We present an extensive study of the two-impurity Kondo problem for spin-1 adatoms on a square lattice using an exact canonical transformation to map the problem onto an effective one-dimensional system that can be numerically solved using the density matrix renormalization group method. We provide a simple intuitive picture and identify the different regimes, depending on the distance between the two impurities, Kondo coupling $J_K$, longitudinal anisotropy $D$, and transverse anisotropy $E$. In the isotropic case, two impurities on opposite (the same) sublattices have a singlet (triplet) ground state. However, the energy difference between the triplet ground state and the singlet excited state is very small and we expect an effectively fourfold-degenerate ground state, i.e., two decoupled impurities. For large enough $J_K$ the impurities are practically uncorrelated forming two independent underscreened states with the conduction electrons, a clear nonperturbative effect. When the impurities are entangled in an RKKY-like state, Kondo correlations persist and the two effects coexist: the impurities are underscreened, and the dangling spin-$1/2$ degrees of freedom are responsible for the interimpurity entanglement. We analyze the effects of magnetic anisotropy in the development of quasiclassical correlations.

Motivated by recent numerical work, we use the boson-vortex duality to study the possible phases of the frustrated spin-$\frac{1}{2}{J}_1\text{−}{J}_2$ XXZ models on the honeycomb lattice. By condensing the vortices, we obtain various gapped phases that either break certain lattice symmetry or preserve all the symmetries. The gapped phases breaking lattice symmetries occur when the vortex band structure has two minima. Condensing one of the two vortex flavors leads to an Ising ordered phase, while condensing both vortex flavors gives rise to a valence-bond-solid state. Both of those phases have been observed in the numerical studies of the $J_1\text{−}{J}_2$ XXZ honeycomb model. Furthermore, by tuning the band structure of vortex and condensing it at the $\mathrm{\Gamma }$ point, we obtain a featureless paramagnet. But the precise nature of this featureless state is still unclear and needs future study.

The interplay between electronic interactions and disorder is neglected in the conventional Boltzmann theory of transport, yet can play an essential role in determining the resistivity of unconventional metals. When quasiparticles are long lived, one can account for these intertwined effects by solving spatially inhomogeneous Boltzmann equations. Assuming smooth disorder and neglecting umklapp scattering, we solve these inhomogeneous kinetic equations and compute the electrical resistivity across the ballistic-to-hydrodynamic transition. An important consequence of electron-electron interactions is the modification of the momentum-relaxation time; this effect is ignored in the homogeneous theory. We characterize precisely when interactions enhance the momentum scattering rate, and when they decrease it. Our approach unifies existing semiclassical theories of transport, and explains how the resistivity can be proportional to the rate of momentum-conserving collisions without Baber scattering. We compare this result with existing transport mysteries, including the disorder-independent $T^2$ resistivity of many Fermi liquids, and the linear-in-$T$ “Planckian-limited” resistivity of many strange metals.

We have developed a formalism of the exact solution to linearized phonon Boltzmann transport equation (BTE) for thermal conductivity calculation including three- and four-phonon scattering. We find strikingly high four-phonon scattering rates in single-layer graphene (SLG) based on the optimized Tersoff potential. The reflection symmetry in graphene, which forbids the three-ZA (out-of-plane acoustic) scattering, allows the four-ZA processes $\mathrm{ZA}+\mathrm{ZA}\rightleftharpoons \mathrm{ZA}+\mathrm{ZA}$ and $\mathrm{ZA}\rightleftharpoons \mathrm{ZA}+\mathrm{ZA}$ + ZA. As a result, the large phonon population of the low-energy ZA branch originated from the quadratic phonon dispersion leads to high four-phonon scattering rates, even much higher than the three-phonon scattering rates at room temperature. These four-phonon processes are dominated by the normal processes, which lead to a failure of the single mode relaxation time approximation. Therefore, we have solved the exact phonon BTE using an iterative scheme and then calculated the length- and temperature-dependent thermal conductivities. We find that the predicted thermal conductivity of SLG is lower than the previously predicted value from the three-phonon scattering only. The relative contribution of the ZA branch is reduced from 70% to 30% when four-phonon scattering is included. Furthermore, we have demonstrated that the four-phonon scattering in multilayer graphene and graphite is not strong due to the ZA splitting by interlayer van der Waals interaction. We also demonstrate that the five-phonon process in SLG is not strong due to the restriction of reflection symmetry.

We study the scattering of phonons from point defects and their effect on lattice thermal conductivity $\kappa$ using a parameter-free ab initio Green's function methodology. Specifically, we focus on the scattering of phonons by boron (B), nitrogen (N), and phosphorus substitutions as well as single- and double-carbon vacancies in graphene. We show that changes of the atomic structure and harmonic interatomic force constants locally near defects govern the strength and frequency trends of the scattering of out-of-plane acoustic (ZA) phonons, the dominant heat carriers in graphene. ZA scattering rates due to N substitutions are nearly an order of magnitude smaller than those for B defects despite having similar mass perturbations. Furthermore, ZA phonon scattering rates from N defects decrease with increasing frequency in the lower-frequency spectrum in stark contrast to expected trends from simple models. ZA phonon-vacancy scattering rates are found to have a significantly softer frequency dependence ($\sim {\omega }^0$) in graphene than typically employed in phenomenological models. The rigorous Green's function calculations demonstrate that typical mass-defect models do not adequately describe ZA phonon-defect scattering rates. Our ab initio calculations capture well the trend of $\kappa$ vs vacancy density from experiments, though not the magnitudes. This work elucidates important insights into phonon-defect scattering and thermal transport in graphene, and demonstrates the applicability of first-principles methods toward describing these properties in imperfect materials.

Mixed spin-singlet and spin-triplet pairing can occur in noncentrosymmetric superconductors. In this respect, a comprehensive characterization of the noncentrosymmetric superconductor BeAu was carried out. It was established that BeAu undergoes a structural phase transition from a low-temperature noncentrosymmetric FeSi structure type to a high-temperature centrosymmetric structure in the CsCl type at $T_{\text{s}}=860$ K. The low-temperature modification exhibits a superconducting transition below $T_{\text{c}}=3.3$ K. The values of lower ($H_{\text{c1}}=32$ Oe) and upper ($H_{\text{c2}}=335$ Oe) critical fields are rather small, confirming that this type-II (${\kappa }_{\text{G-L}}=2.3$) weakly coupled (${\lambda }_{\text{e-p}}=0.5,\mathrm{\Delta }{C}_{\text{e}}/{\gamma }_{\text{n}}{T}_{\text{c}}\approx 1.26$) superconductor can be well understood within the Bardeen-Cooper-Schrieffer theory. The muon spin relaxation analysis indicates that the time-reversal symmetry is preserved when the superconducting state is entered, supporting conventional superconductivity in BeAu. From the density functional band structure calculations, a considerable contribution of the Be electrons to the superconducting state was established. On average, a rather small mass renormalization was found, consistent with the experimental data.

Weak attractive interactions in a spin-imbalanced Fermi gas induce a multiparticle instability, binding multiple fermions together. The maximum binding energy per particle is achieved when the ratio of the number of up- and down-spin particles in the instability is equal to the ratio of the up- and down-spin densities of states in momentum at the Fermi surfaces, to utilize the variational freedom of all available momentum states. We derive this result using an analytical approach, and verify it using exact diagonalization. The multiparticle instability extends the Cooper pairing instability of balanced Fermi gases to the imbalanced case, and could form the basis of a many-body state, analogously to the construction of the Bardeen-Cooper-Schrieffer theory of superconductivity out of Cooper pairs.

We present an advanced method to study spin fluctuations in superconductors quantitatively and entirely from first principles. This method can be generally applied to materials where electron-phonon coupling and spin fluctuations coexist. We employ it here to examine the recently synthesized superconductor iron tetraboride (${\mathrm{FeB}}_4$) with experimental $T_{\mathrm{c}}\sim 2.4$ K [H. Gou et al., Phys. Rev. Lett. 111, 157002 (2013)]. We prove that ${\mathrm{FeB}}_4$ is particularly prone to ferromagnetic spin fluctuations due to the presence of iron, resulting in a large Stoner interaction strength, $I=1.5$ eV, as calculated from first principles. The other important factor is its Fermi surface that consists of three separate sheets, among which two are nested ellipsoids. The resulting susceptibility has a ferromagnetic peak around $\mathbf{q}=0$, from which we calculated the repulsive interaction between Cooper pair electrons using the random phase approximation. Subsequently, we combined the electron-phonon interaction calculated from first principles with the spin fluctuation interaction in fully anisotropic Eliashberg theory calculations. We show that the resulting superconducting gap spectrum is conventional, yet very strongly depleted due to coupling to the spin fluctuations. The critical temperature decreases from $T_{\mathrm{c}}=41$ K, if they are not taken into account, to $T_{\mathrm{c}}=1.7$ K, in good agreement with the experimental value.

The addition of transition-metal (TM) elements into the ${\gamma }^{\prime }$ precipitate phase of a Ni-based single-crystal superalloy can significantly affect its mechanical properties, including the intrinsic mechanical property of compressive strength. Using first-principles density functional calculations, the effects of $3d$ (Sc-Zn), $4d$ (Y-Cd), and $5d$ (Hf-Au) TM alloying elements on the ideal uniaxial compressive strength of ${\gamma }^{\prime }-{\mathrm{Ni}}_3\mathrm{Al}$ were investigated. The stress-strain relationships of pure ${\mathrm{Ni}}_3\mathrm{Al}$ under [100], [110], and [111] compressive loads and the site occupancy behavior of TM elements in ${\mathrm{Ni}}_3\mathrm{Al}$ were previously studied using a total-energy method based on density functional theory. Our results showed that the capacity of TM elements for strengthening the ideal compressive strength was associated with the $d$-electron number. The alloying elements with half-filled $d$ bands (i.e., Cr, Mo, W, Tc, and Re) manifested the greatest efficacy for improving the ideal strength of ${\mathrm{Ni}}_3\mathrm{Al}$ under a deformation along the weakest compressive direction. Furthermore, the charge redistribution of ${\mathrm{Ni}}_3\mathrm{Al}$ doped with $5d$ elements were also analyzed to understand the strengthening mechanisms of TM elements in the ${\gamma }^{\prime }-{\mathrm{Ni}}_3\mathrm{Al}$ phase.

The search for flat-band solid-state realizations is a crucial issue to verify or to challenge theoretical predictions for quantum many-body flat-band systems. For frustrated quantum magnets flat bands lead to various unconventional properties related to the existence of localized many-magnon states. The recently synthesized magnetic compound ${\mathrm{Ba}}_2{\mathrm{CoSi}}_2{\mathrm{O}}_6{\mathrm{Cl}}_2$ seems to be an almost perfect candidate to observe these features in experiments. We develop a theory for ${\mathrm{Ba}}_2{\mathrm{CoSi}}_2{\mathrm{O}}_6{\mathrm{Cl}}_2$ by adapting the localized-magnon concept to this compound. We first show that our theory describes the known experimental facts and then we propose new experimental studies to detect a field-driven phase transition related to a Wigner-crystal-like ordering of localized magnons at low temperatures.

Recent experiments demonstrate the ability to construct cold-atom mixtures with species-selective optical lattices. This allows for the possibility of a mixed-dimension system, where one fermionic atomic species is confined to a two-dimensional lattice, while another species is confined to a three-dimensional lattice that contains the two-dimensional one. We show that by tuning the density of an arbitrary number of three-dimensional atomic species, we can engineer an arbitrary, rotationally symmetric, density-density, effective interaction for the two-dimensional particles. This possibility allows for an effective interaction that favors triplet pairing for two-dimensional, $\text{SU}\left(2\right)$ symmetric particles. Using a functional renormalization-group analysis for the two-dimensional particles, we derive and numerically confirm that the critical temperature for triplet pairing depends exponentially on the effective interaction strength. We then analyze how the stability of this phase is affected by the particle densities and the fine tuning of interaction parameters. We conclude by briefly discussing experimental considerations and the potential to study triplet-pairing physics, including Majorana fermions and spin textures, with cold atoms on optical lattices.

In this paper the interaction potential between static charges in suspended graphene is studied within the quantum Monte Carlo approach. We calculated the dielectric permittivity of suspended graphene for a set of temperatures and extrapolated our results to zero temperature. The dielectric permittivity at zero temperature is found to have the following properties. At zero distance $\epsilon =2.24\pm 0.02$. Then it rises and at a large distance the dielectric permittivity reaches the plateau $\epsilon \simeq 4.20\pm 0.66$. The results obtained in this paper allow us to draw a conclusion that full account of many-body effects in the dielectric permittivity of suspended graphene gives $\epsilon$ very close to the one-loop results. Contrary to the one-loop result, the two-loop prediction for the dielectric permittivity deviates from our result. So one can expect large higher order corrections to the two-loop prediction for the dielectric permittivity of suspended graphene.

We propose a generalization of the linked-cluster expansions to study driven-dissipative quantum lattice models, directly accessing the thermodynamic limit of the system. Our method leads to the evaluation of the desired extensive property onto small connected clusters of a given size and topology. We first test this approach on the isotropic spin-1/2 Hamiltonian in two dimensions, where each spin is coupled to an independent environment that induces incoherent spin flips. Then we apply it to the study of an anisotropic model displaying a dissipative phase transition from a magnetically ordered to a disordered phase. By means of a Padé analysis on the series expansions for the average magnetization, we provide a viable route to locate the phase transition and to extrapolate the critical exponent for the magnetic susceptibility.

Within the standard model of many-body localization, i.e., the disordered chain of spinless fermions, we investigate how the interaction affects the many-body states in the basis of noninteracting localized Anderson states. From this starting point we follow the approach that uses a reduced basis of many-body states. Together with an extrapolation to the full basis, it proves to be efficient for the evaluation of the stiffnesses of local observables, which remain finite within the nonergodic regime and represent the hallmark of the many-body localization (MBL). The method enables a larger span of system sizes and, within the MBL regime, allows for a more careful analysis of the size scaling of calculated quantities. On the other hand, the survival stiffness as the representative of nonlocal quantities, reveals limitations of the reduced-basis approach.

We present a study of the electronic structure and magnetism of ${\mathrm{Co}}_2\mathrm{MnAl}$, CoMnVAl, and their heterostructure. We employ a combination of density-functional theory and dynamical mean-field theory (DFT+DMFT). We find that ${\mathrm{Co}}_2\mathrm{MnAl}$ is a half-metallic ferromagnet, whose electronic and magnetic properties are not drastically changed by strong electronic correlations, static or dynamic. Nonquasiparticle states are shown to appear in the minority spin gap without affecting the spin polarization at the Fermi level predicted by standard DFT. We find that CoMnVAl is a semiconductor or a semimetal, depending on the employed computational approach. We then focus on the electronic and magnetic properties of the ${\mathrm{Co}}_2\mathrm{MnAl}$/CoMnVAl heterostructure, predicted by previous first-principle calculations as a possible candidate for spin-injecting devices. We find that two interfaces, Co-Co/V-Al and Co-Mn/Mn-Al, preserve the half-metallic character, with and without including electronic correlations. We also analyze the magnetic exchange interactions in the bulk and at the interfaces. At the Co-Mn/Mn-Al interface, competing magnetic interactions are likely to favor the formation of a noncollinear magnetic order, which is detrimental for the spin polarization.

High-pressure x-ray absorption spectroscopy was performed at the Ir $L_3$ and $L_2$ absorption edges of ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$. The branching ratio of white-line intensities continuously decreases with pressure, reflecting a reduction in the angular part of the expectation value of the spin-orbit coupling operator, $\langle \mathbf{L}·\mathbf{S}\rangle$. Up to the high-pressure structural transition at 53 GPa, this behavior can be explained within a single-ion model, where pressure increases the strength of the cubic crystal field, which suppresses the spin-orbit induced hybridization of $J_{\text{eff}}=3/2$ and $e_g$ levels. We observe a further reduction of the branching ratio above the structural transition, which cannot be explained within a single-ion model of spin-orbit coupling and cubic crystal fields. This change in $\langle \mathbf{L}·\mathbf{S}\rangle$ in the high-pressure, metallic phase of ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ could arise from noncubic crystal fields or a bandwidth-driven hybridization of $J_{\text{eff}}=1/2,3/2$ states and suggests that the electronic ground state significantly deviates from the $J_{\text{eff}}=1/2$ limit.

The few reported members of the antiperovskite structure class $A{e}_{3}P{n}_{A}P{n}_B$ of alkaline-earth ($Ae=\mathrm{Ca}$, Sr, Ba) pnictide ($Pn=\mathrm{N}$, P, As, Sb, Bi) compounds are all based on the $B$-site anion $P{n}_B=\mathrm{N}$. All can be categorized as narrow-gap semiconductors, making them of interest for several reasons. Because chemical reasoning suggests that more members of this class may be stable, we provide here a density functional theory (DFT)-based survey of this entire class of $3\times 5\times 5$ compounds. We determine first the relative energetic stability of the distribution of pairs of $Pn$ ions in the $A$ and $B$ sites of the structure, finding that the $B$ site always favors the small pnictogen anion. The trends of the calculated energy gaps versus the $Ae$ cation and $Pn$ anions are determined, and we study effects of spin-orbit coupling as well as two types of gap corrections to the conventional DFT electronic spectrum. Because there have been suggestions that this class harbors topological insulating phases, we have given this possibility attention and found that energy gap corrections indicate the cubic structures will provide at most a few topological insulators. Structural instability is addressed by calculating phonon dispersion curves for a few compounds, with one outcome being that distorted structures should be investigated further for thermoelectric and topological character. Examples of the interplay between spin-orbit coupling and strain on the topological nature are provided. A case study of ${\mathrm{Ca}}_3\mathrm{BiP}$ including the effect of strain illustrates how a topological semimetal can be transformed into a topological insulator and Dirac semimetal.

Physical properties for the late-lanthanide-based $R{\mathrm{NiC}}_2$ ($R=\mathrm{Dy}$, Ho, Er, and Tm) ternary compounds are reported. All the compounds show antiferromagnetic ground state with the Néel temperature ranging from 3.4 K for ${\mathrm{HoNiC}}_2$ to 8.5 K for ${\mathrm{ErNiC}}_2$. The results of the transport and galvanomagnetic properties confirm a charge density wave state at and above room temperature with transition temperatures $T_{\mathrm{CDW}}=284$, 335, 366, and 394 K for ${\mathrm{DyNiC}}_2$, ${\mathrm{HoNiC}}_2$, ${\mathrm{ErNiC}}_2$, and ${\mathrm{TmNiC}}_2$, respectively. The Peierls temperature $T_{\mathrm{CDW}}$ scales linearly with the unit cell volume. A similar linear dependence has been observed for the temperature of the lock-in transition $T_1$ as well. Beyond the intersection point of the trend lines, the lock-in transition is no longer observed. In this Rapid Communication we demonstrate an extended phase diagram for the $R{\mathrm{NiC}}_2$ family.

With first-principles calculated electron-phonon coupling matrix elements, the phonon-limited electron and hole mobilities of Si and GaAs are studied using the Boltzmann transport equation. The calculated mobilities agree well with the experimental measurements. For electrons in GaAs, the calculated mobility is very sensitive to the band structure characterized by the effective mass and the energy gap between $\mathrm{\Gamma }$ and L valleys, which clarifies the discrepancies between recent literature findings [J.-J. Zhou and M. Bernardi, Phys. Rev. B 94, 201201(R) (2016); T.-H. Liu et al., Phys. Rev. B 95, 075206 (2017)]. Unlike electrons in GaAs, where the longitudinal optical phonon dominates the scattering, the other phonon branches have a comparable influence on the mobility of holes in GaAs. In Si and GaAs, the spin-orbit coupling interaction has a significant effect on the valence bands and, further, on the hole mobilities, without which the calculated mobility is underestimated, especially at relatively low temperatures, while it has almost no effect on the electrons.

We study the low-energy behavior of the vertex function of a single Anderson impurity away from half filling for finite magnetic fields, using the Ward identities with careful consideration of the antisymmetry and analytic properties. The asymptotic form of the vertex function ${\mathrm{\Gamma }}_{\sigma {\sigma }^{\prime };{\sigma }^{\prime }\sigma }^{}(i\omega ,i{\omega }^{\prime };i{\omega }^{\prime },i\omega )$ is determined up to terms of linear order with respect to the two frequencies $\omega$ and ${\omega }^{\prime }$, as well as the ${\omega }^2$ contribution for antiparallel spins ${\sigma }^{\prime }\ne \sigma$ at ${\omega }^{\prime }=0$. From these results, we also obtain a series of the Fermi-liquid relations beyond those of Yamada-Yosida [Prog. Theor. Phys. 54, 316 (1975)]. The ${\omega }^2$ real part of the self-energy ${\mathrm{\Sigma }}_{\sigma }^{}\left(i\omega \right)$ is shown to be expressed in terms of the double derivative ${\partial }^2{\mathrm{\Sigma }}_{\sigma }^{}\left(0\right)/\partial {\epsilon }_{d\sigma }^2$ with respect to the impurity energy level ${\epsilon }_{d\sigma }^{}$, and agrees with the formula obtained recently by Filippone, Moca, von Delft, and Mora (FMvDM) in the Nozières phenomenological Fermi-liquid theory [Phys. Rev. B 95, 165404 (2017)]. We also calculate the $T^2$ correction of the self-energy and find that the real part can be expressed in terms of the three-body correlation function $\partial {\chi }_{\uparrow \downarrow }/\partial {\epsilon }_{d,-\sigma }^{}$, where ${\chi }_{\uparrow \downarrow }$ is the static susceptibility between antiparallel spins. We also provide an alternative derivation of the asymptotic form of the vertex function. Specifically, we calculate the skeleton diagrams for the vertex function ${\mathrm{\Gamma }}_{\sigma \sigma ;\sigma \sigma }^{}(i\omega ,0;0,i\omega )$ for parallel spins up to order $U^4$ in the Coulomb repulsion $U$. It directly clarifies the fact that the analytic components of order $\omega$ vanish as a result of the cancellation of four related Feynman diagrams, which are related to each other through the antisymmetry operation.