We have studied the impact of nonlocal electronic correlations at all length scales on the Mott-Hubbard metal-insulator transition in the unfrustrated two-dimensional Hubbard model. Combining dynamical vertex approximation, lattice quantum Monte Carlo, and variational cluster approximation, we demonstrate that scattering at long-range fluctuations, i.e., Slater-like paramagnons, opens a spectral gap at weak-to-intermediate coupling, irrespective of the preformation of localized or short-range magnetic moments. This is the reason why the two-dimensional Hubbard model has a paramagnetic phase which is insulating at low enough temperatures for any (finite) interaction and no Mott-Hubbard transition is observed.

We present a comprehensive, ground-state density functional theory study of the size dependence of the optical and electronic properties and the stability of spherical silicon nanocrystals (NCs) with different impurities on the surface. We vary the size of the NCs from 1.0 to 3.5 nm, considering single-bonded $({\mathrm{CH}}_3$, F, Cl, OH) and double-bonded (O, S) impurities and bridged oxygen. We show that the density of states (DOS) and absorption indices of the NCs with single-bonded impurities are very similar to each other and the fully hydrogenated NCs, except for the 1.0-nm NCs, where a slight difference is present. In the case of the NCs with double-bonded impurities, the DOS and absorption indices exhibit a significant difference, compared to the fully hydrogenated NCs, for sizes up to 2.5 nm. We argue that this difference arises from the difference in the contribution from the impurity to the states around the gap, which can considerably change the character of the states. We demonstrate that the double-bonded impurities contribute significantly to the states around the gap, compared to the single-bonded impurities, causing changes in the symmetry of these states. This observation was further supported by analyzing the changes of the Fourier transform of the charge densities of the highest occupied and lowest unoccupied eigenstate. We also show that the formation energies of NCs with bridged oxygen and fluorine are the lowest, regardless of the size. Furthermore, we show that high hydrogen concentration can be used to suppress the addition of oxygen and fluorine on the surface of the Si NCs.

We study the interaction between two magnetic adatom impurities in graphene using the Anderson model. The two-impurity Anderson Hamiltonian is solved numerically by using the quantum Monte Carlo technique. We find that the interimpurity spin susceptibility is strongly enhanced at low temperatures, significantly diverging from the well-known Ruderman-Kittel-Kasuya-Yoshida result which decays as $R^{-3}$.

Simulations of defects in paramagnetic materials at high temperature constitute a formidable challenge to solid-state theory due to the interaction of magnetic disorder, vibrations, and structural relaxations. CrN is a material where these effects are particularly large due to a strong magnetolattice coupling and a tendency for deviations from the nominal 1:1 stoichiometry. In this work, we present a first-principles study of nitrogen vacancies and nitrogen interstitials in CrN at elevated temperature. We report on formation energetics, the geometry of interstitial nitrogen dimers, and the impact on the electronic structure caused by the defects. We find a vacancy formation energy of 2.28 eV with a small effect of temperature, i.e., a formation energy for N interstitial in the form of a $\langle 111\rangle$-oriented split bond of 3.77 eV with an increase to 3.97 at 1000 K. Vacancies are found to add three electrons, while split-bond interstitial adds one electron to the conduction band. The band gap of defect-free CrN is smeared out due to vibrations, although it is difficult to draw a conclusion about the exact temperature at which the band gap closes from our calculations. However, it is clear that at 900 K there is a nonzero density of electronic states at the Fermi level. At 300 K, our results indicate a border case where the band gap is about to close.

The normal modes of a continuum solid endowed with a random distribution of line defects that behave like elastic strings are described. These strings interact with elastic waves in the bulk, generating wave dispersion and attenuation. Explicit formulas are provided that relate these properties to the density of string states. For a density of states that mimics the boson peak (BP) in amorphous materials, the attenuation as a function of frequency $\omega$ behaves as ${\omega }^4$ for low frequencies, and, as frequency increases, crosses over to ${\omega }^2$ near the BP, and then to linear in $\omega$. An Ioffe-Regel criterion is satisfied at the BP. Dispersion is negative in the frequency range where attenuation is quartic and quadratic in frequency, with effective velocity reaching a minimum near the BP. Continuum mechanics can thus be applied to both crystalline materials and their amorphous counterparts at similar length scales. The possibility of linking this model with the microstructure of amorphous materials is discussed.

Energy barrier height for magnetization switching is theoretically studied for a system with uniaxial anisotropy in a circularly polarized microwave magnetic field. A formulation of the Landau-Lifshitz-Gilbert equation in a rotating frame introduces an effective energy that includes the effects of both the microwave field and static field. This allows the effective-energy profiles to rigorously describe the switching paths and corresponding barrier height, which govern thermally activated magnetization switching under microwave assistance. We show that fixed points and limit cycles in the rotating frame lead to various switching paths and that under certain conditions, switching becomes a two-step process with an intermediate state.

Epsilon near zero (ENZ) conditions have been observed to enhance superconducting properties of a composite metamaterial based on random mixing of superconductor and ferroelectic nanoparticles. Here we analyze several other promising experimental geometries, which may considerably enhance electron pairing interaction in a metamaterial superconductor. The proposed geometries may be fabricated at the current level of nanotechnology development. They enable tuning of both frequency and spatial dispersion of the effective dielectric response function ${\varepsilon }_{\mathrm{eff}}(q,\omega )$ of the metamaterial, thus enabling optimization of the metamaterial superconductor properties.

In quantum spin liquid states, the fractionalized spinon excitations can carry fractional crystal symmetry quantum numbers, and this symmetry fractionalization distinguishes different symmetry-enriched spin liquid states with identical intrinsic topological order. In this work we propose a simple way to detect signatures of such crystal symmetry fractionalizations from the crystal symmetry representations of the ground state wave function. We demonstrate our method on projected ${\mathbb{Z}}_2$ spin liquid wave functions on the kagome lattice, and show that it can be used to classify generic wave functions. Particularly our method can be used to distinguish several proposed candidates of ${\mathbb{Z}}_2$ spin liquid states on the kagome lattice.

Ab initio random structure searching (AIRSS) and density functional theory methods are used to predict structures of calcium and magnesium carbonate $({\mathrm{CaCO}}_3$ and ${\mathrm{MgCO}}_3)$ at high pressures. We find a previously unknown ${\mathrm{CaCO}}_3$ structure which is more stable than the aragonite and “post aragonite” phases in the range 32–48 GPa. At pressures from 76 GPa to well over 100 GPa the most stable phase is a previously unknown ${\mathrm{CaCO}}_3$ structure of the pyroxene type with fourfold coordinated carbon atoms. We also predict a stable structure of ${\mathrm{MgCO}}_3$ in the range 85–101 GPa. Our results lead to a revision of the phase diagram of ${\mathrm{CaCO}}_3$ over more than half the pressure range encountered within the Earth's mantle, and smaller changes to the phase diagram of ${\mathrm{MgCO}}_3$. We predict ${\mathrm{CaCO}}_3$ to be more stable than ${\mathrm{MgCO}}_3$ in the Earth's mantle above 100 GPa, and that ${\mathrm{CO}}_2$ is not a thermodynamically stable compound under deep mantle conditions. Our results have significant implications for understanding the Earth's deep carbon cycle.

The majority of unconventional superconductors has close proximity to a magnetic phase. In many cases, the magnetic phase coexists with superconductivity in some fraction of the phase diagram. The response of these two competing phases to disorder can be used as a tool to gain a better understanding of these complex systems. Here I consider the effect of disorder on a multiband superconductor appropriate for the ferro-pnictide superconductors. I consider both interband and intraband scattering for a two-band model consisting of a hole pocket and an electron pocket. The scattering from pointlike impurities is treated within the self-consistent Born approximation. I calculate the effect of disorder on the transition temperature to the superconducting state. The influence of impurity scattering on the low-energy excitation spectrum in the superconducting state is also studied for different kinds of gap structures.

We propose a novel mechanism for nematicity potentially relevant in some iron-based superconductors (SCs). We demonstrate that the mixed $S_{\pm }+d_{x^2-y^2}$ SC state is a physically accessible state and may emerge under generic conditions, lowering spontaneously the fourfold rotational symmetry $C_4$ to $C_2$. We provide a detailed study of the mixed $S_{\pm }+d_{x^2-y^2}$ nematic state including its behavior under a Zeeman field. As a fingerprint of this state, we predict at low temperatures a first-order Zeeman-field-induced transition from the mixed nematic SC phase to the pure $d_{x^2-y^2}$ SC phase. The Zeeman field–temperature phase diagram for a nodeless mixed nematic state exhibits three distinct SC phases and a tetracritical point, remarkably reminiscent of the one observed in ${\mathrm{UPt}}_3$. Our mechanism for nematicity may also be relevant for nonsuperconducting nematic states involving mixed $S_{\pm }+d_{x^2-y^2}$ spin/charge density waves.

We investigated the electronic and magnetic properties of fully oxidized ${\mathrm{BaFeO}}_3$ thin films, which show ferromagnetic-insulating properties with cubic crystal structure, by hard x-ray photoemission spectroscopy (HAXPES), x-ray absorption spectroscopy (XAS), and soft x-ray magnetic circular dichroism (XMCD). We analyzed the results with configuration-interaction (CI) cluster-model calculations for ${\mathrm{Fe}}^{4+}$, which showed good agreement with the experimental results. We also studied ${\mathrm{SrFeO}}_3$ thin films, which have an ${\mathrm{Fe}}^{4+}$ ion helical magnetism in cubic crystal structure, but are metallic at all temperatures. We found that ${\mathrm{BaFeO}}_3$ thin films are insulating with large magnetization ( 1.$7{\mu }_B$/formula unit) under $\sim 1$ T, using valence-band HAXPES and Fe $2p$ XMCD, which is consistent with the previously reported resistivity and magnetization measurements. Although Fe $2p$ core-level HAXPES and Fe $2p$ XAS spectra of ${\mathrm{BaFeO}}_3$ and ${\mathrm{SrFeO}}_3$ thin films are quite similar, we compared the insulating ${\mathrm{BaFeO}}_3$ to metallic ${\mathrm{SrFeO}}_3$ thin films with valence-band HAXPES. The CI cluster-model analysis indicates that the ground state of ${\mathrm{BaFeO}}_3$ is dominated by $d^5\underline{L}(\underline{L}$: ligand hole) configuration due to the negative charge transfer energy, and that the band gap has significant O $2p$ character. We revealed that the differences of the electronic and magnetic properties between ${\mathrm{BaFeO}}_3$ and ${\mathrm{SrFeO}}_3$ arise from the differences in their lattice constants, through affecting the strength of hybridization and bandwidth.

We study the nonequilibrium dynamics of a simple model for ${\mathrm{V}}_2{\mathrm{O}}_3$ that consists of a quarter-filled Hubbard model for two orbitals that are split by a weak crystal field. Peculiarities of this model are (1) a Mott insulator whose gap corresponds to transferring an electron from the occupied lower orbital to the empty upper one, rather than from the lower to the upper Hubbard subbands; (2) a Mott transition generically of first order even at zero temperature. We simulate by means of time-dependent Gutzwiller approximation the evolution within the insulating phase of an initial state endowed by a nonequilibrium population of electrons in the upper orbital and holes in the lower one. We find that the excess population may lead, above a threshold, to a gap collapse and drive the insulator into the metastable metallic phase within the coexistence region around the Mott transition. This result foresees a nonthermal pathway to revert a Mott insulator into a metal. Even though this physical scenario is uncovered in a very specific toy model, we argue it might apply to other Mott insulating materials that share similar features.

We analyze the interplay between charge-density-wave (CDW) and pair-density-wave (PDW) orders within the spin-fermion model for the cuprates. We specifically consider CDW order with transferred momenta $(\pm Q,0)/(0,\pm Q)$, as seen in experiments on the cuprates, and PDW order with total momenta $(0,\pm Q)/(\pm Q,0)$. Both orders have been proposed to explain the pseudogap phase in the cuprates. We show that both emerge in the spin-fermion model near the onset of antiferromagnetism. Each order parameter is constructed out of pairs of fermions in “hot” regions on the Fermi surface, breaks $\mathrm{U}\left(1\right)$ translational symmetry, and changes sign when the momenta of the fermions change by $(\pi ,\pi )$. We further show that the two orders are nearly degenerate due to an approximate $\mathrm{SU}\left(2\right)$ particle-hole symmetry of the model. This near degeneracy is similar in origin to that relating conventional $d$-wave superconducting order and bond charge order with momentum $(Q,\pm Q)$. The $\mathrm{SU}\left(2\right)$ symmetry becomes exact if one neglects the curvature of the Fermi surface in hot regions, in which case $\mathrm{U}\left(1\right)$, CDW, and PDW order parameters become components of an $\mathrm{SO}\left(4\right)$-symmetric PDW/CDW “supervector.” We develop a Ginzburg-Landau theory for four PDW/CDW order parameters and find two possible ground states: a “stripe” state in which both CDW and PDW orders develop with either $(\pm Q,0)$ or $(0,\pm Q)$, and a “checkerboard” state, where each order can develop with $(\pm Q,0)$ and $(0,\pm Q)$. We show that the $\mathrm{SO}\left(4\right)$ symmetry between CDW and PDW can be broken by two separate effects. One is the inclusion of Fermi surface curvature, which selects a PDW order immediately below the instability temperature. Another is the overlap between different hot regions, which favors CDW order at low temperatures. For the stripe state, we show that the competition between the two effects gives rise to a first-order transition from PDW to CDW inside the ordered state. We also argue that beyond mean-field theory, the onset temperature for CDW order is additionally enhanced due to feedback from a preemptive breaking of ${\mathbb{Z}}_2$ time-reversal symmetry. We discuss the ground-state properties of a pure PDW state and a pure CDW state, and show in particular that the PDW checkerboard state yields a vortex-antivortex lattice. For the checkerboard state, we considered a situation when both CDW and PDW orders are present at low $T$ and show that at small but finite Fermi surface curvature the presence of both condensates induces a long sought chiral $s+i{d}_{xy}$ superconductivity.

In a recent paper [Phys. Rev. B 90, 115134 (2014)] we put forward a diagrammatic expansion for the self-energy which guarantees the positivity of the spectral function. In this work we extend the theory to the density-response function. We write the generic diagram for the density-response spectrum as the sum of “partitions.” In a partition the original diagram is evaluated using time-ordered Green's functions on the left half of the diagram, antitime-ordered Green's functions on the right half of the diagram, and lesser or greater Green's function gluing the two halves. As there exists more than one way to cut a diagram in two halves, to every diagram corresponds more than one partition. We recognize that the most convenient diagrammatic objects for constructing a theory of positive spectra are the half-diagrams. Diagrammatic approximations obtained by summing the squares of half-diagrams do indeed correspond to a combination of partitions which, by construction, yield a positive spectrum. We develop the theory using bare Green's functions and subsequently extend it to dressed Green's functions. We further prove a connection between the positivity of the spectral function and the analytic properties of the polarizability. The general theory is illustrated with several examples and then applied to solve the long-standing problem of including vertex corrections without altering the positivity of the spectrum. In fact already the first-order vertex diagram, relevant to the study of gradient expansion, Friedel oscillations, etc., leads to spectra which are negative in certain frequency domain. We find that the simplest approximation to cure this deficiency is given by the sum of the zeroth-order bubble diagram, the first-order vertex diagram, and a partition of the second-order ladder diagram. We evaluate this approximation in the three-dimensional homogeneous electron gas and show the positivity of the spectrum for all frequencies and densities.

Finding an accurate ab initio approach for calculating the electronic properties of transition-metal oxides has been a problem for several decades. In this paper, we investigate the electronic structure of the transition-metal monoxides MnO, CoO, and NiO in their undistorted rocksalt structure within a fully iterated quasiparticle self-consistent $GW$ ($\mathrm{QPsc}GW$) scheme. We study the convergence of the $\mathrm{QPsc}GW$ method, i.e., how the quasiparticle energy eigenvalues and wave functions converge as a function of the $\mathrm{QPsc}GW$ iterations, and we compare the converged outputs obtained from different starting wave functions. We find that the convergence is slow and that a one-shot $G_0{W}_0$ calculation does not significantly improve the initial eigenvalues and states. It is important to notice that in some cases the “path” to convergence may go through energy band reordering which cannot be captured by the simple initial unperturbed Hamiltonian. When we reach a fully iterated solution, the converged density of states, band gaps, and magnetic moments of these oxides are found to be only weakly dependent on the choice of the starting wave functions and in reasonably good agreement with the experiment. Finally, this approach provides a clear picture of the interplay between the various orbitals near the Fermi level of these simple transition-metal monoxides. The results of these accurate ab initio calculations can provide input for models aiming at describing the low-energy physics in these materials.

We show how a ground-state trial wave function of a Fermi liquid can be systematically improved by introducing a sequence of renormalized coordinates through an iterative backflow transformation. We apply this scheme to calculate the ground-state energy of liquid ${}^3\mathrm{He}$ in two dimensions at freezing density using variational and fixed-node diffusion Monte Carlo. Compared with exact transient estimate results for systems with a small number of particles, we find that variance extrapolations provide accurate results for the true ground state together with stringent lower bounds. For larger systems these bounds can in turn be used to quantify the systematic bias of fixed-node calculations. These wave functions are size consistent and the scaling of their computational complexity with the number of particles is the same as for standard backflow wave functions.

In the higher Landau levels $(N>0)$ a reentrant integer quantum Hall effect (RIQHE) state, which resides at fractional filling factors but exhibits integer Hall plateaus, has been previously observed and studied extensively. The nonlinear dynamics of the RIQHE were measured by microwave resonance, with the results consistent with an electronic bubble phase pinned by impurities. We have carried out depinning experiments on the $N=2$ bubble phases by using Corbino geometry, where depinning threshold values have been systematically measured as a function of magnetic fields and temperatures. Domain sizes and pinning potential of the bubble phases have been estimated from the nonlinear transport data.

We perform a first-principles study of Mg adatom/adislands on the $\mathrm{Mg}(0001)$ surface, and Be adatom on $\mathrm{Be}\left(0001\right)$, to obtain further insight into the previously reported energetic preference of the fcc faulty stacking of Mg monomers on $\mathrm{Mg}(0001)$. We first provide a viewpoint on how Friedel oscillations influence ionic relaxation on these surfaces. Our three-dimensional charge-density analysis demonstrates that Friedel oscillations have maxima which are more spatially localized than what one-dimensional average density or two-dimensional cross-sectional plots could possibly inform: The well-known charge-density enhancement around the topmost surface layer of $\mathrm{Mg}(0001)$ is strongly localized at its fcc hollow sites. The charge accumulation at this site explains the energetically preferred stacking fault of the Mg monomer, dimer, and trimer. Yet, larger islands prefer the normal hcp stacking. Surprisingly, the mechanism by which the fcc site becomes energetically more favorable is not that of enhancing the surface-adatom bonds but rather those between surface atoms. To confirm our conclusions, we analyze the stacking of a Be adatom on $\mathrm{Be}\left(0001\right)$—a surface also largely influenced by Friedel oscillations. We find, in fact, a much stronger effect: The charge enhancement at the fcc site is even larger and, consequently, the stacking-fault energy favoring the fcc site is quite large—$44\mathrm{meV}$.

The absolute values of solids' surface energies are among the least well-known physical quantities, despite their fundamental importance. Experimental values obtained by various methods often differ by over 100%, mostly because the measurements are indirect and complicated. Reliable computational methods for predicting surface energies would therefore be extremely valuable. Here we assess the utility of using exact exchange (EXX) in conjunction with the many-electron perturbation theory extension of density functional theory, i.e., the random phase approximation (RPA), when predicting surface energies. The EXX + RPA approach was used to calculate the surface energies and cleavage properties of LiH, Mg, Pb, MgO, and NiAl, materials for which reliable experimental surface energies are available. The calculated values agreed well with the experimental data in all cases, suggesting that the longstanding problem of reliably predicting surface energies has been solved.