We provide strong numerical evidence, using improved variational wave functions, for a ground state with vanishing spin gap in the spin-$1/2$ quantum Heisenberg model on the kagome lattice. Starting from the algebraic $U\left(1\right)$ Dirac spin liquid state proposed by Ran et al. [Phys. Rev. Lett. 98, 117205 (2007)] and iteratively applying a few Lanczos steps, we compute the lowest $S=2$ excitation constructed by exciting spinons close to the Dirac nodes. Our results are compatible with a vanishing spin gap in the thermodynamic limit and in consonance with a power-law decay of long distance spin-spin correlations in real space. The competition with a gapped (topological) spin liquid is discussed.

Theoretical prediction of self-diffusion in a metal oxide in a wide range of thermodynamic conditions has been a long-standing challenge. Here, we establish that combining the formation free energies and migration barriers of all charged oxygen defects as calculated by density functional theory, within the random-walk diffusion theory framework, is a viable approach to predicting oxygen self-diffusion in metal oxides. We demonstrate this approach on tetragonal ZrO${}_2$ by calculating oxygen self-diffusivity as a function of temperature and oxygen partial pressure or, alternatively, temperature and off-stoichiometry. Arrhenius analysis on the isobaric (or constant off-stoichiometry) self-diffusivities yields a spectrum of effective activation barriers and prefactors. This provides reconciliation for the wide scatter in the experimentally determined activation barriers and prefactors for many oxides.

We derive and analyze an effective Ginzburg-Landau (GL) functional for a charge density wave for a model of electrons on a tight-binding square lattice with density-density interactions. We show, using realistic electronic dispersions for the cuprates, that for the simplest GL theory, the preferred symmetry is typically unidirectional (stripe) type, but inclusion of third-order terms tends to destabilize this in favor of a checkerboard pattern depending on the strength and range of the interaction. This is of interest given the recent observation of such charge order in underdoped YBa${}_2$Cu${}_3$O${}_{6+x}$.

We show that in crystals where light ions are symmetrically intercalated between heavy ions, the electron-phonon coupling for carriers located at the light sites cannot be described by a Holstein model. We introduce the double-well electron-phonon coupling model to describe the most interesting parameter regime in such systems and study it in the single-carrier limit using the momentum average approximation. For sufficiently strong coupling, a small polaron with a robust phonon cloud appears at low energies. While some of its properties are similar to those of a Holstein polaron, we highlight some crucial differences. These prove that the physics of the double-well electron-phonon coupling model cannot be reproduced with a linear Holstein model.

Anderson's idea of a (short-ranged) resonating valence bond (RVB) spin liquid has been the first ever proposal of what we now call a topologically ordered phase. Since then, a wealth of exactly solvable lattice models have been constructed that have topologically ordered ground states. For a long time, however, it has been difficult to realize Anderson's original vision in such solvable models, according to which the ground state has an unbroken SU(2) spin rotational symmetry and is dominated by fluctuation of singlet bonds. The kagome lattice is the simplest lattice geometry for which parent Hamiltonians stabilizing a prototypical spin-1$/$2 short-ranged RVB wave function has been constructed and strong evidence has been given that this state belongs to a topological phase. The uniqueness of the desired RVB-type ground states has, however, not been rigorously proven for the simplest possible such Hamiltonian, which acts on 12 spins at a time. Rather, this uniqueness has been demonstrated for a longer ranged (19-site) variant of this Hamiltonian by Schuch et al., via making contact with powerful results for projected entangled-pair states. In this paper, we extend this result to the 12-site Hamiltonian. Our result is based on numerical studies on finite clusters, for which we demonstrate a “ground state intersection property” with implications for arbitrary system size. We also review the relations between various constructions schemes for RVB parent Hamiltonians found in the literature.

We present an experimental and theoretical study of multiple Bragg diffraction from synthetic opals. An original setup permits us to overcome the problem of the total internal light reflection in an opal film and to investigate the diffraction from both the $\left(111\right)$ and $\left(\overline{1}11\right)$ systems of planes responsible for the effect. As a result, angle- and frequency-resolved diffraction and transmission measurements create a picture of multiple Bragg diffraction that includes general agreement between dips in the transmission spectra and diffraction peaks for each incident white light angle and a twin-peak structure at frequencies of the photonic stop band edges. Two opposite cases of the interference are discussed: an interference of two narrow Bragg bands that leads to multiple Bragg diffraction with anticrossing regime for dispersion photonic branches and an interference of a narrow Bragg band and broad disorder-induced Mie background that results in a Fano resonance. A good quantitative agreement between the experimental data and calculated photonic band structure has been obtained.

Carbon is a common impurity in the group-III nitrides, often unintentionally incorporated during growth. Nevertheless, the properties of carbon impurities in the nitrides are still not fully understood. We investigate the impact of carbon impurities on the electrical and optical properties of GaN, AlN, and InN using density functional calculations based on a hybrid functional. We examine the stability of substitutional and interstitial configurations as a function of the Fermi-level position and chemical potentials. In all nitrides studied here, C${}_{\mathrm{N}}$ acts as a deep acceptor and gives rise to deep, broad photoluminescence bands. Carbon on the cation site acts as a shallow donor in InN and GaN, but behaves as a $DX$ center in AlN. A split interstitial is the most stable configuration for the C impurity in InN, where it acts as a double donor and likely contributes to $n$-type conductivity.

We calculate the spectrum of states that are localized at the interface between two regions of opposite bias in trilayer graphene (TLG). These potential profiles, also known as potential kinks, have been predicted to support two different branches of localized states for the case of bilayer graphene, and show similarities to the surface states of topological insulators. On the other hand, we found that ABC stacked TLG exhibits three different unidimensional branches of states in each valley that are confined to the kink interface. They have the property $E\left(k_y\right)=-E(-k_y)$ when belonging to the same valley and $E_K\left(k_y\right)=-E_{K^{\prime }}(-k_y)$. A kink-antikink potential profile opens a gap in the spectrum of these one-dimensional states.

We consider single-layer plane graphene with electronic excitations described by the Dirac equation. Using a known representation of the polarization tensor in terms of the spinor loop, we show the existence of surface modes, i.e., undamped in time excitations of the electromagnetic field, propagating along the graphene. These show up in the TE polarization and exist at zero temperature. We start with a finite-mass gap, which can be shrunk to zero at the end preserving the existence of the plasmon found. We also discuss the scattering modes.

Heavy-fermion systems represent a prototypical setting to study magnetic quantum phase transitions. A particular focus has been on the physics of Kondo destruction, which captures quantum criticality beyond the Landau framework of order-parameter fluctuations. In this context, we study the spin one-half Kondo-Heisenberg model on a honeycomb lattice at half filling. The problem is approached from the Kondo-destroyed, antiferromagnetically ordered insulating phase. We describe the local moments in terms of a coarse grained quantum nonlinear sigma model, and show that the skyrmion defects of the antiferromagnetic order parameter host a number of competing order parameters. In addition to the spin Peierls, charge and current density wave order parameters, we identify for the first time Kondo singlets as the competing orders of the antiferromagnetism. We show that the antiferromagnetism and various competing singlet orders can be related to each other via generalized chiral transformations of the underlying fermions. We also show that the conduction electrons acquire a Berry phase through their coupling to the hedgehog configurations of the Néel order, which cancels the Berry phase of the local moments. Our results demonstrate the competition between the Kondo singlet formation and spin-Peierls order when the antiferromagnetic order is suppressed, thereby shedding new light on the global phase diagram of heavy-fermion systems at zero temperature.

We investigate the electronic structure of the strongly anisotropic, quasi-low-dimensional purple bronze Li${}_{0.9}$Mo${}_6$O${}_{17}$. Building on all-electron ab initio band-structure calculations, we obtain an effective model in terms of four maximally localized Wannier orbitals, which turn out to be far from atomiclike. We find two half-filled orbitals arranged in chains running along one crystallographic direction and two full orbitals in perpendicular directions, respectively. The possibility to reduce this model to only two orbitals forming two chains per unit cell with interchain coupling is discussed. Transport properties of these models show high anisotropy, reproducing trends of the experimentally determined values for the dc conductivity. We also consider basic effects of electron-electron interactions using the (extended) variational cluster approach and dynamical mean field theory. We find good agreement with experimental photoemission data upon adding moderate onsite interaction of the order of the bandwidth to the ab initio derived tight-binding Hamiltonian. The obtained models provide a profound basis for further investigations on low-energy Luttinger-liquid properties or to study electronic correlations within computational many-body theory.

We elucidate the close relationship between spontaneous time-reversal symmetry breaking and the physics of excitonic instabilities in strongly correlated multiband systems. The underlying mechanism responsible for the spontaneous breaking of time-reversal symmetry in a many-body system is closely related to the Cooper-like pairing instability of interband particle-hole pairs involving higher-order symmetries. Studies of such pairing instabilities have, however, mainly focused on the mean-field aspects of the virtual exciton condensate, which ignores the presence of the underlying collective Fermi-liquid excitations. We show that this relationship can be exploited to systematically derive the coupling of the condensate order parameter to the intraband Fermi-liquid particle-hole excitations. Surprisingly, we find that the static susceptibility is negative in the ordered phase when the coupling to the Fermi-liquid collective excitations are included, suggesting that a uniform condensate of virtual excitons, with or without time-reversal breaking, is an unstable phase at $T=0$.

Electron states in an inhomogeneous Ge/Si quantum dot array with groups of closely spaced quantum dots were studied by the conventional continuous-wave electron spin resonance and spin-echo techniques. We have found that the existence of quantum dot groups allows increasing the spin relaxation time in the system. The created structures permit us to change the effective localization radius of electrons by an external magnetic field. With the localization radius being close to the size of a quantum dot group, we obtain a fourfold increase in the spin relaxation time $T_1$ as compared to conventional homogeneous quantum dot arrays. This effect is attributed to an averaging of the local magnetic fields produced by ${}^{29}$Si nuclear spins and a stabilization of the $S_z$ polarization during the electron back-and-forth motion within a quantum dot group.

The Kitaev-Heisenberg (KH) model has been proposed to capture magnetic interactions in iridate Mott insulators on the honeycomb lattice. We show that analogous interactions arise in many other geometries built from edge-sharing IrO${}_6$ octahedra, including the pyrochlore and hyperkagome lattices relevant to Ir${}_2$O${}_4$ and Na${}_4$Ir${}_3$O${}_8$, respectively. The Kitaev spin liquid exact solution does not generalize to these lattices. However, a different, exactly soluble point of the honeycomb lattice KH model, obtained by a four-sublattice transformation to a ferromagnet, generalizes to all of these lattices and even to certain additional further neighbor Heisenberg couplings. A Klein four-group $\cong$${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ structure is associated with this mapping (hence Klein duality). A finite lattice admits the duality if a simple geometrical condition is met. This duality predicts fluctuation-free ordered states on these different 2D and 3D lattices, which are analogues of the honeycomb lattice KH stripy order. This result is used in conjunction with a semiclassical Luttinger-Tisza approximation to obtain phase diagrams for KH models on the different lattices. We also discuss a Majorana fermion based mean-field theory at the Kitaev point, which is exact on the honeycomb lattice, for the KH models on the different lattices. We attribute the rich behavior of these models to the interplay of geometric frustration and frustration induced by spin-orbit coupling.

We present the high-temperature expansion (HTE) up to tenth order of the specific heat $C$ and the uniform susceptibility $\chi$ for Heisenberg models with arbitrary exchange patterns and arbitrary spin quantum number $s$. We encode the algorithm in a c++ program provided in the Supplemental Material [http://link.aps.org/supplemental/10.1103/PhysRevB.89.014415] which allows to explicitly get the HTE series for concrete Heisenberg models. We apply our algorithm to pyrochlore ferromagnets and kagome antiferromagnets using several Padé approximants for the HTE series. For the pyrochlore ferromagnet, we use the HTE data for $\chi$ to estimate the Curie temperature $T_c$ as a function of the spin quantum number $s$. We find that $T_c$ is smaller than that for the simple-cubic lattice, although both lattices have the same coordination number. For the kagome antiferromagnet, the influence of the spin quantum number $s$ on the susceptibility as a function of renormalized temperature $T/s(s+1)$ is rather weak for temperatures down to $T/s(s+1)\sim 0.3$. On the other hand, the specific heat as a function of $T/s(s+1)$ noticeably depends on $s$. The characteristic maximum in $C\left(T\right)$ is monotonously shifted to lower values of $T/s(s+1)$ when increasing $s$.

We present a theoretical model for the longitudinal spin-Seebeck effect (LSSE) in bilayers made of a ferromagnetic insulator (FMI), such as yttrium iron garnet (YIG), and a normal metal (NM), such as platinum (Pt), that relies on the bulk magnon spin current created by the temperature gradient across the thickness of the FMI. We show that the spin current pumped into the NM layer by the magnon accumulation in the FMI provides continuity of the spin current at the FMI/NM interface and is essential for the existence of the longitudinal spin-Seebeck effect. The results of the theory are in good agreement with experimental data for the variation of the LSSE with the sample temperature and with the FMI layer thickness in YIG/Pt bilayers.

We investigate the magnetic ordering and dynamics of the stripe phase of La${}_{5/3}$Sr${}_{1/3}$CoO${}_4$, a material shown to have an hourglass magnetic excitation spectrum. A combination of muon-spin relaxation, nuclear magnetic resonance, and magnetic susceptibility measurements strongly suggest that the physics is determined by a partially disordered configuration of charge and spin stripes whose frustrated magnetic degrees of freedom are dynamic at high temperature and which undergo an ordering transition around 35 K with coexisting dynamics that freeze out in a glassy manner as the temperature is further reduced.

A density functional theory (DFT) study of the 1/2$\langle 111\rangle$ screw dislocation was performed in the following body-centered cubic transition metals: V, Nb, Ta, Cr, Mo, W, and Fe. The energies of the easy, hard, and split core configurations, as well as the pathways between them, were investigated and used to generate the two-dimensional (2D) Peierls potential, i.e. the energy landscape seen by the dislocation as a function of its position in the (111) plane. In all investigated elements, the nondegenerate easy core is the minimum energy configuration, while the split core configuration, centered in the immediate vicinity of a $\langle 111\rangle$ atomic column, has a high energy near or above that of the hard core. This unexpected result yields 2D Peierls potentials very different from the usually assumed landscapes. The 2D Peierls potential in Fe differs from the other transition metals, with a monkey saddle instead of a local maximum located at the hard core. An estimation of the Peierls stress from the shape of the Peierls barrier is presented in all investigated metals. A strong group dependence of the core energy is also evidenced, related to the position of the Fermi level with respect to the minimum of the pseudogap of the electronic density of states.

Functional renormalization group (FRG) has become a diverse and powerful tool to derive effective low-energy scattering vertices of interacting many-body systems. Starting from a free expansion point of the action, the flow of the RG parameter $\Lambda$ allows us to trace the evolution of the effective one- and two-particle vertices towards low energies by taking into account the vertex corrections between all parquet channels in an unbiased fashion. In this work, we generalize the expansion point at which the diagrammatic resummation procedure is initiated from a free UV limit to a cluster product state. We formulate a cluster FRG scheme where the noninteracting building blocks (i.e., decoupled spin clusters) are treated exactly, and the intercluster couplings are addressed via RG. As a benchmark study, we apply our cluster FRG scheme to the spin-$\frac{1}{2}$ bilayer Heisenberg model (BHM) on a square lattice where the neighboring sites in the two layers form the individual two-site clusters. Comparing with existing numerical evidence for the BHM, we obtain reasonable findings for the spin susceptibility, the spin-triplet excitation energy, and quasiparticle weight even in coupling regimes close to antiferromagnetic order. The concept of cluster FRG promises applications to a large class of interacting electron systems.

Using a canonical transformation, it is possible to faithfully represent the Kondo lattice model in terms of Majorana fermions. Studying this representation, we discovered an exact mapping between the Kondo lattice Hamiltonian and a Hamiltonian describing three spinless fermions interacting on a lattice. This alternative form of the Hamiltonian is suitable for an immediate identification of the competing effects that operate in the Kondo lattice model. In particular, a term describing the double-exchange mechanism appears explicitly in the Hamiltonian. We investigate the effectiveness of this three-fermion representation by performing a zero-temperature mean-field study of the phase diagram at different couplings and fillings for the one-dimensional case, focusing on the appearance of ferromagnetism. The solutions show interesting features that agree in many respects with the known numerical and analytical results. In particular, in the ferromagnetic region connected to the solution at zero electron density, we have a quantitative agreement on the value of the “commensurability parameter” discovered in recent density matrix renormalization group (in one dimension) and dynamical mean-field theory (in infinite dimensions) simulations; furthermore, we provide a theoretical justification for it, identifying a symmetry of the Hamiltonian. This ferromagnetic phase is stabilized by the emergence of a spin-selective Kondo insulator, which is described quite conveniently by the three spinless fermions. We discover, however, that such a phase cannot be the correct description for all the ferromagnetic phases of the one-dimensional Kondo lattice model. We found in fact a different ferromagnetic phase at high filling and low couplings. This phase resembles the Ruderman-Kittel-Kasuya-Yosida (RKKY) ferromagnetic phase existing at vanishing filling, but it incorporates much more of the Kondo effect, making it energetically more favorable than the typical spiral (spin ordered) mean-field ground states. We believe that this second phase represents a prototype for the strange ferromagnetic tongue identified by numerical simulations inside the paramagnetic dome. At the end of the work, we also provide a discussion of possible orders different from the ferromagnetic one. In particular, at half-filling, where we obtain as ground state at high coupling the correct Kondo insulating state.