In the hexagonal crystal structure of ${\mathrm{Pr}}_3{\mathrm{Ru}}_4{\mathrm{Al}}_{12}$, the Pr atoms form a distorted kagome lattice, and their magnetic moments, are subject to competing exchange and anisotropy interactions. We performed magnetization, magnetic-susceptibility, specific-heat, electrical-resistivity, and neutron-scattering measurements. ${\mathrm{Pr}}_3{\mathrm{Ru}}_4{\mathrm{Al}}_{12}$ is a uniaxial ferromagnet with $T_{\text{C}}=39$ K that displays a collinear magnetic structure (in the high-temperature range of the magnetically ordered state) for which the only crystallographic position of Pr is split into two sites carrying different magnetic moments. A spin-reorientation phase transition is found at 7 K. Below this temperature, part of the Pr moments rotate towards the basal plane, resulting in a noncollinear magnetic state with a lower magnetic symmetry. We argue that unequal RKKY exchange interactions competing with the crystal electric field lead to a moment instability and qualitatively explain the observed magnetic phases in ${\mathrm{Pr}}_3{\mathrm{Ru}}_4{\mathrm{Al}}_{12}$.

Here we present theoretical results for estimation of electromagnetic field energy density and absorbed energy in dispersive lossy chiral single-component metamaterials which consist of an ensemble of identical helical resonators as inclusions. The shape of the helical resonator can vary over a wide range, from a straight wire to a flat split ring. An interaction of the inclusions with harmonic circularly polarized electromagnetic plane waves is studied. We focus on how the inclusion shape influences the mentioned metamaterial properties. The derived general solution for the problem is in good agreement with previous partial and alternative solutions obtained for split ring resonators, straight wires, and helices. The study reveals the optimal geometry of helical lossy resonators for their strongest selectivity of interaction with circularly polarized radiation.

We report a systematic study of the Nernst effect in films of the electron-doped cuprate superconductor $\mathrm{L}{\mathrm{a}}_{2-x}\mathrm{C}{\mathrm{e}}_x\mathrm{Cu}{\mathrm{O}}_4$ as a function of temperature and magnetic field (up to 14 T) over a range of doping from underdoped ($x=0.08$) to overdoped ($x=0.16$). We have determined the characteristic field scale $H_{C2}^{*}$ of superconducting fluctuation which is found to track the domelike dependence of superconductivity ($T_C$). The fall of $H_{C2}^{*}$ and $T_C$ with underdoping is most likely due to the onset of long-range antiferromagnetic order. We also report the temperature onset, $T_{\mathrm{onset}}$, of superconducting fluctuations above $T_C$. For optimally doped $x=0.11T_{\mathrm{onset}}$ ($\cong 39\mathrm{K}$) is high compared to $T_C$ (26 K). For higher doping $T_{\mathrm{onset}}$ decreases and tends to zero along with the critical temperature at the end of the superconducting dome. The superconducting gap closely tracks $H_{C2}^{*}$ measured from the temperature- and field-dependent Nernst signal.

We have used synchrotron x-ray and Raman spectroscopic studies combined with molecular dynamics to investigate the ${\mathrm{I}}_2-{\mathrm{H}}_2$ system at high pressure. By laser heating the mixture above 25 GPa we synthesized the molecular compound $\mathrm{HI}{\left({\mathrm{H}}_2\right)}_{13}$, with the ${AB}_{13}$ structure type and unusually high volumetric hydrogen content. The isolation of HI molecules by ${\left({\mathrm{H}}_2\right)}_{13}$ supramolecular clusters stabilizes the compound over a remarkable pressure range from 9 to at least 130 GPa. At lower pressures and 300 K another compound, hydrogen diiodane ${\mathrm{H}}_2{\left(\mathrm{HI}\right)}_2$, spontaneously forms, being stable up to 12.5 GPa.

Iterative neural-network-based three-dimensional structural optimization of atomic positions over tens of nanometers is performed using transmission electron microscope (TEM) diffraction data simulated from density functional theory (DFT) all-electron densities, thus retrieving parameter variations along the beam direction. We first use experimental data to show that the GPAW DFT code's all-electron densities are considerably more accurate for electron diffraction calculations compared to conventional isolated-atom scattering factors, and they also compare well to Wien2K DFT simulations. This DFT-TEM combination is then integrated into an iterative neural-network-optimization-based algorithm (PRIMES, parameter retrieval and inversion from multiple electron scattering) to retrieve nanometer-scale ferroelectric polarization domains and strain in theoretical bulklike specimens from TEM data. DFT and isolated-atom methods produce substantially different diffraction patterns and retrieved polarization domain parameters, and DFT is sufficient to retrieve strain properties from a silicon specimen simulated using experimentally derived structure factors. Thus, we show that the improved accuracy, fast computation, and intuitive integration make the GPAW DFT code well suited for three-dimensional materials characterization and demonstrate this using an iterative neural-network algorithm that is verifiable on the mesoscale and, with DFT integration, self-consistent on the nanoscale.

We investigate the role of disorder in a two-dimensional semi-Dirac material characterized by a linear dispersion in one direction and a parabolic dispersion in the orthogonal direction. Using the self-consistent Born approximation, we show that disorder can drive a topological Lifshitz transition from an insulator to a semimetal, as it generates a momentum-independent off-diagonal contribution to the self-energy. Breaking time-reversal symmetry enriches the topological phase diagram with three distinct regimes—single-node trivial, two-node trivial, and two-node Chern. We find that disorder can drive topological transitions from both the single- and two-node trivial to the two-node Chern regime. We further analyze these transitions in an appropriate tight-binding Hamiltonian of an anisotropic hexagonal lattice by calculating the real-space Chern number. Additionally, we compute the disorder-averaged entanglement entropy which signals both the topological Lifshitz and Chern transition as a function of the anisotropy of the hexagonal lattice. Finally, we discuss experimental aspects of our results.

We study the superconducting order in a two-dimensional square lattice Hubbard model with weak repulsive interactions, subject to a Zeeman field and weak Rashba spin-orbit interactions. Diagonalizing the noninteracting Hamiltonian leads to two separate bands, and by deriving an effective low-energy interaction we find the mean field gap equations for the superconducting order parameter on the bands. Solving the gap equations just below the critical temperature, we find that superconductivity is caused by Kohn-Luttinger-type interaction, while the pairing symmetry of the bands is indirectly affected by the spin-orbit coupling. The dominating attractive momentum channel of the Kohn-Luttinger term depends on the filling fraction $n$ of the system, and it is therefore possible to change the momentum dependence of the order parameter by tuning $n$. Moreover, $n$ also determines which band has the highest critical temperature. Rotating the magnetic field changes the momentum dependence from states that for small momenta reduce to a chiral $p_x\pm i{p}_y$ type state for out-of-plane fields, to a nodal $p$-wave-type state for purely in-plane fields.

Using the disordered local moments approach in combination with the ab initio molecular dynamics method, we simulate the behavior of a paramagnetic phase of NiO at finite temperatures to investigate the effect of magnetic disorder, thermal expansion, and lattice vibrations on its electronic structure. In addition, we study its lattice dynamics. We verify the reliability of our theoretical scheme via comparison of our results with available experiment and earlier theoretical studies carried out within static approximations. We present the phonon dispersion relations for the paramagnetic rock-salt (B1) phase of NiO and demonstrate that it is dynamically stable. We observe that including the magnetic disorder to simulate the paramagnetic phase has a small yet visible effect on the band gap. The amplitude of the local magnetic moment of Ni ions from our calculations for both antiferromagnetic and paramagnetic phases agree well with other theoretical and experimental values. We demonstrate that the increase of temperature up to 1000 K does not affect the electronic structure strongly. Taking into account the lattice vibrations and thermal expansion at higher temperatures have a major impact on the electronic structure, reducing the band gap from $\sim 3.5$ eV at 600 K to $\sim 2.5$ eV at 2000 K. We conclude that static lattice approximations can be safely employed in simulations of the paramagnetic state of NiO up to relatively high temperatures $(\sim 1000$ K), but as we get closer to the melting temperature vibrational effects become quite large and therefore should be included in the calculations.

Under symmetry breaking, a three-dimensional nodal-line semimetal can turn into a topological insulator or Weyl semimetal, accompanied by the generation of momentum-space Berry curvature. We develop a theory that unifies their circular dichroism and highlights the roles of Berry curvature distribution and light incident direction. Nontrivially, these phases exhibit distinct dichroic optical absorption and radial Hall effects, with characteristic scalings with photon energy and electric field. Our findings offer a diagnosis tool for examining topological phases of matter.

The Hofstadter model describes noninteracting fermions on a lattice in the presence of an external magnetic field. Motivated by the plethora of solid-state phases emerging from electron interactions, we consider an interacting version of the Hofstadter model, including a Hubbard repulsion $U$. We investigate this model in the large-$U$ limit corresponding to a $t–J$ Hamiltonian with an external (orbital) magnetic field. By using renormalized mean-field theory supplemented by exact diagonalization calculations of small clusters, we find evidence for competing symmetry-breaking phases, exhibiting (possibly coexisting) charge, bond, and superconducting orders. Topological properties of the states are also investigated, and some of our results are compared to related experiments involving ultracold atoms loaded on optical lattices in the presence of a synthetic gauge field.

Various ab initio approaches to the band structure of $A\mathrm{NiSn}$ and $A\mathrm{CoSb}$ half-Heusler compounds ($A=$ Ti, Zr, Hf) are compared and their consequences for the prediction of thermoelectric properties are explored. Density functional theory with the generalized-gradient approximation (GGA), as well as the hybrid density functional HSE06 and ab initio many-body perturbation theory in the form of the $G{W}_0$ approach, are employed. The $G{W}_0$ calculations confirm the trend of a smaller band gap (0.75 to 1.05 eV) in $A\mathrm{NiSn}$ compared to the $A\mathrm{CoSb}$ compounds (1.13 to 1.44 eV) already expected from the GGA calculations. While in $A\mathrm{NiSn}$ materials the $G{W}_0$ band gap is 20% to 50% larger than in HSE06, the fundamental gap of $A\mathrm{CoSb}$ materials is smaller in $G{W}_0$ compared to HSE06. This is because $G{W}_0$, similar to PBE, locates the valence band maximum at the $L$ point of the Brillouin zone, whereas it is at the $\mathrm{\Gamma }$ point in the HSE06 calculations. The differences are attributed to the observation that the relative positions of the $d$ levels of the transition metal atoms vary among the different methods. Using the calculated band structures and scattering rates taking into account the band effective masses at the extrema, the Seebeck coefficients, thermoelectric power factors, and figures of merit $ZT$ are predicted for all six half-Heusler compounds. Comparable performance is predicted for the $n$-type $A\mathrm{NiSn}$ materials, whereas clear differences are found for the $p$-type $A\mathrm{CoSb}$ materials. Using the most reliable $G{W}_0$ electronic structure, ZrCoSb is predicted to be the most efficient material with a power factor of up to 0.07 W/(${\mathrm{K}}^2$ m) at a temperature of 600 K. We find strong variations among the different ab initio methods not only in the prediction of the maximum power factor and $ZT$ value of a given material, but also in comparing different materials to each other, in particular in the $p$-type thermoelectric materials. Thus we conclude that the most elaborate, but also most costly $G{W}_0$ method is required to perform a reliable computational search for the optimum material.

We extend the microscopic Fermi-liquid theory for the Anderson impurity [Phys. Rev. B 64, 153305 (2001)] to explore nonequilibrium transport at finite magnetic fields. Using the Ward identities in the Keldysh formalism with the analytic and antisymmetric properties of the vertex function, the spin-dependent Fermi-liquid corrections of order $T^2$ and ${\left(eV\right)}^2$ are determined at low temperatures $T$ and low bias voltages $eV$. Away from half filling, these corrections can be expressed in terms of the linear and nonlinear static susceptibilities which represent the two-body and three-body fluctuations, respectively. We calculate the nonlinear susceptibilities using the numerical renormalization group, to explore the differential conductance $dI/dV$ through a quantum dot. We find that the two-body fluctuations dominate the corrections in the Kondo regime at zero magnetic field. The contribution of the three-body fluctuations becomes significant far away from half filling, especially in the valence-fluctuation regime and empty-orbital regimes. In finite magnetic fields, the three-body contributions become comparable to the two-body contributions, and play an essential role in the splitting of the zero-bias conductance peak occurring at a magnetic field of the order of the Kondo energy scale. We also apply our microscopic formulation to the magnetoresistance and thermal conductivity of dilute magnetic alloys away from half filling.

Recent tunneling spectroscopy experiments in semiconducting nanowires with proximity-induced superconductivity have reported robust zero-bias conductance peaks. Such a feature can be compatible with the existence of topological Majorana bound states (MBSs) and with a trivial Andreev bound state (ABS) near zero energy. Here, we argue that additional information, that can distinguish between the two cases, can be extracted from Coulomb blockade experiments of Majorana islands. The key is the ratio of peak heights of consecutive conductance peaks gives information about the electron and hole components of the lowest-energy subgap state. In the MBS case, this ratio goes to one-half for long wires, whereas for short wires with finite MBS overlap it oscillates a function of Zeeman energy with the same period as the MBS energy splitting. We explain how the additional information might help to distinguish a trivial ABS at zero energy from a true MBS and show case examples.

We report a Cs-doping-induced band inversion and the direct observation of a surface resonance state with an elliptical Fermi surface in black phosphorus (BP) using angle-resolved photoemission spectroscopy. By selectively inducing a higher electron concentration ($1.7\times {10}^{14}{\mathrm{cm}}^{-2}$) in the topmost layer, the changes in the Coulomb potential are sufficiently large to cause surface band inversion between the parabolic valence band of BP and a parabolic surface state around the $\mathrm{\Gamma }$ point of the BP Brillouin zone. Tight-binding calculations reveal that band gap openings at the crossing points in the two high-symmetry directions of the Brillouin zone require out-of-plane hopping and breaking of the glide mirror symmetry. Ab initio calculations are in very good agreement with the experiment if a stacking fault on the BP surface is taken into account. The demonstrated level of control over the band structure suggests the potential application of few-layer phosphorene in topological field-effect transistors.

The emerging material, topological insulator, has provided new opportunities for spintronic applications, owing to its strong spin-orbit character. Topological insulator based heterostructures that display spin-charge coupling driven by topology at surfaces have great potential for the realization of novel spintronic devices. Here, we report the observation of anomalous photogalvanic effect in (${\mathrm{Bi}}_{0.5}{\mathrm{Sb}}_{0.5}$)${}_2{\mathrm{Te}}_3$ thin films grown on GaAs substrate. We demonstrate that the magnitude, direction, and temperature dependence of the helicity-dependent photocurrent (HDPC) can be modulated by the gate voltage. From spatially resolved photocurrent measurements, we show that the line profile of HDPC in (${\mathrm{Bi}}_{0.5}{\mathrm{Sb}}_{0.5}$)${}_2{\mathrm{Te}}_3$/GaAs is unaffected by the variation of beam size, in contrast to the photocurrent response measured in a (${\mathrm{Bi}}_{0.5}{\mathrm{Sb}}_{0.5}$)${}_2{\mathrm{Te}}_3$/mica structure.

Stannous selenide is a layered semiconductor that is a polar analog of black phosphorus and of great interest as a thermoelectric material. Unusually, hole doped SnSe supports a large Seebeck coefficient at high conductivity, which has not been explained to date. Angle-resolved photoemission spectroscopy, optical reflection spectroscopy, and magnetotransport measurements reveal a multiple-valley valence-band structure and a quasi-two-dimensional dispersion, realizing a Hicks-Dresselhaus thermoelectric contributing to the high Seebeck coefficient at high carrier density. We further demonstrate that the hole accumulation layer in exfoliated SnSe transistors exhibits a field effect mobility of up to $250{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$ at $T=1.3\mathrm{K}$. SnSe is thus found to be a high-quality quasi-two-dimensional semiconductor ideal for thermoelectric applications.

The electrical evaluation of the crystallinity of hexagonal boron nitride ($h$-BN) is still limited to the measurement of dielectric breakdown strength, in spite of its importance as the substrate for two-dimensional van der Waals heterostructure devices. In this study, physical phenomena for degradation and failure in exfoliated single-crystal $h$-BN films were investigated using the constant-voltage stress test. At low electrical fields, the current gradually reduced and saturated with time, while the current increased at electrical fields higher than $\sim 8\mathrm{MV}/\mathrm{cm}$ and finally resulted in the catastrophic dielectric breakdown. These transient behaviors may be due to carrier trapping to the defect sites in $h$-BN because trapped carriers lower or enhance the electrical fields in $h$-BN depending on their polarities. The key finding is the current enhancement with time at the high electrical field, suggesting the accumulation of electrons generated by the impact ionization process. Therefore, a theoretical model including the electron generation rate by an impact ionization process was developed. The experimental data support the expected degradation mechanism of $h$-BN. Moreover, the impact ionization coefficient was successfully extracted, which is comparable to that of $\mathrm{Si}{\mathrm{O}}_2$, even though the fundamental band gap for $h$-BN is smaller than that for $\mathrm{Si}{\mathrm{O}}_2$. Therefore, the dominant impact ionization in $h$-BN could be band-to-band excitation, not defect-assisted impact ionization.

At the same time that two-dimensional (2D) systems open possibilities for new physics and applications, they present a higher challenge for electronic structure calculations, especially concerning excitations. The achievement of a fast and accurate practical model that incorporates approximate quasiparticle corrections can further open an avenue for more reliable band structure calculations of complex systems such as interactions of 2D materials with substrates or molecules, as well as the formation of van der Waals heterostructures. In this work, we demonstrate that the performance of the fast and parameter-free DFT-1/2 method is comparable with state-of-the-art $\mathit{GW}$ and superior to the HSE06 hybrid functional in the majority set of the 34 different 2D materials studied. Moreover, based on the knowledge of the method and chemical information of the material, we can predict the small number of cases in which the method is not so effective and also provide the best recipe for an optimized DFT-1/2 method based on the electronegativity difference of the bonding atoms.

Using a combination of single-crystal neutron scattering and reverse Monte Carlo refinements, we study the magnetic structure of paramagnetic MnO at a temperature (160 K) substantially below the Curie-Weiss temperature $\left|\theta \right|\sim 550$ K. The microscopic picture we develop reveals a locally ordered domain structure that persists over distances many times larger than the correlation length implied by direct analysis of the spin-correlation function. Moreover, the directional dependence of paramagnetic spin correlations in paramagnetic MnO differs in some important respects from that of its incipient ordered antiferromagnetic state. Our results demonstrate that atomistic refinement to large three-dimensional neutron-scattering datasets is a practical approach, and have implications for the understanding of paramagnetic states in weakly frustrated systems, including high-temperature superconductors.