We show that a topologically trivial zero-bias conductance peak is produced in semiconductor-superconductor hybrid structures due to a suppressed superconducting pair potential and/or an excess Zeeman field at the ends of the heterostructure, both of which can occur in experiments. The zero-bias peak (ZBP) (a) appears above a threshold parallel bulk Zeeman field, (b) is stable for a range of bulk field before splitting, (c) disappears with rotation of the bulk Zeeman field, and (d) is robust to weak disorder fluctuations. The topologically trivial ZBPs are also expected to produce splitting oscillations with the applied field similar to those from Majorana fermions. Because of such strong similarity with the phenomenology expected from Majorana fermions, we find that the only unambiguous way to distinguish these trivial ZBPs (of height $4e^2/h$) from those arising from Majorana fermions (of height $2e^2/h$) is by comparing the (zero-temperature) peak height and/or through an interference experiment.

The internal structure of neutral 180${}^{\circ }$ domain walls in perovskite-type ferroelectrics is studied in terms of Landau theory taking into account electromechanical coupling. The study is focused on the wall bistability, a factor of potential interest for information storage. A strong impact of elastic effects on the wall structure is demonstrated. It is shown that the conclusion derived earlier by Houchmandzadeh et al. [J. Phys.: Condens. Matter 3, 5163 (1991)], neglecting the electrostictive coupling, that all the domain walls near the boundary between two ordered phases become bistable may not hold due to the elastic effects. Criteria for domain-wall bistability are formulated in terms of the materials thermodynamic properties and the wall orientation. The obtained general results are applied to the analysis of bistability of 180${}^{\circ }$ domain walls in Pb(Zr${}_c$,Ti${}_{1-c}$)O${}_3$ near the tetragonal-rhombohedral morphotropic boundary. It is shown that, on the tetragonal side, the electrostrictive interaction suppresses the wall bistability that was predicted in terms of the theory neglecting the elastic effects. On the rhombohedral side, the domain walls are found bistable or not depending on the anisotropy of the correlation energy, the information on which is not presently available. It is also shown that, in the rhombohedral phase, the anisotropy of the correlation energy results in appearance of additional polarization component in the plane of the wall.

Solid-state phase transitions in SiC are investigated using diffuse x-ray scattering and Monte Carlo simulations. As an example, the 3C-6H transformation is investigated in detail. The transformation is modeled with a statistical algorithm based on the concept of double cross-slipping and subsequent dissociation of basal plane dislocations. The corresponding diffuse x-ray scattering curves are calculated and quantitatively compared with experimental data obtained from 3C-SiC crystals annealed at high temperatures (1700–2100${}^{\circ }\mathrm{C}$). From the simulations, it is demonstrated that the transformation implies the multiplication and ordering of double and triple stacking faults (SFs). The transformation level and root-mean-squared strains associated with the dislocations are determined from the simulations. The defect structure formed during the transition can be rationalized by considering the relative energies of the SFs. Using an axial next-nearest-neighbor Ising interaction model we show that single SFs are not energetically favored, whereas the simultaneous occurrence of double and triple SFs implies that their relative energy difference remains below a critical value ($\sim$8–9%).

Local reversible structural changes in ${\mathrm{SrTiO}}_3$ single crystals in an external electric field are induced by oxygen redistribution. We present in situ x-ray diffraction measurements during and immediately after electroformation. Several reflections are monitored and show an elongation of the cubic unit cell of strontium titanate. Raman investigations verify that the expansion of the unit cell involves a transition from the centrosymmetric to a lower symmetry phase. During a complete formation cycle, including the hold time of the electric field and relaxation time without field, two different dynamics are observed for the reversible transitions from cubic symmetry to tetragonal distortion: a slow one during the increase of the lattice constant in field direction and a fast one after switching off the electric field. Based on the experimental data, we propose the formation of a polar strontium titanate unit cell at room temperature stabilized by the electric field, which is referred to as migration-induced field-stabilized polar phase.

Tetragonal piezoelectric copper metaborate CuB${}_2$O${}_4$ (space group $I\overline{4}2d$, $Z=12$) became a subject of active research during the last decade because it demonstrates unique magnetic, optical, and magnetooptical properties. We report results of the optical studies of polarized infrared reflection and transmission spectra and Raman back-scattering spectra in the range from 20 to 2500 cm${}^{-1}$. In accordance with the symmetry analysis, infrared studies allowed us to identify all polar $B_2\left(z\right)$, and $E\left(x,y\right)$ normal vibrational modes. Frequencies of all longitudinal (LO) and transverse (TO) optical phonons were determined by fitting the observed infrared reflection spectra. Raman measurements revealed the frequencies of the majority of nonpolar $A_1(xx,yy,zz)$ and $B_1(xx,yy)$ modes and polar $B_2\left(z\right)$ and $E\left(x,y\right)$ LO modes. We show that several groups of closely spaced spectral lines observed in the vibrational spectra of CuB${}_2$O${}_4$ can be considered as a result of the Davydov splitting, which takes place in the case of several equivalent molecular units in a primitive crystal cell. Multiphonon absorption in the range of 1200–2500 cm${}^{-1}$ was analyzed and a tentative assignment of some features was given. Ab initio calculations of all zone-center polar and nonpolar modes were performed using density functional theory (DFT). The computed frequency distribution is in a good agreement with observed line positions in the infrared and Raman spectra. All these results allowed us to suggest reliable identification of all zone-center phonon modes thus providing a firm basis for further experimental and theoretical studies of this material with complex crystal, magnetic, and electronic structures and fascinating physical properties.

We have developed a self-consistent scheme of generating variational basis based on the exact diagonalization, which can be applied efficiently to various types of electron-phonon systems. This scheme is quite general and brings down the size of the variational space by an order of magnitude or even more in some cases to reproduce the most precise ground state energies and correlation functions available in the literature. This method has enormous potential for application to systems with more electrons or in higher dimensions, which are still beyond the reach of exact diagonalization just because of the sheer size of their variational space needed to get reasonably convergent results.

Co${}_{10}$Ge${}_3$O${}_{16}$ crystallizes in an intergrowth structure featuring alternating layers of spinel and rock salt. Variable-temperature powder synchrotron x-ray and neutron diffraction, magnetometry, and heat capacity experiments reveal a magnetostructural transition at $T_{\mathrm{N}}=203$ K. This rhombohedral-to-monoclinic transition involves a slight elongation of the CoO${}_6$ octahedra along the apical axis. Below $T_{\mathrm{N}}$, the application of a large magnetic field causes a reorientation of the Co${}^{2+}$ Ising spins. This metamagnetic transition is first order as evidenced by a latent heat observed in temperature-dependent measurements. This transition is initially seen at $T=180$ K as a broad upturn in the $M$–$H$ near $H_{\mathrm{C}}=3.9$ T. The upturn sharpens into a kink at $T=120$ K and a “butterfly” shape emerges, with the transition causing hysteresis at high fields while linear and reversible behavior persists at low fields. $H_{\mathrm{C}}$ decreases as temperature is lowered and the loops at positive and negative fields merge beneath $T=20$ K. The antiferromagnetism is described by $k_{\mathrm{M}}=\left(00\frac{1}{2}\right)$ and below $T=20$ K a small uncompensated component with $k_{\mathrm{M}}=\left(000\right)$ spontaneously emerges. Despite the Curie-Weiss analysis and ionic radius indicating the Co${}^{2+}$ is in its high-spin state, the low-temperature $M$–$H$ trends toward saturation at $M_{\mathrm{S}}=1.0$ ${\mu }_{\mathrm{B}}$/Co. We conclude that the field-induced state is a ferrimagnet, rather than a $S=1/2$ ferromagnet. The unusual $H$–$T$ phase diagram is discussed with reference to other metamagnets and Co(II) systems.

The electronic structure and magnetic properties of pure and doped Fe${}_{16}$N${}_2$ systems have been studied in the local-density (LDA) and quasiparticle self-consistent $\mathit{GW}$ approximations. The $\mathit{GW}$ magnetic moment of pure Fe${}_{16}$N${}_2$ is somewhat larger compared to LDA but not anomalously large. The effects of doping on magnetic moment and exchange coupling were analyzed using the coherent potential approximation. Our lowest estimate of the Curie temperature in pure Fe${}_{16}$N${}_2$ is significantly higher than the measured value, which we mainly attribute to the quality of available samples and the interpretation of experimental results. We found that different Fe sites contribute very differently to the magnetocrystalline anisotropy energy (MAE), which offers a way to increase the MAE by small site-specific doping of Co or Ti for Fe. The MAE also increases under tetragonal strain.

Amorphous Eu${}_2$TiO${}_4$ and EuTiO${}_3$ have been studied by a combination of the Faraday effect in the visible region and polarization-dependent x-ray absorption spectroscopy at the Eu $M_{4,5}$ and $L_{2,3}$ edges to examine the role of Eu 4$f$-5$d$ exchange interactions on the ferromagnetic behavior. The bulk-sensitive x-ray absorption spectra (XAS) for Eu $L_{2,3}$ edges show that most of the europium ions are present as the divalent state in the amorphous Eu${}_2$TiO${}_4$ and EuTiO${}_3$. The Eu $M_{4,5}$ edge x-ray magnetic circular dichroism (XMCD) signals, measured for the amorphous Eu${}_2$TiO${}_4$, dramatically increase upon cooling through the Curie temperature (16 K) determined by a superconducting quantum interference device (SQUID) magnetometer. Sum-rule analysis of the XMCD at Eu $M_{4,5}$ edges measured at 10 K yields a 4$f$ spin magnetic moment of 6.6${\mu }_{\mathrm{B}}$ per Eu${}^{2+}$ ion. These results confirm that the ferromagnetic properties exclusively arise from 4$f$ spins of Eu${}^{2+}$. In addition, for both the amorphous Eu${}_2$TiO${}_4$ and EuTiO${}_3$, the temperature and magnetic-field dependence of Eu $L_{2,3}$ edge XMCD signals can be scaled with the corresponding magnetization measured by SQUID, indicating that the 5$d$ magnetic polarization of Eu${}^{2+}$ is involved in the process to cause the ferromagnetic interaction between Eu${}^{2+}$ ions. We further discuss the origin of ferromagnetism in the amorphous system on the basis of the energy diagram of Eu 4$f$ and 5$d$ levels deduced from the Faraday effect in the visible region. From the wavelength dependence of Faraday rotation angles of the amorphous EuO-TiO${}_2$ system in comparison with those of the divalent Eu chalcogenides as reported previously, it is found that the magnitude of crystal-field splitting of Eu 5$d$ levels in the former is on the same order as that in the latter, which explains an enhanced ferromagnetic exchange interaction between Eu 4$f$ and 5$d$ states.

We consider the magnetization dynamics induced by thermally induced spin transfer torques in thin Fe|MgO|Fe tunnel junctions. The magnetization dynamics is described by the Landau-Lifshitz-Gilbert equation, including the thermal torques as computed from first principles. We show that the angular skewness of the torques importantly modifies the dynamics, e.g., leading to different instability criteria.

We report evidence of large, nonlocal correlations between two spatially separated normal-metals in superconductor/normal-metal (SN) heterostructures, which manifest themselves as nonlocal voltage generated in response to a driving current. Unlike prior experiments in SN heterostructures, the nonlocal correlations are mediated not by a superconductor, but by a proximity-coupled normal-metal. The nonlocal correlations extend over relatively long length scales in comparison to the superconducting case. At very low temperatures, we find a reduction in the nonlocal voltage for small applied currents that cannot be explained by the quasiclassical theory of superconductivity, which we believe is a signature of new long-range quantum correlations in the system.

The orbital upper critical field $H_{c2}$ is evaluated for isotropic materials with arbitrary transport and pair-breaking scattering rates. It is shown that unlike transport scattering which enhances $H_{c2}$, the pair breaking suppresses the upper critical field and reduces the dimensionless ratio $h^{*}\left(0\right)=H_{c2}\left(0\right)/T_c{(d{H}_{c2}/dT)}_{T_c}$ from the Helfand-Werthamer value of $\approx 0.7$ to 0.5 for a strong pair breaking. $h^{*}\left(T\right)$ is evaluated for arbitrary transport and pair-breaking scattering. A phenomenological model for the pair-breaking suppression by magnetic fields is introduced. It shows qualitative features such as a positive curvature of $H_{c2}\left(T\right)$ and the low temperature upturn usually associated with multiband superconductivity.

We employ the Klemm-Clem transformations to map the equations of motion for the Green functions of a clean superconductor with a general ellipsoidal Fermi surface (FS) characterized by the effective masses $m_1,m_2$, and $m_3$ in the presence of an arbitrarily directed magnetic induction $\mathit{B}=B(\sin \theta \cos \varphi ,\sin \theta \sin \varphi ,\cos \theta )$ onto those of a spherical FS. We then obtain the transformed gap equation for a transformed pairing interaction $\tilde{V}(\widehat{\tilde{\mathit{k}}},{\widehat{\tilde{\mathit{k}}}}^{\prime })$ appropriate for any orbital order parameter symmetry. We use these results to calculate the upper critical induction $B_{c2}(\theta ,\varphi )$ for an orthorhombic ferromagnetic superconductor with transition temperatures $T_{\mathrm{Curie}}>T_c$. We assume the FS is split by strong spin-orbit coupling, with a single parallel-spin ($\uparrow \uparrow$) pairing interaction of the $p$-wave polar state form locked onto the ${\widehat{\mathit{e}}}_3$ crystal axis normal to the spontaneous magnetization ${\mathit{M}}_0\perp {\widehat{\mathit{e}}}_3$ due to the ferromagnetism. The orbital harmonic oscillator eigenvalues are modified according to $B\to B\alpha$, where $\alpha (\theta ,\varphi )=\sqrt{m_3/m}\sqrt{{\cos }^2\theta +{\gamma }^{-2}\left(\varphi \right){\sin }^2\theta }$, ${\gamma }^2\left(\varphi \right)=m_3/(m_1{\cos }^2\varphi +m_2{\sin }^2\varphi )$ and $m={\left(m_1{m}_2{m}_3\right)}^{1/3}$. At fixed $\varphi$, the order parameter anisotropy causes $B_{c2}$ to exhibit a novel $\theta$ dependence, which for ${\gamma }^2\left(\varphi \right)>3$ becomes a double peak at $0^{\circ }<{\theta }^{*}<{90}^{\circ }$ and at ${180}^{\circ }-{\theta }^{*}$, providing a sensitive bulk test of the order parameter orbital symmetry in both phases of URhGe and in similar compounds still to be discovered.

We establish the spectral line shape of orbital excitations created by resonant inelastic x-ray scattering for the model Mott insulator CoO. Improved experimental energy resolution reveals that the line shapes are strikingly different from expectations in a first-principles-based atomic multiplet model. Extended theoretical simulations are performed to identify the underlying physical origins, which include a pronounced thermal tail reminiscent of anti-Stokes scattering on the energy gain side of excitations, and an essential contribution from interatomic many-body dynamics on the energy loss side of excitations.

A theory of combined interference and interaction effects on the diffusive transport properties of 3D topological insulator surface states is developed. We focus on a slab geometry (characteristic for most experiments) and show that interactions between the top and bottom surfaces are important at not too high temperatures. We treat the general case of different surfaces (different carrier densities, uncorrelated disorder, arbitrary dielectric environment, etc.). In order to access the low-energy behavior of the system, we renormalize the interacting diffusive $\sigma$ model in the one loop approximation. It is shown that intersurface interaction is relevant in the renormalization group (RG) sense and the case of decoupled surfaces is therefore unstable. An analysis of the emerging RG flow yields a rather rich behavior. We discuss realistic experimental scenarios and predict a characteristic nonmonotonic temperature dependence of the conductivity. In the infrared (low-temperature) limit, the system flows into a metallic fixed point. At this point, even initially different surfaces have the same transport properties. Investigating topological effects, we present a local expression of the ${\mathbb{Z}}_2$ theta term in the sigma model by first deriving the Wess-Zumino-Witten theory for class DIII by means of non-Abelian bosonization and then breaking the symmetry down to AII. This allows us to study a response of the system to an external electromagnetic field. Further, we discuss the difference between the system of Dirac fermions on the top and bottom surfaces of a topological insulator slab and its nontopological counterpart in a double-well structure with strong spin-orbit interaction.

By means of density functional theory (DFT) calculations [with and without inclusion of spin-orbit (SO) coupling] we present a detailed study of the electronic structure and corresponding microscopic Hamiltonian parameters of Na${}_2$IrO${}_3$. In particular, we address the following aspects: (i) We investigate the role of the various structural distortions and show that the electronic structure of Na${}_2$IrO${}_3$ is exceptionally sensitive to structural details. (ii) We discuss both limiting descriptions for Na${}_2$IrO${}_3$—quasimolecular orbitals (small SO limit, itinerant) versus relativistic orbitals (large SO limit, localized)—and show that the description of Na${}_2$IrO${}_3$ lies in an intermediate regime. (iii) We investigate whether the nearest neighbor Kitaev-Heisenberg model is sufficient to describe the electronic structure and magnetism in Na${}_2$IrO${}_3$. In particular, we verify the recent suggestion of an antiferromagnetic Kitaev interaction and show that it is not consistent with actual or even plausible electronic parameters. Finally, (iv) we discuss correlation effects in Na${}_2$IrO${}_3$. We conclude that while the Kitaev-Heisenberg Hamiltonian is the most general expression of the quadratic spin-spin interaction in the presence of spin-orbit coupling (neglecting single-site anisotropy), the itinerant character of the electrons in Na${}_2$IrO${}_3$ makes other terms beyond this model (including, but not limited to, 2nd and 3rd neighbor interactions) essential.

The connection between the Fermi surface and charge-density-wave (CDW) order is revisited in 2$H$-TaSe${}_2$. Using angle-resolved photoemission spectroscopy, ab initio band-structure calculations, and an accurate tight-binding model, we develop the empirical $k$-resolved susceptibility function, which we use to highlight states that contribute to the susceptibility for a particular q vector. We show that although the Fermi surface is involved in the peaks in the susceptibility associated with CDW order, it is $\mathit{not}$ through conventional Fermi surface nesting, but rather through finite energy transitions from states located far from the Fermi level. Comparison with monolayer TaSe${}_2$ illustrates the different mechanisms that are involved in the absence of bilayer splitting.

We demonstrate that hidden long-range order is always present in the gapped phases of interacting fermionic systems on one dimensional lattices. It is captured by correlation functions of appropriate nonlocal charge and/or spin operators, which remain asymptotically finite. The corresponding microscopic orders are classified. The results are confirmed by DMRG numerical simulation of the phase diagram of the extended Hubbard model, and of a Haldane insulator phase.

The spin dynamics in chemically synthesized CdSe/CdS core/shell nanocrystals (NCs) are studied by polarization- and time-resolved photoluminescence (PL) techniques in high magnetic fields and at low temperatures. Analysis of the recombination dynamics shows that the emission of thin-shell NCs is contributed by neutral excitons, while for thick-shell NCs it is dominated by charged excitons (trions). The sign of the PL polarization unambiguously demonstrates that these trions are negatively charged. A theoretical model of the PL polarization in an ensemble of randomly oriented NCs describes well magnetic field and time dependences of the PL polarization degree and allows us to determine the hole $g$ factor in CdSe/CdS NCs, $g_h=-0.54$. From direct measurements of the spin relaxation rate dependences on magnetic field and temperature, we identify the mechanism of the negative trion spin relaxation as two-phonon-assisted Raman scattering between the hole spin sublevels mixed by the applied magnetic field.

We report the observation of dynamic nuclear polarization in a vertical double quantum dot, as a result of a hyperfine interaction with three confined electrons. Our data allow us to distinguish three pumping regimes, characterized by different magnitudes and directions of polarization. Corresponding electron-nuclear spin dynamics is understood by considering relevant three-electron states mixed by hyperfine interaction. Also, an extremely long nuclear spin relaxation time is reported.