Topologically ordered states are quantum states of matter with topological ground-state degeneracy and quasiparticles carrying fractional quantum numbers and fractional statistics. The topological spin ${\theta }_a=2\pi h_a$ is an important property of a topological quasiparticle, which is the Berry phase obtained in the adiabatic self-rotation of the quasiparticle by $2\pi$. For chiral topological states with robust chiral edge states, another fundamental topological property is the edge state chiral central charge $c$. In this paper we propose an approach to compute the topological spin and chiral central charge in lattice models by defining a quantity that we call the momentum polarization. Momentum polarization is defined on the cylinder geometry as a universal subleading term in the average value of a “partial translation operator.” We show that the momentum polarization is a quantum entanglement property which can be computed from the reduced density matrix, and our analytic derivation based on edge conformal field theory shows that the momentum polarization measures the combination $h_a-\frac{c}{24}$ of topological spin and central charge. Results are obtained for two example systems, the non-Abelian phase of the honeycomb lattice Kitaev model and the $\nu =1/2$ Laughlin state of a fractional Chern insulator described by a variational Monte Carlo wave function, which verify the analytic formula with high accuracy and further suggest that this result remains robust even when the edge states cannot be described by a conformal field theory. Our result provides an efficient approach to extract characteristic quantities of topological states of matter from finite size numerics.

Through relativistic photoemission calculations for the Au(111) surface state at the Fermi level, we study the photon energy dependence of circular dichroism. The dichromatic signal ($D_S$) pattern changes 23 times with photon energies between 7 and 100 eV, and we have found 13 different patterns in the $k_{\parallel }$ map at the Fermi level for the $D_S$ from the Au(111) surface state with normal incidence light. We show that the photon energy dependence of $D_S$ is very complex even in the simplest case. The sign change in the circular dichroism as a function of photon energy is related to the relative phases of the complex expansion coefficients of different outgoing partial waves in a time-reversed low-energy electron diffraction state. With off-normal incidence, the $z$ component of the incoming photon field is dominant, and the fine structure seen in the $D_S$ in the normal incidence case is lost very rapidly, moving from a normal to an off-normal incidence. We also report that the Rashba split surface state of Au(111) has a significant component of $d$-type orbital due to relativistic effects and the computational setup used.

An optical nanoantenna and adjacent atomic systems are strongly coupled when an excitation is repeatedly exchanged between these subsystems prior to its eventual dissipation into the environment. It remains challenging to reach the strong-coupling regime but it is equally rewarding. Once they are achieved, promising applications such as signal processing at the nanoscale and at the single-photon level would immediately become available. Here, we study such hybrid configuration from different perspectives. The configuration we consider consists of two identical atomic systems, described in a two-level approximation, which are strongly coupled to an optical nanoantenna. First, we investigate when this hybrid system requires a fully quantum description, and we provide a simple analytical criterion. Second, a design for a nanoantenna is presented that enables the strong-coupling regime. In addition to a vivid time evolution, the strong coupling is documented in experimentally accessible quantities, such as the extinction spectra. The latter are shown to be strongly modified if the hybrid system is weakly driven and operates in the quantum regime. We find that the extinction spectra depend sensitively on the number of atomic systems coupled to the nanoantenna.

Coupling a semiconducting nanowire to a microwave cavity provides a powerful means to assess the presence or absence of isolated Majorana fermions in the nanowire. These exotic bound states can cause a significant cavity frequency shift but also a strong cavity nonlinearity leading, for instance, to light squeezing. The dependence of these effects on the nanowire gate voltages gives direct signatures of the unique properties of Majorana fermions, such as their self-adjoint character and their exponential confinement.

We report on the observation of orbital excitations in YVO${}_3$ by means of resonant inelastic x-ray scattering (RIXS) at energies across the vanadium $L$${}_3$ and oxygen $K$ absorption edges. At the V $L$${}_3$ edge, we are able to resolve the full spectrum of orbital excitations up to 5 eV. In order to unravel the effect of superexchange interactions and the crystal field on the orbital excitations, we analyzed the energy and temperature dependence of the intra-$t_{2g}$ excitations at 0.1–0.2 eV in detail. While these results suggest a dominant influence of the crystal field, peak shifts of about 13–20 meV observed as a function of the transferred momentum $q\parallel a$ reflect a finite dispersion of the orbital excitations. This is puzzling since theoretical models based on superexchange interactions predict a dispersion only for $q\parallel c$. Furthermore, we demonstrate that RIXS at the O $K$ edge is very sensitive to intersite excitations. At the O $K$ edge, we observe excitations across the Mott-Hubbard gap and an additional feature at 0.4 eV, which we attribute to two-orbiton scattering, i.e., an exchange of orbitals between adjacent sites. Altogether, our results indicate that both superexchange interactions and the crystal field are important for a quantitative understanding of the orbital excitations in YVO${}_3$.

We study the supercritical instability in gapped graphene with two charged impurities separated by distance $R$ using the two-dimensional Dirac equation for electron quasiparticles. Attention is paid to a situation when charges of impurities are subcritical, whereas their total charge exceeds a critical one. The critical distance $R_{\mathrm{cr}}$ in the system of two charged centers is defined as that at which the electron bound state with the lowest energy reaches the boundary of the lower continuum. A variational calculation of the critical distance $R_{\mathrm{cr}}$ separating the supercritical $(R<R_{\mathrm{cr}})$ and subcritical $(R>R_{\mathrm{cr}})$ regimes is carried out. It is shown that the critical distance $R_{\mathrm{cr}}$ increases as the quasiparticle gap decreases. The energy and width of a quasistationary state as functions of the distance between two impurities are derived in the quasiclassical approximation.

Neutron scattering is used to investigate the single-ion spin and orbital excitations below the Mott-Hubbard gap in CoO. Three excitations are reported at $0.870\pm 0.009$ eV, $1.84\pm 0.03$, and $2.30\pm 0.15$ eV. These were parametrized within a weak crystal field scheme with an intraorbital exchange of $J\left(dd\right)=1.3\pm 0.2$ eV and a crystal field splitting $10Dq=0.94\pm 0.10$ eV. A reduced spin-orbit coupling of $\lambda =-0.016\pm 0.003$ eV is derived from dilute samples of Mg${}_{0.97}$Co${}_{0.03}$O, measured to remove effects due to spin exchange and structural distortion parameters which break the cubic phase degeneracy of the orbital excitations complicating the inelastic spectrum. The peak at 1.84 eV, while reported using resonant x-ray and optical techniques, was absent or weak for nonresonant x-ray experiments and overlaps with the expected position of a ${}^4{A}_2$ level. This transition is absent in the dipolar approximation but expected to have a finite quadrupolar matrix element that can be observed with neutron scattering techniques at larger momentum transfers. Our results agree with a crystal field analysis (in terms of Racah parameters and Tanabe-Sugano diagrams) and with previous calculations performed using local-density band theory for Mott insulating transition metal oxides. The results also demonstrate the use of neutron scattering for measuring dipole forbidden transitions in transition metal oxide systems.

Photonic crystals affect the photon emission of embedded emitters due to an altered local density of photon states (LDOS). We review the calculation of the LDOS from eigenmodes in photonic crystals and propose a rate equation model for fluorescent emitters to determine the changes in emission induced by the LDOS. We show how to calculate the modifications of three experimentally accessible characteristics: emission spectrum (spectral redistribution), emitter quantum yield, and fluorescence lifetime. As an example, we present numerical results for the emission of the dye Rhodamine B inside an opal photonic crystal. For such photonic crystals with small permittivity contrast, the LDOS is only weakly modified, resulting in rather small changes. We point out that in experiments, however, usually only part of the emitted light is detected, which can have a very different spectral distribution (e.g., due to a photonic band gap in the direction of detection). We demonstrate the calculation of this detected spectrum for a typical measurement setup. With this reasoning, we explain the previously not fully understood experimental observation that strong spectral modifications occurred, while at the same time only small changes in lifetime were found. With our approach, the mentioned effects can be quantitatively calculated for fluorescent emitters in any photonic crystal.

We present a dielectric charging model that combines ab initio calculations of trap levels with a continuum-level transport model and apply it to interpret charging currents in amorphous silicon nitride. Density functional theory calculations on an ensemble of structures predict a distribution of electron trap levels up to 1.8 eV below the conduction band edge and provide insight into the physical trapping mechanisms. Incorporating this information in the continuum model, as opposed to the standard approach of a single adjustable trap level, not only leads to a more accurate description of experimental current transients in metal-insulator-metal capacitors, but also to a more precise and physical determination of associated material properties such as metal-dielectric barrier height.

We present results of a detailed study on the electron dispersions and Fermi surface of lead telluride doped with 2% of thallium, which is a resonant impurity in PbTe. Using the Korringa-Kohn-Rostoker method with the coherent potential approximation (KKR-CPA), Bloch spectral functions (BSFs), which replace the dispersion relations in alloys, are calculated, and BSF intensity maps over the Brillouin zone (alloy Fermi surface cross sections) are presented. It is shown that, close to the valence band edge, Tl does not create an isolated impurity band, but due to its resonant character, strongly disturbs the host electronic bands, leading to the disappearance of sharp and well-defined electronic energy bands. The consequences of this effect on the transport properties are discussed and a qualitative explanation for the improvement in the thermoelectric properties of PbTe:Tl is suggested.

Since any realistic electronic device has some degree of disorder, predicting disorder effects in quantum transport is a critical problem. Here, we report the theory of nonequilibrium coherent potential approximation (NECPA) for analyzing disorder effects in nonequilibrium quantum transport of nanoelectronic devices. The NECPA is formulated by contour-ordered nonequilibrium Green's function where the disorder average is carried out within the coherent potential approximation on the complex-time contour. We have derived a set of rules that supplement the celebrated Langreth theorem and, as a whole, the generalized Langreth rules allow us to derive NECPA equations for real-time Green's functions. The solution of NECPA equations provides the disorder-averaged nonequilibrium density matrix as well as other relevant quantities for quantum transport calculations. We establish the excellent accuracy of NECPA by comparing its results to brute force numerical calculations of disordered tight-binding models. Moreover, the connection of NECPA equations which are derived on the complex-time contour to the nonequilibrium vertex correction theory which is derived on the real-time axis is made. As an application, we demonstrate that NECPA can be combined with density functional theory to enable analysis of nanoelectronic device physics from atomistic first principles.

Symmetry breaking perturbations in an electronically conducting medium are known to produce Friedel oscillations in various physical quantities of an otherwise pristine material. Here we show in a mathematically transparent fashion that Friedel oscillations in graphene have a strong sublattice asymmetry. As a result, the presence of impurities and/or defects may impact the distinct graphene sublattices very differently. Furthermore, such an asymmetry can be used to explain the recent observations that nitrogen atoms and dimers are not randomly distributed in graphene but prefer to occupy one of its two distinct sublattices. We argue that this feature is not exclusive of nitrogen and that it can be seen with other substitutional dopants.

We have employed parameter-free density functional theory calculations to study the thermodynamic stability and structural parameters as well as elastic and electronic properties of Ni${}_4$N in eight selected crystallographic phases. In agreement with the experimental findings, the cubic structure with Pearson symbol cP5, space group $Pm\overline{3}m$ (221) is found to be the most stable and it is also the only thermodynamically stable structure at $T=0$ K with respect to decomposition to the elemental Ni crystal and N${}_2$ gas phase. We determine structural parameters, bulk moduli, and their pressure derivatives for all eight allotropes. The thermodynamic stability and bulk modulus is shown to be anticorrelated. Comparing ferromagnetic and nonmagnetic states, we find common features between the magnetism of elemental Ni and studied ferromagnetic Ni${}_4$N structures. For the ground-state Ni${}_4$N structure and other two Ni${}_4$N cubic allotropes, we predict a complete set of single-crystalline elastic constants (in the equilibrium and under hydrostatic pressure), the Young and area moduli, as well as homogenized polycrystalline elastic moduli obtained by different homogenization methods. We demonstrate that the elastic anisotropy of the ground-state Ni${}_4$N is qualitatively opposite to that in the elemental Ni, i.e., these materials have hard and soft crystallographic directions interchanged. Moreover, one of the studied metastable cubic phases is found auxetic, i.e., exhibiting negative Poisson ratio.

We present a detailed experimental study on Mo${}_{1-x}$Si${}_x$ thin films, an archetypal alloy system combining metallic and semiconductor materials. The correlations between structure and elastic response are comprehensively investigated. We focus on assessing trends for understanding the evolution of elastic properties upon Si alloying in relation to the structural state (crystalline vs amorphous), bonding character (metallic vs covalent), and local atomic environment. By combining picosecond ultrasonics and Brillouin light scattering techniques, a complete set of effective elastic constants and mechanical moduli ($B$, $G$, $E$) is provided in the whole compositional range, covering bcc solid solutions ($x$ < 0.20) and the amorphous phase (0.20 < $x$ < 1.0). A softening of the shear and Young moduli and a concomitant decrease of the Debye temperature is revealed for crystalline alloys, with a significant drop being observed at $x$ ∼ 0.2 corresponding to the limit of crystal lattice stability. Amorphous alloys exhibit a more complex elastic response, related to variations in coordination number, atomic volume, and bonding state, depending on Si content. Finally, distinct evolutions of the G/B ratio as a function of Cauchy pressure are reported for crystalline and amorphous alloys, enabling us to identify signatures of ductility vs brittleness in the features of the local atomic environment. This work paves the way to design materials with improved mechanical properties by appropriate chemical substitution or impurity incorporation during thin-film growth.

We report electronic structure calculations for Ta${}_2$PdS${}_5$, which is a layered superconductor containing heavy elements and displaying an upper critical field, $H_{c2}\left(0\right)$, $\sim 3$ times higher than the estimated Pauli limit. We show that this is a multiband superconductor that is most likely in the strong coupling regime. This provides an alternative explanation to strong spin-orbit scattering for the high upper critical field.

The local structure and electronic properties of Rb${}_{1-x}$Fe${}_{2-y}$Se${}_2$ are investigated by means of site selective polarized x-ray absorption spectroscopy at the iron and selenium $K$ edges as a function of pressure. A combination of dispersive geometry and a nanodiamond anvil pressure cell has permitted us to reveal a steplike decrease in the Fe-Se bond distance at $p\simeq 11$ GPa and, at the same pressure, the local atomic structure of Rb${}_{1-x}$Fe${}_{2-y}$Se${}_2$ becomes more ordered. Thus, at this pressure the phase separation might be suppressed, which has a large influence on the electronic structure, as evidenced by changes in the Fe $K$-edge prepeak. The present results provide compelling evidence that the reemerging superconductivity in $A_{1-x}$Fe${}_{2-y}$Se${}_2$ is closely related to the transition to a locally more ordered state, which has a different electronic structure.

We have investigated the structural phase transitions of crystalline Si (insulator-metal), SiO${}_2$ (insulator-insulator), and Zr (metal-metal) under pressure, as a test of several density functionals for the exchange-correlation energy. While meta-generalized gradient approximations (meta-GGAs) such as revTPSS (revised Tao-Perdew-Staroverov-Scuseria) are more sophisticated than GGAs such as PBE (Perdew-Burke-Ernzerhof), and are more accurate without empiricism for atomization energies of molecules, lattice constants of solids, and surface energies, we confirm that these meta-GGAs tend to give smaller and less realistic transition pressures than the PBE GGA does. But we also show that the recent functionals of the meta-GGA made simple family (MGGA_MS) behave differently, predicting larger and often more realistic transition pressures. We suggest that further refinement of the meta-GGA can lead to a functional that is more accurate for properties of molecules and solids at equilibrium or under compression. We also show that, contrary to recent suggestions but in line with older ones, an accurate fundamental gap in the noninteracting band structure is not necessary for an accurate prediction of the transition pressure. Unlike the semilocal GGAs and meta-GGAs, and unlike the local density approximation also tested here, the screened hybrid functional HSE06 (Heyd-Scuseria-Ernzerhof) is fully nonlocal and predicts more realistic fundamental gaps. HSE06 is better than the semilocal functionals for the transition pressures of Si and SiO${}_2$, but seriously overestimates the transition pressure in Zr. Besides the transition pressures, we report the transition energies and volumes, binding energy curves, and structural parameters at zero and transition pressure. Finally, we discuss how the performance of a functional can reflect its plottable exchange enhancement factor, and why the structural phase transitions are especially challenging for approximate density functionals.

As part of a search for enhanced superconductivity, we explore theoretically the ground-state structures and properties of some hydrides of niobium over a range of pressures and particularly those with significant hydrogen content. A primary motivation originates with the observation that under normal conditions niobium is the element with the highest superconducting transition temperature ($T_c$), and moreover some of its compounds are metals again with very high $T_c$'s. Accordingly, combinations of niobium with hydrogen, with its high dynamic energy scale, are also of considerable interest. This is reinforced further by the suggestion that close to its insulator-metal transition, hydrogen may be induced to enter the metallic state somewhat prematurely by the addition of a relatively small concentration of a suitable transition metal. Here, the methods used correctly reproduce some ground-state structures of niobium hydrides at even higher concentrations of niobium. Interestingly, the particular stoichiometries represented by NbH${}_4$ and NbH${}_6$ are stabilized at fairly low pressures when proton zero-point energies are included. While no paired H${}_2$ units are found in any of the hydrides we have studied up to 400 GPa, we do find complex and interesting networks of hydrogens around the niobiums in high-pressure NbH${}_6$. The Nb-Nb separations in NbH${}_n$ are consistently larger than those found in Nb metal at the respective pressures. The structures found in the ground states of the high hydrides, many of them metallic, suggest that the coordination number of hydrogens around each niobium atom grows approximately as 4$n$ in NbH${}_n$ ($n$ $=$ 1–4), and is as high as 20 in NbH${}_6$. NbH${}_4$ is found to be a plausible candidate to become a superconductor at high pressure, with an estimated $T_c$ ∼ 38 K at 300 GPa.

A muon spin rotation (μSR), neutron, and synchrotron diffraction study of the reentrant spin-glass material IrSr${}_2$Sm${}_{1.15}$Ce${}_{0.85}$Cu${}_2$O${}_{10}$ is presented. The synthesis has been optimized, and Rietveld refinement of the diffraction patterns shows no sign of the previously reported Ir/Cu cation exchange but confirms the structure along with the disordered tilts and rotations of IrO${}_6$ octahedra. The zero-field-μSR response indicates a complex temperature dependence to the magnetism with multiple transitions that are confirmed to be bulk phenomena. Consecutive transitions are reported at $t_1$ $=$ 140, $t_2$ $=$ 20, and $t_3$ $=$ 6 K. The broad transition at 140 K is assigned to antiferromagnetic ordering of Ir${}^{4+}$ spins with a stripe spin structure. The low-temperature transitions are a result of antiferromagnetic ordering of Cu${}^{2+}$ spins followed by the freezing of a disordered Ir spin component, further evidenced by a strong damping of the oscillation amplitude below 6 K. These observations confirm the bulk nature of the previously reported reentrant spin-glass behavior of this complex magnetic system.

The coupling strengths for intra- and interband electron-phonon pair scattering are calculated for LiFeAs. While the sum of these couplings, which gives the total electron-phonon coupling $\lambda$, is of order 0.2, we find that their contribution to the presumed $s^{\pm }$ superconducting state is reduced by approximately an order of magnitude.