The lead chalcogenides represent an important family of functional materials, in particular due to the benchmark high-temperature thermoelectric performance of PbTe. A number of recent investigations, experimental and theoretical, have aimed to gather insight into their unique lattice dynamics and electronic structure. However, the majority of first-principles modeling has been performed at fixed temperatures, and there has been no comprehensive and systematic computational study of the effect of temperature on the material properties. We report a comparative lattice-dynamics study of the temperature dependence of the properties of PbS, PbSe, and PbTe, focusing particularly on those relevant to thermoelectric performance, viz. phonon frequencies, lattice thermal conductivity, and electronic band structure. Calculations are performed within the quasiharmonic approximation, with the inclusion of phonon-phonon interactions from many-body perturbation theory, which are used to compute phonon lifetimes and predict the lattice thermal conductivity. The results are critically compared against experimental data and other calculations, and add insight to ongoing research on the PbX compounds in relation to the off-centering of Pb at high temperatures, which is shown to be related to phonon softening. The agreement with experiment suggests that this method could serve as a straightforward, powerful, and generally applicable means of investigating the temperature dependence of material properties from first principles.

To assess the accuracy of hybrid functional and many-body GW methods, we study the band offsets for a set of lattice-matched semiconductor heterojunctions, including AlAs/GaAs(100), AlP/GaP(100), Si/GaP(110), Ge/GaAs(110), Ge/AlAs(110), Ge/ZnSe(110), and ZnSe/GaAs(110). The band-edge positions are first obtained for the bulk semiconductors and then aligned through the lineup of a local reference potential at the interface. The band-edge positions critically depend on the electronic-structure method, while the interface dipole is already well accounted for with semilocal density functionals. The two advanced electronic-structure schemes yield consistent valence-band offsets in close agreement with experiment, slightly improving upon semilocal functionals. At variance, conduction-band offsets are subject to larger deviations and improve with the accuracy of the calculated band gaps. In case one is willing to take band gaps from experiment, the best description of the band alignment for the present heterojunctions is achieved by relying on the calculated valence band offsets rather than on hybrid functionals in which the exchange mixing parameter is adjusted.

We report first-principle atomistic simulations of the effect of local strain gradients on the nanoscale domain morphology of free-standing ${\mathrm{PbTiO}}_3$ ultrathin films. First, the ferroelectric properties of free films at the atomic level are reviewed. For the explored thicknesses (10 to 23 unit cells), we find flux-closure domain structures whose morphology is thickness dependent. A critical value of 20 unit cells is observed: thinner films show structures with ${90}^{\circ }$ domain loops, whereas thicker ones develop, in addition, ${180}^{\circ }$ domain walls, giving rise to structures of the Landau-Lifshitz type. When a local and compressive strain gradient at the top surface is imposed, the gradient is able to switch the polarization of the downward domains, but not to the opposite ones. The evolution of the domain pattern as a function of the strain gradient strength consequently depends on the film thickness. Our simulations indicate that in thinner films, first the ${90}^{\circ }$ domain loops migrate towards the strain-gradient region, and then the polarization in that zone is gradually switched. In thicker films, instead, the switching in the strain-gradient region is progressive, not involving domain-wall motion, which is attributed to less mobile ${180}^{\circ }$ domain walls. The ferroelectric switching is understood based on the knowledge of the local atomic properties, and the results confirm that mechanical flexoelectricity provides a means to control the nanodomain pattern in ferroelectric systems.

The phonon dispersions of the bcc and fcc phases of pure iron ($\alpha$-Fe, $\gamma$-Fe, and $\delta$-Fe) at ambient pressure were investigated close to the respective phase transition temperatures. In the open bcc structure the transverse phonons along T${}_1\left[\xi \xi 0\right]$ and T${}_1\left[\xi \xi 2\xi \right]$ are of particularly low energy. The eigenvectors of these phonons correspond to displacements needed for the transformation to the fcc $\gamma$ phase. Especially these phonons, but also all other phonons, soften considerably with increasing temperature. Comparing thermodynamic properties of the fcc and the two bcc phases it is shown that the high-temperature bcc phase is stabilized predominantly by vibrational entropy, whereas for the stabilization of the fcc phase electronic entropy provides an equal contribution.

The proximity effect refers to the phenomenon whereby superconducting properties are induced in a normal conductor that is in contact with an intrinsically superconducting material. In particular, the combination of nanostructured semiconductors with bulk superconductors is of interest because these systems can host unconventional electronic excitations such as Majorana fermions when the semiconductor's charge carriers are subject to a large spin-orbit coupling. The latter requirement generally favors the use of hole-doped semiconductors. On the other hand, basic symmetry considerations imply that states from typical simple-metal superconductors will predominantly couple to a semiconductor's conduction-band states and, therefore, in the first instance generate a proximity effect for band electrons rather than holes. In this article, we show how the superconducting correlations in the conduction band are transferred also to hole states in the valence band by virtue of interband coupling. A general theory of the superconducting proximity effect for bulk and low-dimensional hole systems is presented. The interplay of interband coupling and quantum confinement is found to result in unusual wave-vector dependencies of the induced superconducting gap parameters. One particularly appealing consequence is the density tunability of the proximity effect in hole quantum wells and nanowires, which creates new possibilities for manipulating the transition to nontrivial topological phases in these systems.

The diamagnetism is an essential property of all superconductors. However, we will show that small topological (or unconventional) superconductors can be intrinsically paramagnetic by solving the quasiclassical Eilenberger equation and the Maxwell equation self-consistently on two-dimensional superconducting disks in weak magnetic fields. Because of the topologically nontrivial character of the wave function, the unconventional superconductors host the zero-energy surface Andreev bound states, which always accompany so-called odd-frequency Cooper pairs. The paramagnetic property of the odd-frequency pairs explains the paramagnetic response of the disks at low temperature.

Using density functional theory (DFT) within the local density approximation (LDA), we calculate the physical and electronic properties of ${\text{PbTiO}}_3$ (PTO) and a series of hypothetical compounds ${\text{PbTiO}}_{3-x}{\text{S}}_x$ $x=0.2$, 0.25, 0.33, 0.5, 1, 2, and 3 arranged in the corner-sharing cubic perovskite structure. We determine that replacing the apical oxygen atom in the PTO tetragonal unit cell with a sulfur atom reduces the $x=0$ LDA calculated band gap of 1.47 eV to 0.43–0.67 eV for $x=0.2$–1 and increases the polarization. PBE0 and $GW$ methods predict that the compositions $x=0.2$–2 will have band gaps in the visible range. For all values of $x$ < 2, the oxysulfide perovskite retains the tetragonal phase of ${\text{PbTiO}}_3$, and the $a$ lattice parameter remains within 2.5% of the oxide. Thermodynamic analysis indicates that chemical routes using high-temperature gas, such as ${\text{H}}_2$S and ${\text{CS}}_2$, can be used to substitute O for S in PTO for the compositions $x=0.2$–0.5.

We address the nature and possible observable consequences of singular one-electron states that appear when strong defects are introduced in the metallic family of graphene, namely, metallic carbon nanotubes and nanotori. In its simplest form, after creating two defects on the same sublattice, a state may emerge at the Fermi energy presenting very unusual properties: It is unique, normalizable, and features a wave function equally distributed around both defects. As a result, the exchange coupling between the magnetic moments generated by the two defects is anomalous. The intrinsic spins couple ferromagnetically, as expected, but do not present an antiferromagnetic excited state at any distance. We propose the use of metallic carbon nanotubes as an electronic device based on this anomalous coupling between spins which can be useful for the robust transmission of magnetic information at large distances.

In thin topological insulator (TI) films, the top and bottom surfaces are coupled by tunneling, which restores backscattering and strongly affects screening. We calculate the dielectric function in the random phase approximation obtaining a closed-form result. Unlike independent TI surfaces, the dielectric function of thin films exhibits a valley as a function of wave number $q$ and tunneling, as well as a cusp at $q=2k_F$, with $k_F$ the Fermi wave vector. As a result of the cusp, Friedel oscillations decay with distance $r$ as $sin\left(2k_{F}r\right)/{\left(2k_{F}r\right)}^2$. We determine the longitudinal conductivity $\sigma$ in the first Born approximation at low temperatures where screened impurities provide the dominant scattering mechanism. At high electron densities $n_e$, $\sigma \propto n_e$, while at low densities $\sigma \propto n_e^{3/2}$.

We study the transverse spin-Seebeck effect (SSE) on the surface of a three-dimensional topological insulator (TI) thin film, such as Bi${}_2$Se${}_3$, which is sandwiched between two normal metal leads. The temperature bias $\Delta T$ applied between the leads generates surface charge current which becomes spin polarized due to strong spin-orbit coupling on the TI surface, with polarization vector acquiring a component $P_x\simeq 60\%$ parallel to the direction of transport. When the third nonmagnetic voltage probe is attached to the portion of the TI surface across its width $L_y$, pure spin current will be injected into the probe where the inverse spin Hall effect (ISHE) converts it into a voltage signal $|V_{\mathrm{ISHE}}{|}^{\max }/\Delta T\simeq 2.5\mu$V/K (assuming the SH angle of the Pt voltage probe and $L_y=1$ mm). The existence of predicted nonequilibrium spin polarization parallel to the direction of electronic transport and the corresponding electron-driven SSE crucially relies on orienting quintuple layers (QLs) of Bi${}_2$Se${}_3$ orthogonal to the TI surface and tilted by ${45}^{\circ }$ with respect to the direction of transport. Our analysis is based on the Landauer–Büttiker-type formula for spin currents in the leads of a multiterminal quantum-coherent junction, which is constructed by using nonequilibrium Green function formalism within which we show how to take into account arbitrary orientation of QLs via the self-energy describing coupling between semi-infinite normal metal leads and the TI sample.

Gadolinium nitride (GdN) nanocontacts were recently experimentally shown to be efficient spin filters. Our study is aimed at identifying and analyzing the physical processes responsible for the high spin polarization of the tunneling current in GdN nanostructures. By the example of planar contacts and atomic chains attached to Cu electrodes we assert, using first principle techniques, that a 100% spin-filtering effect can be indeed achieved in GdN nanocontacts. Our analysis shows that the spin filtering is due to the predominant role of nitrogen majority $p$ states in the electron transport, while minority conductance decays exponentially with contact size due to the presence of a minority band gap at the Fermi level. Additionally, GdN zigzag infinite chains are found to be as efficient spin filters as their planar contact counterparts, also exhibiting a 100% spin-filtering effect, which is robust against chain geometry changes.

By exactly analyzing the spin-$\frac{1}{2}$ Luttinger liquid (LL) and numerically solving a model of a mobile impurity electron in the LL, we obtain the one-electron spectral function $A(p,\omega )$ in a one-dimensional metal in an entire range of $p$ at zero temperature. For $\left|p\right|$ near the Fermi point $p_{\mathrm{F}}$, $A(p,\omega )$ is featured by two prominent peaks of spinon and (anti)holon representing spin-charge separation, but we also find an additional cusp structure between them. For $\left|p\right|\gg p_{\mathrm{F}}$, this structure evolves as a main peak in $A(p,\omega )$ by swallowing the antiholon mode and its dispersion relation approaches that of a free electron, implying the existence of an electron excitation in the whole region, but not quite a quasiparticle in the Fermi liquid due to ever existing power-law decay of the excitation.

It is shown that topological insulating phases driven by interactions can be realized without the need for spin-orbit coupling or large intersite interaction in a two-dimensional system of spin-$\frac{1}{2}$ fermions with a single pair of parabolically touching bands. Using a weak-coupling, Wilsonian renormalization group procedure, we show that a quantum anomalous Hall phase is realized for Hubbard interaction, while a quantum spin Hall phase is favored for longer-ranged interactions.

The toroidal dipole is a peculiar electromagnetic excitation that can not be presented in terms of standard electric and magnetic multipoles. A static toroidal dipole has been shown to lead to violation of parity in atomic spectra and many other unusual electromagnetic phenomena. The existence of electromagnetic resonances of toroidal nature was experimentally demonstrated only recently, first in the microwave metamaterials, and then at optical frequencies, where they could be important in spectroscopy analysis of a wide class of media with constituents of toroidal symmetry, such as complex organic molecules, fullerenes, bacteriophages, etc. Despite the experimental progress in studying toroidal resonances, no direct link has yet been established between microscopic toroidal excitations and macroscopic scattering characteristics of the medium. To address this essential gap in the electromagnetic theory, we have developed an analytical approach for calculating the transmissivity and reflectivity of thin slabs of materials that exhibit toroidal dipolar excitations.

Our primary goal is to provide a rigorous treatment of scattering nonlocality in semiconductor nanostructures. On the one hand, starting from the conventional density-matrix formulation and employing as ideal instrument for the study of the semiclassical limit the well-known Wigner-function picture, we shall perform a fully quantum-mechanical derivation of the space-dependent Boltzmann equation. On the other hand, we shall examine the validity limits of such semiclassical framework, pointing out, in particular, regimes where scattering-nonlocality effects may play a relevant role; to this end we shall supplement our analytical investigation with a number of simulated experiments, discussing and further expanding preliminary studies of scattering-induced quantum diffusion in GaN-based nanomaterials. As for the case of carrier-carrier relaxation in photoexcited semiconductors, our analysis will show the failure of simplified dephasing models in describing phonon-induced scattering nonlocality, pointing out that such limitation is particularly severe for the case of quasielastic dissipation processes.

We use density functional theory to calculate the electronic band structures, cohesive energies, phonon dispersions, and optical absorption spectra of two-dimensional In${}_2$$X_2$ crystals, where X is S, Se, or Te. We identify two crystalline phases ($\alpha$ and $\beta$) of monolayers of hexagonal In${}_2$$X_2$, and show that they are characterized by different sets of Raman-active phonon modes. We find that these materials are indirect-band-gap semiconductors with a sombrero-shaped dispersion of holes near the valence-band edge. The latter feature results in a Lifshitz transition (a change in the Fermi-surface topology of hole-doped In${}_2$$X_2$) at hole concentrations $n_{\mathrm{S}}=6.86\times {10}^{13}$ cm${}^{-2}$, $n_{\mathrm{Se}}=6.20\times {10}^{13}$ cm${}^{-2}$, and $n_{\mathrm{Te}}=2.86\times {10}^{13}$ cm${}^{-2}$ for X=S, Se, and Te, respectively, for $\alpha$-In${}_2$$X_2$ and $n_{\mathrm{S}}=8.32\times {10}^{13}$ cm${}^{-2}$, $n_{\mathrm{Se}}=6.00\times {10}^{13}$ cm${}^{-2}$, and $n_{\mathrm{Te}}=8.14\times {10}^{13}$ cm${}^{-2}$ for $\beta$-In${}_2$$X_2$.

We investigate the effect of ring exchange on the ground-state properties and magnetic excitations of the $S=1/2$ Heisenberg model on the anisotropic triangular lattice with ring exchange at $T=0$ using linear spin-wave theory. Classically, we find stable Néel, spiral and collinear magnetically ordered phases. Upon including quantum fluctuations to the model, linear spin-wave theory shows that ring exchange induces a large quantum disordered region in the phase diagram, completely wiping out the classically stable collinear phase. Analysis of the spin-wave spectra for each of these three models demonstrates that the large spin-liquid phase observed in the full model is a direct manifestation of competing classical orders. To understand the origin of these competing phases, we introduce models where either the four spin contributions from ring exchange, or the renormalization of the Heisenberg terms due to ring exchange are neglected. We find that these two terms favor rather different physics.