding configurations of impurities. We report VEELS maps for isolated Si impurities in graphene, which are known to exist in two distinct configurations. We also report simulations of the maps, based on density functional theory and dynamical scattering theory, which agree with and provide direct interpretation of observed features. We show that theoretical VEELS maps exhibit distinct and unambiguous signatures for the threefold- and fourfold-coordinated configurations of Si impurities in different energy-loss windows, corresponding to impurity-induced bound states, resonances, and antiresonances. With the advent of new monochromators and detectors with high energy resolution and low signal-to-noise ratio, the present work ushers an atomically resolved STEM-based spectroscopy of individual impurities as an alternative to conventional spectroscopies for probing impurities and defects.

Transient four-wave mixing studies of bulk GaAs under conditions of broad bandwidth excitation of primarily interband transitions have enabled four-particle correlations tied to degenerate (exciton-exciton) and nondegenerate (exciton-carrier) interactions to be studied. Real two-dimensional Fourier-transform spectroscopy (2DFTS) spectra reveal a complex response at the heavy-hole exciton emission energy that varies with the absorption energy, ranging from dispersive on the diagonal through absorptive for low-energy interband transitions to dispersive with the opposite sign for interband transitions high above band gap. Simulations using a multilevel model augmented by many-body effects provide excellent agreement with the 2DFTS experiments and indicate that excitation-induced dephasing (EID) and excitation-induced shift (EIS) affect degenerate and nondegenerate interactions equivalently, with stronger exciton-carrier coupling relative to exciton-exciton coupling by approximately an order of magnitude. These simulations also indicate that EID effects are three times stronger than EIS in contributing to the coherent response of the semiconductor.

Collective excitations in graphene are numerically investigated in the random-phase approximation based on one-particle states in an effective-mass approximation. For plasmons in doped graphene, when the plasmon wave vectors normalized by the Fermi wave vector are the same, the plasmon peak intensities in optical absorption spectra exhibit linear dependencies on the Fermi energy, which are characteristic of two-dimensional Dirac electrons. In the case of nondoped graphene, excitonic collective states to which optical transitions are forbidden appear at energies less than those of interband continuum states. The random-phase approximation with electron-hole attractive interactions well describes both the plasmons and the excitonic states while the Tamm–Dancoff approximation fails to describe the plasmons appropriately.

The geometrical and electronic properties of the monolayer (ML) of tetracene (Tc) molecules on Ag(111) are systematically investigated by means of DFT calculations with the use of a localized basis set. The bridge and hollow adsorption positions of the molecule in the commensurate $\gamma$-Tc/Ag(111) are revealed to be the most stable and equally favorable irrespective to the approximation chosen for the exchange-correlation functional. The binding energy is entirely determined by the long-range dispersive interaction. The former lowest unoccupied molecular orbital remains being unoccupied in the case of $\gamma$-Tc/Ag(111) as well as in the $\alpha$ phase with increased coverage. The unit cell of the $\alpha$ phase with point-on-line registry was adapted for calculations based on the available experimental data and computed structures of the $\gamma$ phase. The calculated position of the Tc/Ag(111) interface state is found to be noticeably dependent on the lattice constant of the substrate, however its energy shift with respect to the Shockley surface state of the unperturbed clean side of the slab is sensitive only to the adsorption distance and in good agreement with the experimentally measured energy shift.

We theoretically study the properties of thermal conductance in a normal-insulator-superconductor junction of silicene for both thin and thick barrier limit. We show that while thermal conductance displays the conventional exponential dependence on temperature, it manifests a nontrivial oscillatory dependence on the strength of the barrier region. The tunability of the thermal conductance by an external electric field is also investigated. Moreover, we explore the effect of doping concentration on thermal conductance. In the thin barrier limit, the period of oscillations of the thermal conductance as a function of the barrier strength comes out be $\pi /2$ when doping concentration in the normal silicene region is small. On the other hand, the period gradually converts to $\pi$ with the enhancement of the doping concentration. Such change of periodicity of the thermal response with doping can be a possible probe to identify the crossover from specular to retro Andreev reflection in Dirac materials. In the thick barrier limit, thermal conductance exhibits oscillatory behavior as a function of barrier thickness $d$ and barrier height $V_0$ while the period of oscillation becomes $V_0$ dependent. However, amplitude of the oscillations, unlike in tunneling conductance, gradually decays with the increase of barrier thickness for arbitrary height $V_0$ in the highly doped regime. We discuss experimental relevance of our results.

The pressure-induced phase transition of monazite-type ${\mathrm{LaPO}}_4$ at $\approx 26$ GPa is studied by single-crystal x-ray diffraction and second harmonic generation (SHG) up to 31 GPa. The structure of the postmonazite phase of ${\mathrm{LaPO}}_4$ has been obtained and it is shown that it corresponds to a post-barite-type structure with an acentric space group $P{2}_1{2}_1{2}_1$. A strong increase of the SHG signal at the transition confirms that the high-pressure polymorph is noncentrosymmetric. The phase transition involves a significant discontinuous decrease of the unit-cell volume by 6%, which is mainly due to a strong contraction of the $a$ lattice parameter. Enthalpy differences between polymorphs with monazite-, barite-, and post-barite-type structures have been obtained from density-functional-theory-based calculations. They also yield a transition pressure of 21 GPa for the monazite to postbarite phase transition, but indicate that the barite-type phase is significantly more stable, implying that the transition into this phase may be kinetically hindered. As the transition pressure for the monazite-type to post-barite-type structure is reproduced with reasonable accuracy, we predict the corresponding phase-transition pressures of ${\mathrm{NdPO}}_4$ and ${\mathrm{GdPO}}_4$ to be 35 and 45 GPa, respectively.

We study the effects of crystal anisotropy on optical phonon resonances in the second harmonic generation (SHG) from silicon carbide (SiC) in its reststrahl region. By comparing experiments and simulations for isotropic 3C-SiC and anisotropic 4H-SiC in two crystal cuts, we identify several pronounced effects in the nonlinear response, which arise solely from the crystal anisotropy. Specifically, we demonstrate that the axial and planar transverse optical phonon resonances selectively and exclusively appear in the corresponding tensor elements of the nonlinear susceptibility, enabling observation of an intense SHG peak originating from a weak phonon mode due to zone folding along the $c$ axis of 4H-SiC. Similarly, we identify an anisotropy factor $\zeta \equiv {\epsilon }_{\perp }/{\epsilon }_{\parallel }$ responsible for a steep enhancement of the transmitted fundamental fields at the axial longitudinal optical phonon frequency, resulting in strongly enhanced SHG. We develop a general recipe to extract all these features that is directly applicable to all wurtzite-structure polar dielectrics, where a very similar behavior is expected. Our model study illustrates the opportunities for utilizing the crystal anisotropy for selectively enhancing nonlinear-optical effects in polar dielectrics, which could potentially be extended to built-in anisotropy in artificially designed hybrid materials.