We present the results of theoretical study of surface state properties in a two-dimensional model for triplet $p$-wave superconductors. We derive boundary conditions for Eilenberger equations at rough interfaces and develop the approach for self-consistent solution for the spatial dependence of $p_x$- and $p_x+i{p}_y$-wave pair potentials. In the $p_x$ case we demonstrate the robustness of the zero-energy peak in the density of states (DoS) with respect to surface roughness, in contrast to the suppression of such a peak in the case of $d_{xy}$ symmetry. This effect is due to stability of odd-frequency pairing state at the surface with respect to disorder. In the case of the chiral $p_x+i{p}_y$ state we demonstrate the appearance of a complex multipeak subgap structure in the spectrum with increasing surface roughness.

Motivated by the unusual evolution of magnetic phases in stoichiometric and Co-doped ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$, we study Heisenberg models with competing ferromagnetic and antiferromagnetic ordering combined with competing anisotropies in exchange interactions and $g$ factors. Utilizing large-scale classical Monte Carlo simulations, we analyze the ingredients required to obtain the characteristic crossing point of uniform susceptibilities observed experimentally near the ferromagnetic ordering of $\mathrm{Yb}\left({\mathrm{Rh}}_{0.73}{\mathrm{Co}}_{0.27}\right){}_2{\mathrm{Si}}_2$. The models possess multicritical points, which we speculate to be relevant for the behavior of clean as well as doped ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$. We also make contact with experimental data on ${\mathrm{YbNi}}_4{\mathrm{P}}_2$, where a similar susceptibility crossing has been observed.

We derive a closed-form expression for the quantum corrections to the kinetic energy density in the Thomas-Fermi limit of a linear potential model system in three dimensions (the Airy gas). The universality of the expression is tested numerically in a number of three-dimensional model systems: (i) jellium surfaces, (ii) confinement in a hydrogenlike potential (the Bohr atom), (iii) particles confined by a harmonic potential in one and (iv) all three dimensions, and (v) a system with a cosine potential (the Mathieu gas). Our results confirm that the usual gradient expansion of extended Thomas-Fermi theory does not describe the quantum oscillations for systems that incorporate surface regions where the electron density drops off to zero. We find that the correction derived from the Airy gas is universally applicable to relevant spatial regions of systems of types (i), (ii), and (iv), but somewhat surprisingly not (iii). We discuss possible implications of our findings to the development of functionals for the kinetic energy density.

We consider the Kane-Mele-Hubbard model with a magnetic $\pi$ flux threading each honeycomb plaquette. The resulting model has remarkably rich physical properties. In each spin sector, the noninteracting band structure is characterized by a total Chern number $C=\pm 2$. Fine-tuning of the intrinsic spin-orbit coupling $\lambda$ leads to a quadratic band crossing point associated with a topological phase transition. At this point, quantum Monte Carlo simulations reveal a magnetically ordered phase that extends to weak coupling. Although the spinful model has two Kramers doublets at each edge and is explicitly shown to be a $Z_2$ trivial insulator, the helical edge states are protected at the single-particle level by translation symmetry. Drawing on the bosonized low-energy Hamiltonian, we predict a correlation-induced gap as a result of umklapp scattering for half-filled bands. For strong interactions, this prediction is confirmed by quantum Monte Carlo simulations.

We show how to generalize the concepts of identifying and classifying symmetry protected topological phases in 1D to the case of an arbitrary mixed state. The pure-state concepts are reviewed using a concrete spin-1 model. For the mixed-state setup, we demonstrate our findings numerically using matrix product state algorithms. Starting from the ground state and applying various types of noise sources, we find a transient regime where the system is driven out of equilibrium while retaining its topological properties.

So far, it represents a challenging task to reproduce angle-resolved photoelectron (ARPES) spectra of epitaxial silicene by first-principles calculations. Here, we report on the resolution of the previously controversial issue related to the structural configuration of silicene on the $\mathrm{Zr}{\mathrm{B}}_2$(0001) surface and its band structure. In particular, by representing the band structure in a large Brillouin zone associated with a single Si atom, it is found that the imaginary part of the one-particle Green's function follows the spectral weight observed in ARPES spectra. By additionally varying the in-plane lattice constant, the results of density functional theory calculations and ARPES data obtained in a wide energy range converge into the “planarlike” phase and provide the orbital character of electronic states in the vicinity of the Fermi level. It is anticipated that the choice of a smaller commensurate unit cell for the representation of the electronic structure will be useful for the study of epitaxial two-dimensional materials on various substrates in general.

There is no assurance that interface states can be found at the boundary separating two materials. While a strong perturbation typically favors wave localization, we show on the contrary that in some two-dimensional photonic crystals (PCs) possessing a Dirac-like cone at k = 0 derived from monopole and dipoles excitation, a small perturbation is sufficient to create interface states. The conical dispersion together with the flat band at the zone center generates the existence of gaps in the projected band structure and the existence of single mode interface states inside the projected band gaps stems from the geometric phases of the bulk bands. The underlying physics for the existence of an interface state is related to the sign change of the surface impedance in the gaps above and below the flat band. The established results are applicable for long wavelength regimes where there is only one propagating diffraction order for an interlayer scattering.

Atomistic tight-binding calculations show that two-dimensional topological insulators can be obtained using Ge or Ge/Si nanotechnologies. The strong quantum confinement is used to open energy gaps in the valence band of artificial graphene made of Ge. These gaps are topologically nontrivial due to the combination of the honeycomb nanogeometry and the spin-orbit coupling. Gap widths above 10 meV can be obtained using realistic structures. With light effective masses, a strong spin-orbit coupling, and a high compatibility with microelectronic processes, Ge is an excellent substrate for the fabrication of spintronic devices based on topological insulator states.

We investigate the conductance of an Aharonov-Bohm (AB) interferometer coupled to a quantum dot and two Majorana bound states on the edge of the topological superconductor with finite length. When the tunnel couplings between the Majorana bound states and the Aharonov-Bohm interferometer are fixed to the specific phase, the differential conductance becomes zero irrespective of all the parameters as long as the hoppings to the two Majorana fermions on the opposite side are equal. The conductance at the zero bias voltage does not change with the magnetic flux penetrating the ring for all cases. When the energy level of the quantum dot is equal to the energy of the Majorana bound states, the AB oscillation shows $\pi$ periodicity due to the particle-hole symmetry. The breaking of the time-reversal symmetry of the topological superconductor results in $2\pi$ periodicity of the AB oscillation for the specific phase of the tunnel coupling while the time-reversal symmetry breaking leads to the mixing of the triplet and singlet states in the quantum dot in another specific phase.

Symmetry protected quantization of the Berry phase is discussed in relation to edge states. Assuming the existence of an adiabatic process that protects the quantization of the Berry phase, a nontrivial Berry phase $\gamma \propto 2\pi \rho$ ($\rho$ is the local filling of particles) for the bulk suggests appearance of edge states with boundaries. We have applied this generic consideration for the Bloch states of a two-dimensional model with massless Dirac fermions where $\gamma =\pm \pi /2$ implies the edge states. The entanglement entropy is evaluated for the models and its relation to the bulk-edge correspondence of Dirac fermions is discussed as well.

Binary information encoded within the spin of carriers can be transferred into corresponding right- or left-handed circularly polarized photons emitted from an active semiconductor medium via carrier-photon angular momentum conversion. In order to attain maximized spin injection at out-of-plane magnetic remanence, a number of material systems have been explored as possible solid-state spin injectors. However, the circular polarization $\left(P_{\mathrm{C}}\right)$ of emitted light was still limited at 3–4% at remanence. Here, we demonstrate a sizable electroluminescence circular polarization from a III-V-based spin light-emitting diode at zero magnetic field with a perpendicular spin injector consisting of an ultrathin CoFeB ferromagnetic layer (1.2 nm) grown on a MgO tunnel barrier (2.5 nm). The maximum value of $P_{\mathrm{C}}$ measured at zero field is as large as 20% at 25 K and still 8% at 300 K. These types of ultrathin perpendicular spin injectors are of great interest (i) to realize the electrical switching of the magnetization of the injector layer owing to the advanced spin-transfer torque properties of the CoFeB layer and (ii) to be directly embedded in optical cavities for spin lasers due to their very low optical absorption loss.

We address the nature of the disordered state that results from the adsorption of adatoms in graphene. For adatoms that sit at the center of the honeycomb plaquette, as in the case of most transition metals, we show that the ones that form a zero-energy resonant state lead to Anderson localization in the vicinity of the Dirac point. Among those, we show that there is a symmetry class of adatoms where Anderson localization is suppressed, leading to an exotic metallic state with large and rare charge droplets, that localizes only at the Dirac point. We identify the experimental conditions for the observation of the Anderson transition for adatoms in graphene.

Based on first-principles calculations, we predict two new thermodynamically stable layered-phases of silicon, named as silicites, which exhibit strong directionality in the electronic and structural properties. As compared to silicon crystal, they have wider indirect band gaps but also increased absorption in the visible range making them more interesting for photovoltaic applications. These stable phases consist of intriguing stacking of dumbbell patterned silicene layers having trigonal structure with $\sqrt{3}\times \sqrt{3}$ periodicity of silicene and have cohesive energies smaller but comparable to that of the cubic diamond silicon. Our findings also provide atomic scale mechanisms for the growth of multilayer silicene as well as silicites.

We show that quantum oscillations of the magnetization can occur when the Fermi surface consists of points (massless Dirac points) or even when the chemical potential is in an energy gap by studying tight-binding electrons on a honeycomb lattice in a uniform magnetic field. The quantum oscillations of the magnetization as a function of the inverse magnetic field are known as de Haas–van Alphen (dHvA) oscillations and the frequency is proportional to the area of the Fermi surface. The dominant period of the oscillations shown in this paper corresponds to the area of the first Brillouin zone and its phase is zero. The origin of these quantum oscillations is the characteristic magnetic field dependence of the energy known as the Hofstadter butterfly and the Harper broadening of Landau levels. These oscillations are not caused by the crossing of the chemical potential and Landau levels, which is the case in dHvA oscillations. These oscillations can be observed experimentally in systems with a large supercell such as a graphene antidot lattice or ultracold atoms in an optical lattice at an external magnetic field of a few Tesla when the area of the supercell is ${10}^4$ times larger than that of graphene.

The Bradley-Shipman theory explains the genesis of the highly ordered hexagonal arrays of nanodots that can result from normal-incidence ion bombardment of a binary material [R. M. Bradley and P. D. Shipman, Phys. Rev. Lett. 105, 145501 (2010)]. To facilitate experimental testing of the theory, we generalize it to oblique-incidence bombardment with two diametrically opposed beams. Using analytical methods valid in the weakly nonlinear regime and computer simulations, we demonstrate that an unusual “dots-on-ripples” topography can emerge for nonzero angles of ion incidence $\theta$. In such a pattern, nanodots arranged in a hexagonal array sit atop a ripple topography. We find that if dots-on-ripples are supplanted by surface ripples as $\theta$ or the ion energy are varied, the transition is continuous rather than hysteretic.

Ferromagnet/graphene (F/Gr) junctions are important building blocks for graphene spintronics. While simple models of spin injection are very successful for macroscopic metallic junctions, they reveal many deficiencies in describing F/Gr junctions. First-principles methods are key to assess such Gr-based junctions, but the computational cost is often too high. We focus on Ni(111)/Gr junctions and include van der Waals interactions from first principles, crucial for their correct description. We formulate a computationally inexpensive model to examine the nonuniformity and bias dependence of spin injection and elucidate proximity effects using spin polarization maps. Our results could extend the applicability of simple spin injection models in F/Gr junctions.

High-throughput density functional theory (DFT) calculations have been performed on the Li-Si and Li-Ge systems. Lithiated Si and Ge, including their metastable phases, play an important technological role as Li-ion battery (LIB) anodes. The calculations comprise structural optimizations on crystal structures obtained by swapping atomic species to Li-Si and Li-Ge from the $X-Y$ structures in the International Crystal Structure Database, where $X=\left\{\text{Li,}\text{Na,}\text{K,}\text{Rb,}\text{Cs}\right\}$ and $Y=\left\{\text{Si,}\text{Ge,}\text{Sn,}\text{Pb}\right\}$. To complement this at various Li-Si and Li-Ge stoichiometries, ab initio random structure searching (AIRSS) was also performed. Between the ground-state stoichiometries, including the recently found ${\mathrm{Li}}_{17}{\mathrm{Si}}_4$ phase, the average voltages were calculated, indicating that germanium may be a safer alternative to silicon anodes in LIB due to its higher lithium insertion voltage. Calculations predict high-density ${\mathrm{Li}}_1{\mathrm{Si}}_1$ and ${\mathrm{Li}}_1{\mathrm{Ge}}_1$ $P4/mmm$ layered phases which become the ground states above 2.5  and 5 GPa, respectively, and reveal silicon and germanium's propensity to form dumbbells in the ${\mathrm{Li}}_x\mathrm{Si}$, $x=2.33$–3.25, stoichiometry range. DFT predicts the stability of the ${\mathrm{Li}}_{11}{\mathrm{Ge}}_6$ $Cmmm$, ${\mathrm{Li}}_{12}{\mathrm{Ge}}_7$ $Pnma$, and ${\mathrm{Li}}_7{\mathrm{Ge}}_3$ $P{32}_{1}2$ phases and several new Li-Ge compounds, with stoichiometries ${\mathrm{Li}}_5{\mathrm{Ge}}_2$, ${\mathrm{Li}}_{13}{\mathrm{Ge}}_5$, ${\mathrm{Li}}_8{\mathrm{Ge}}_3$ and ${\mathrm{Li}}_{13}{\mathrm{Ge}}_4$.

We report on the spin dynamics and discovery of magnetoelectricity in the coupled-spin tetrahedral compound ${\mathrm{Cu}}_2{\mathrm{Te}}_2{\mathrm{O}}_5{\mathrm{Cl}}_2$. ${}^{125}\mathrm{Te}$ NMR measurements show an anomalous resonance frequency shift and a signal wipe-out phenomenon around the Néel temperature $T_N$ = 18.2 K, which could be attributed to the anomalous critical slowing down of the Cu spin fluctuations on the NMR time scale ($\sim 10$–100 MHz). The critical exponent of ${\left(T_{1}T\right)}^{-1}\propto {(T-T_N)}^{-\alpha }$ is 0.40 ± 0.03, as compared to 0.5 for a three-dimensional mean-field model. This is in contrast to the Br compound [S.-H. Baek et al., Phys. Rev. B 86, 180405 (2012)], which exhibits pronounced singlet dynamics with a large spin gap. Electric polarization ($P_{\mathrm{c}}$) is observed along the $c$ axis for temperatures below $T_N$ under finite magnetic field but not sensitive to the electric poling. $P_{\mathrm{c}}$ increases sharply over zero to 2 T and then reaches saturation. Below $T_N{}_{,}$ $P_{\mathrm{c}}$ changes its sign depending on the applied magnetic field direction, positive for the $H\perp c$ axis and negative for $H$ ∥ $c$ axis. We discuss possible explanations for the observed magnetoelectric (ME) behavior in terms of linear ME effect, spin-driven multiferroicity, and an exchange striction of intertetrahedral exchange paths involving the ${\mathrm{Te}}^{4+}$ lone-pair ions. Our results suggest that ${\mathrm{Cu}}_2{\mathrm{Te}}_2{\mathrm{O}}_5{\mathrm{Cl}}_2$ is a type of ME material whose properties are tuned by intertetrahedral exchange interactions involving polarizable ${\mathrm{Te}}^{4+}$ ions.

Pyrochlore iridates have recently attracted growing interest in condensed matter physics because of their potential for realizing new topological states. In order to achieve such quantum states, it is essential to understand the magnetic properties of these compounds, as their electronic structures are strongly coupled with their magnetic ground states. In this work, we report a systematic study of the magnetic properties of pyrochlore ${\mathrm{Y}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ and its hole-doped compounds by performing magnetic, electron spin resonance, electrical transport, and x-ray photoelectron spectroscopy (XPS) measurements. We demonstrate the existence of weak ferromagnetism on top of a large antiferromagnetic background in the undoped compound. Hole doping by calcium was found to enhance both the ferromagnetism and the electrical conductivity. The XPS characterization shows the coexistence of ${\mathrm{Ir}}^{4+}$ and ${\mathrm{Ir}}^{5+}$ in the undoped compound, and the amount of ${\mathrm{Ir}}^{5+}$ increases with Ca doping, which highlights the possible origins of the weak ferromagnetism associated with the formation of ${\mathrm{Ir}}^{5+}$. We also observe a vertical shift in the $M-H$ curves after field cooling, which may arise from a strong coupling between the ferromagnetic phase and the antiferromagnetic background.