We have performed density functional theory (DFT) based calculations for aluminum in extreme conditions of both pressure and temperature, up to five times compressed ambient density, and over 1 000 000 K in temperature. In order to cover such a domain, DFT methods including phonon calculations, quantum molecular dynamics, and orbital-free DFT are employed. The results are then used to construct a SESAME equation of state for the aluminum 1100 alloy, encompassing the fcc, hcp, and bcc solid phases as well as the liquid regime. We provide extensive comparison with experiment, and based on this we also provide a slightly modified equation of state for the aluminum 6061 alloy.

A salient feature of cyclically driven first-order phase transformations in crystals is their scale-free avalanche dynamics. This behavior has been linked to the presence of a classical critical point but the mechanism leading to criticality without extrinsic tuning remains unexplained. Here we show that the source of scaling in such systems is an annealed disorder associated with transformation-induced slip which coevolves with the phase transformation, thus ensuring the crossing of a critical manifold. Our conclusions are based on a model where annealed disorder emerges in the form of a random field induced by the phase transition. Such a disorder exhibits supertransient chaotic behavior under thermal loading, obeys a heavy-tailed distribution, and exhibits long-range spatial correlations. We show that the universality class is affected by the long-range character of elastic interactions. In contrast, it is not influenced by the heavy-tailed distribution and spatial correlations of disorder.

We extend the Lieb-Schupp theorem to Heisenberg models with higher-order interactions on nonfrustrated or frustrated finite lattices. These lattices are constructed by even-numbered rings with or without crossing bonds and have reflection symmetry. The results show that the ground state has total spin zero in wide interaction parameter regions which are not covered by the results of Marshall-Lieb-Mattis-type arguments.

Topologically stable structures include vortices in a wide variety of matter, skyrmions in ferro- and antiferromagnets, and hedgehog point defects in liquid crystals and ferromagnets. These are characterized by integer-valued topological quantum numbers. In this context, closed surfaces are a prominent subject of study as they form a link between fundamental mathematical theorems and real physical systems. Here we perform an analysis on the topology and stability of equilibrium magnetization states for a thin spherical shell with easy-axis anisotropy in normal directions. Skyrmion solutions are found for a range of parameters. These magnetic skyrmions on a spherical shell have two distinct differences compared to their planar counterpart: (i) they are topologically trivial and (ii) can be stabilized by curvature effects, even when Dzyaloshinskii-Moriya interactions are absent. Due to its specific topological nature a skyrmion on a spherical shell can be simply induced by a uniform external magnetic field.

Spontaneous symmetry breaking is deeply related to the dimensionality of a system. The Néel order going with spontaneous breaking of $\mathrm{U}\left(1\right)$ symmetry is safely allowed at any temperature for three-dimensional systems but allowed only at zero temperature for purely two-dimensional systems. We closely investigate how smoothly the ordering process of the three-dimensional system is modulated into that of the two-dimensional one with reduction of dimensionality, considering spatially anisotropic quantum antiferromagnets. We first show that the Néel temperature is kept finite even in the two-dimensional limit although the Néel order is greatly suppressed for low dimensionality. This feature of the Néel temperature is highly nontrivial, which dictates how the order parameter is squashed under the reduction of dimensionality. Next, we investigate this dimensional modulation of the order parameter. We develop our argument taking as an example a coupled spin-ladder system relevant for experimental studies. The ordering process is investigated multidirectionally using theoretical techniques of a mean-field method combined with analytical (exact solutions of quantum field theories) or numerical (density-matrix renormalization-group) methods, a variational method, a renormalization-group study, linear spin-wave theory, and quantum Monte Carlo simulations. We show that these methods independent of each other lead to the same conclusion about the dimensional modulation.

We consider the coupling of the magnetic Goldstone modes, or magnons, in both quantum ferromagnets and antiferromagnets to the longitudinal order-parameter fluctuations and the resulting nonanalytic behavior of the longitudinal susceptibility. In classical magnets it is well known that long-range correlations induced by the magnons lead to a singular wave-number dependence of the form $1/k^{4-d}$ in all dimensions $2<d<4$, for both ferromagnets and antiferromagnets. At zero temperature we find a profound difference between the two cases. Consistent with naive power counting, the longitudinal susceptibility in a quantum antiferromagnet scales as $k^{d-3}$ for $1<d<3$, whereas in a quantum ferromagnet the analogous result, $k^{d-2}$, is absent due to a zero scaling function. This absence of a nonanalyticity in the longitudinal susceptibility is due to the lack of magnon number fluctuations in the ground state of a quantum ferromagnet; correlation functions that are sensitive to other fluctuations do exhibit the behavior predicted by simple power counting. Also of interest is the dynamical behavior as expressed in the longitudinal part of the dynamical structure factor, which is directly measurable via neutron scattering. For both ferromagnets and antiferromagnets there is a logarithmic singularity at the magnon frequency with a prefactor that vanishes as $T\to 0$. In addition, in the antiferromagnetic case there is a nonzero contribution at $T=0$ that is missing for ferromagnets. Magnon damping due to quenched disorder restores the expected scaling behavior of the longitudinal susceptibility in the ferromagnetic case; it scales as $k^{d-2}$ if the order parameter is not conserved (magnetic disorder), or as $k^d$ if it is (nonmagnetic disorder). Detailed predictions are made for both two- and three-dimensional systems at both $T=0$ and in the limit of low temperatures, and the physics behind the various nonanalytic behaviors is discussed.

A few self-consistent schemes to solve the Hedin equations are presented. They include vertex corrections of different complexity. Commonly used quasiparticle approximation for the Green's function and static approximation for the screened interaction are avoided altogether. Using alkali metals Na and K as well as semiconductor Si and wide-gap insulator LiF as examples, it is shown that both the vertex corrections in the polarizability $P$ and in the self-energy $\mathrm{\Sigma }$ are important. Particularly, vertex corrections in $\mathrm{\Sigma }$ with proper treatment of frequency dependence of the screened interaction always reduce calculated bandwidths/band gaps, improving the agreement with experiment. The complexity of the vertex included in $P$ and in $\mathrm{\Sigma }$ can be different. Whereas in the case of polarizability one generally has to solve the Bethe-Salpeter equation for the corresponding vertex function, it is enough (for the materials in this study) to include the vertex of the first order in the self-energy. The calculations with appropriate vertices show remarkable improvement in the calculated bandwidths and band gaps as compared to the self-consistent $GW$ approximation as well as to the self-consistent quasiparticle $GW$ approximation.

The two-dimensional electron liquid, at the (001) interface between band insulators ${\mathrm{LaAlO}}_3$ and ${\mathrm{SrTiO}}_3$, undergoes Lifshitz transition as the interface is doped with carriers. At a critical carrier density, two additional orbitals populate at the Fermi level, with a concomitant change in the Fermi surface topology. Using dynamical mean-field theory, formulated within a realistic three-orbital model, we study the influence of the Lifshitz transition and local electron correlations on the transport properties. We look at the thermal conductivity, optical conductivity, Seebeck coefficient, and angle-resolved photoemission spectra and find that at a critical density, both the thermal and dc conductivities rise sharply to higher values while the Seebeck coefficient shows a cusp. The interorbital electron-electron interaction transfers spectral weight near the $\mathrm{\Gamma }$ point towards lower energy, thereby reducing the critical density. In the presence of external magnetic field, the critical density further reduces due to exchange splitting. Beyond a sufficiently large field, multiple cusps appear in the Seebeck coefficient revealing multiple Lifshitz transitions.

Band structure is systematically studied in an effective-mass scheme in collapsed armchair and zigzag nanotubes based on the model in which collapsed tubes are regarded as bilayer ribbons with closed edges. Boundary conditions at closed edges, describing the connection of the envelope wave functions between the bottom and top layers, are derived. Among electronic states in bilayers, which change sensitively depending on the relative displacement of two layers, those having wave functions matching well with the obtained boundary conditions, i.e., unaffected by the presence of closed edges, constitute important states near the Fermi level in collapsed nanotubes.

Strongly interacting electrons in a ZnO quantum well reveal intriguing electronic properties that were not observed in traditional semiconductor systems, such as in a GaAs heterojunction. In a tilted magnetic field, the even-denominator fractional quantum Hall states in this system exhibit unique phase transitions that necessitate a proper understanding. Since here the Landau level gap is very small, it is essential to consider a screened Coulomb potential in order to include the effects of all Landau levels. We observe an incompressible state–compressible state phase transition induced by the tilted field with different properties for the $\frac{3}{2}$ and $\frac{7}{2}$ filling factors. Additionally, the disappearance of the $\frac{5}{2}$ state in the experiment is most likely due to the presence of a screened Coulomb potential. We, however, propose that a wider quantum well may help to stabilize the incompressible phase of the $\frac{5}{2}$ filling factor, and thereby make the fractional quantum Hall effect observable in this state.

I generalize the theory of phonon topological band structures of isostatic lattices to frustrated antiferromagnets. I achieve this with a discovery of a many-body supersymmetry (SUSY) in the phonon problem of balls and springs and its connection to local constraints satisfied by ground states. The Witten index of the SUSY model demands the Maxwell-Calladine index of mechanical structures. “Spontaneous supersymmetry breaking” is identified as the need to gap all modes in the bulk to create the topological isostatic lattice state. Since ground states of magnetic systems also satisfy local constraint conditions (such as the vanishing of the total spin on a triangle), I identify a similar SUSY structure for many common models of antiferromagnets including the square, triangluar, kagome, pyrochlore nearest-neighbor antiferromagnets, and the $J_2=J_1/2$ square-lattice antiferromagnet. Remarkably, the kagome family of antiferromagnets is the analog of topological isostatic lattices among this collection of models. Thus, a solid-state realization of the theory of phonon topological band structure may be found in frustrated magnetic materials.

Kondo insulator $\mathrm{Sm}{\mathrm{B}}_6$ has attracted attention because it can realize new topological phenomena driven by the interplay between strong correlation effect and topology. However, its topological nature is still under debate. To examine the topological aspect, we demonstrate the nonmagnetic La and magnetic Ce doping dependence of the resistance of $\mathrm{Sm}{\mathrm{B}}_6$. Moreover, the resistance ratios of different thicknesses are analyzed to confirm the surface contribution. Lightly doped La samples show a purely conducting surface region at low temperature, whereas the lightly doped Ce samples do not have any conducting region at low temperature. Furthermore, based on the analysis of the electrical transport data of $\mathrm{S}{\mathrm{m}}_{1-x}\mathrm{L}{\mathrm{a}}_x{\mathrm{B}}_6$ $\left(0.0\le x\le 1.0\right)$, an electronic phase diagram was found, composed of four regions: region I $\left(0.0\le x\le 0.06\right)$, II $\left(0.1\le x\le 0.15\right)$, III $(x\approx 0.2)$, and IV $\left(0.25\le x\le 1.0\right)$. Region I is characterized by the presence of conducting surface states, region II is characterized by the insulating phase due to the $d-f$ hybridization gap without the conducting surface state, region III is characterized by the disappearance of the $d-f$ hybridization gap and the existence of valence fluctuation, and region IV is a typical metallic state.

We present detailed spectral calculations for small Lieb lattices having up to $N=4$ number of cells, in the regime of half-filling, an instance of particular relevance for the nanomagnetism of discrete systems such as quantum dot arrays, due to the degenerate levels at midspectrum. While for the Hubbard interaction model—and even number of sites—the ground state spin is given by the Lieb theorem, the inclusion of long-range interaction—or odd number of sites—makes the spin state not known a priori, which justifies our approach. We calculate also the excitation energies, which are of experimental importance, and find significant variation induced by the interaction potential. One obtains insights on the mechanisms involved that impose as ground state the Lieb state with lower spin rather than the Hund one with maximum spin for the degenerate levels, showing this in the first and second orders of the interaction potential for the smaller lattices. The analytical results agree with the numerical ones, which are performed by exact diagonalization calculations or by a combined mean-field and configuration interaction method. While the Lieb state is always lower in energy than the Hund state, for strong long-range interaction, when possible, another minimal spin state is imposed as ground state.

Topological insulators (TI) are a phase of matter that host unusual metallic surface states. Unlike the states that exist on the surface of conventional materials, these so-called topological surfaces states (TSS) are protected against disorder-related localization effects by time reversal symmetry through strong spin-orbit coupling. By combining transport measurements, angle-resolved photoemission spectroscopy, and scanning tunneling microscopy, we show that there exists a critical level of disorder beyond which the TI $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ loses its ability to protect the metallic TSS and transitions to a fully insulating state. The absence of the metallic surface channels dictates that there is a change in the material's topological character, implying that disorder can lead to a topological phase transition even without breaking the time reversal symmetry. This observation challenges the conventional notion of topologically protected surface states and should prompt new studies as to the fundamental nature of topological phase of matter in the presence of disorder.

Organic semiconductors tend to self-assemble into highly ordered and oriented morphologies with anisotropic optical properties. Studying these optical anisotropies provides insight into processing-dependent structural properties and informs the photonic design of organic photovoltaic and light-emitting devices. Here we measure the anisotropic optical properties of spin-cast films of the $n$-type polymer P(NDI2OD-T2) using momentum-resolved absorption and emission spectroscopies. We quantify differences in the optical anisotropies of films deposited with distinct face-on and edge-on morphologies. In particular, we infer a substantially larger out-of-plane tilt angle of the optical transition dipole moment in high temperature annealed, edge-on films. Measurements of spectral differences between in-plane and out-of-plane dipoles, further indicate regions of disordered polymers in low temperature annealed face-on films that are otherwise obscured in traditional x-ray and optical characterization techniques. The methods and analysis developed in this work provide a way to identify and quantify subtle optical and structural anisotropies in organic semiconductors that are important for understanding and designing highly efficient thin film devices.

We use ab initio calculations to systematically study the phase diagram of multiferroic ${\mathrm{Sr}}_{1-x}{\mathrm{Ba}}_x{\mathrm{MnO}}_3$ ($0\le x\le 1$) as a function of chemical doping, epitaxial strain, and external pressure. We find that by replacing Sr with Ba in cubic ${\mathrm{SrMnO}}_3$ and imposing epitaxial strain, the material can be tuned to the vicinity of a first order transition between two multiferroic phases, one antiferromagnetic with a smaller polarization and one ferromagnetic with a larger polarization. A giant effective magnetoelectric coupling and cross-field control (electric field control of magnetism or magnetic field control of polarization) can be achieved in the vicinity of the transition. The dependence of the theoretically computed transition point on the choice of exchange correlation functionals is determined and is found to be non-negligible. We also show that the perovskite structure of ${\mathrm{BaMnO}}_3$ can be stabilized relative to its hexagonal polymorphs at pressures larger than 20 GPa.

We investigate the effect of shear and strain in graphene bilayers, under conditions where the distortion of the lattice gives rise to a smooth one-dimensional modulation in the stacking sequence of the bilayer. We show that strain and shear produce characteristic Moiré patterns which can have the same visual appearance on a large scale, but representing graphene bilayers with quite different electronic properties. The different features in the low-energy electronic bands can be ascribed to the effect of a fictitious non-Abelian gauge field mimicking the smooth modulation of the stacking order. Strained and sheared bilayers show a complementary behavior, which can be understood from the fact that the non-Abelian gauge field acts as a repulsive interaction in the former, expelling the electron density away from the stacking domain walls, while behaving as a confining interaction leading to localization of the electronic states in the sheared bilayers. In this latter case, the presence of the effective gauge field explains the development of almost flat low-energy bands, resembling the form of the zeroth Landau level characteristic of a Dirac fermion field. The estimate of the gauge field strength in those systems gives a magnitude of the order of several tens of tesla, implying a robust phenomenology that should be susceptible of being observed in suitably distorted bilayer samples.

Colored nitrogen-vacancy (NV) centers in nanosize diamonds ($d\sim 5$ nm) are promising probe materials because their optical transitions are sensitive to mechanical, vibrational, and spin changes in the surroundings. Here, a linear response time-dependent density functional theory approach is used to describe the optical transitions in several NV-doped diamond quantum dots (QDs) in order to investigate size effects on the absorption spectra. By computing the full optical spectrum up to band-to-band transitions, we analyze both the localized “pinned” midgap and the charge-transfer excitations for an isolated reduced NV center. Subband charge-transfer excitations are shown to be size dependent, involving the excitation of the dopant $s{p}^3$ electrons to the diamond conduction band. Additionally, the NV-doped systems exhibit characteristic $s{p}^3-s{p}^3$ excitations whose experimental energies are reproduced well and do not depend on QD size. However, the NV position and global cluster symmetry can affect the amount of the energy splitting of the vertical excitation energies of the midgap transitions.