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The dependence of the energies and orbital structure of local states in the CuO monolayer on intra- and interatomic Coulomb interactions on copper and oxygen orbitals is studied. The electronic system is described within the eight-band p-d model in the hole representation with the on-site energies and hopping integrals obtained using density functional theory. CuO cluster multiparticle eigenstates are calculated using exact diagonalization. The difference between the energy dependencies on the Coulomb parameters for the states with the predominant probability density on the d-orbital and the states in which hole occupies p-orbitals leads to crossover of d- and p-states. The ground single-hole and two-hole states which determine the electronic structure of the low-energy excitations have the character of d- or p-orbitals in the different regions of the Coulomb parameters space. The gap between the energies of the dispersionless quasiparticles forming the top of the valence band and conductivity band also have different values in these two regions. The magnitude of this gap and the orbital character of the local multiparticle states change sharply even with an insignificant change in the Coulomb interactions within the boundary region of parameters between the regions in which the local states are formed by the d- or p-orbitals., Comment: 30 pages, 10 figures (13 with subfigures), 4 tables, 2 appendices

VO2 features concomitant structural and metal-insulator transitions. This poses a challenge for understanding the underlying mechanism: is the transition triggered by a structural or by an electronic instability? Here, we address this question by studying pre-transitional fluctuations in the metallic state. By measuring resonant diffuse X-ray scattering we find no evidence that spatial fluctuations of d-electrons are any different from those of vanadium ion cores. That is, charge and lattice remain coupled as they fluctuate jointly towards the insulating phase, strongly supporting the case that the VO2 metal-insulator transition is triggered by a structural instability. Our work offers a novel approach to solve similar problems in other strongly correlated systems.

To study thermodynamical properties of the disorder-induced transition between $s_{\pm}$ and $s_{++}$ superconducting gap functions, we calculate the grand thermodynamic potential $\Omega$ in the normal and the superconducting states. Expression for the difference between the two, $\Delta\Omega$, is derived for a two-band model for Fe-based systems with nonmagnetic impurities. The disorder is considered in a $\mathcal{T}$-matrix approximation within the multiband Eliashberg theory. In the vicinity of the Born limit near the $s_{\pm}$-to-$s_{++}$ transition, we find two solutions obtained for opposite directions of the system's evolution with respect to the impurity scattering rate. By calculating the change in entropy $\Delta S$ and the change in electronic specific heat $\Delta C$ from $\Delta\Omega$, we show that such a hysteresis is not due to the time-reversal symmetry breaking state, but it rather points out to the first order phase transition induced by the nonmagnetic disorder. Based on the $\Delta\Omega$ calculations, phase diagram is plotted representing the energetically favourable $s_{\pm}$ and $s_{++}$ states and the transition between them. At finite temperature, a first order phase transition line there is limited by a critical end point. Above that point, the sharp $s_{\pm} \to s_{++}$ transition transforms to a crossover between $s_{\pm}$ and $s_{++}$ states., Comment: 9 pages, 7 figures

In geometrically frustrated magnetic systems, weak interactions or slight changes to the structure can tip the delicate balance of exchange interactions, sending the system into a different ground state. Brochantite, Cu$_4$SO$_4$(OH)$_6$, has a copper sublattice composed of distorted triangles, making it a likely host for frustrated magnetism, but exhibits stacking disorder. The lack of synthetic single crystals has limited research on the magnetism in brochantite to powders and natural mineral crystals. We grew crystals which we find to be a new polytype with a tendency toward ABAC stacking and some anion disorder, alongside the expected stacking disorder. Comparison to previous results on natural mineral specimens suggests that cation disorder is more deleterious to the magnetism than anion and stacking disorder. Our specific heat data suggest a double transition on cooling into the magnetically ordered state., Comment: 9.5 pages, CIF files available as arXiv ancillary files

$\mathrm{CuO}$ atomic thin monolayer ($\mathrm{mlCuO}$) was synthesized recently. Interest in the $\mathrm{mlCuO}$ is based on its close relation to $\mathrm{CuO_2}$ layers in typical high temperature cuprate superconductors. Here, we present the calculation of the band structure, the density of states and the Fermi surface of the flat $\mathrm{mlCuO}$ as well as the corrugated $\mathrm{mlCuO}$ within the density functional theory (DFT) in the generalized gradient approximation (GGA). In the flat $\mathrm{mlCuO}$, the $\mathrm{Cu}$-$3d_{x^2-y^2}$ band crosses the Fermi level, while the $\mathrm{Cu}$-$3d_{xz,yz}$ hybridized band is located just below it. The corrugation leads to a significant shift of the $\mathrm{Cu}$-$3d_{xz,yz}$ hybridized band down in energy and a degeneracy lifting for the $\mathrm{Cu}$-$3d_{x^2-y^2}$ bands. Corrugated $\mathrm{mlCuO}$ is more energetically favorable than the flat one. In addition, we compared the electronic structure of the considered $\mathrm{CuO}$ monolayers with bulk $\mathrm{CuO}$ systems. We also investigated the influence of a crystal lattice strain (which might occur on some interfaces) on the electronic structure of both $\mathrm{mlCuO}$ and determined the critical strains of topological Lifshitz transitions. Finally, we proposed a number of different minimal models for the flat and the corrugated $\mathrm{mlCuO}$ using projections onto different Wannier functions basis sets and obtained the corresponding Hamiltonian matrix elements in a real space., Comment: 10 pages, published version

We consider the effect of the nematic order on the formation of the superconducting state in iron pnictides and chalcogenides. Nematic order with the $B_{2g}$ symmetry is modelled as the $d$-type Pomeranchuk instability and treated within the mean-field approach. Calculated nematic order parameter depends on the nematic interaction coefficient and abruptly changes with the coefficient's increase. The superconducting solution is obtained within the spin-fluctuation pairing theory. We show that the leading solution in the nematic phase has a $s_{\pi\pm}$ structure. From the critical temperature $T_c$ estimations, we conclude that the nematic superconducting state of the $s_{\pi\pm}$ type is more favorable than the usual $s_\pm$ and $d_{x^2-y^2}$ type states appearing in the absence of the nematicity., Comment: 5 pages, published version

We consider a natural distance function on the period space of a hyperk\"ahler manifold associated to non-holonomic constraints imposed by twistor lines. These metrics were introduced by Verbitsky in the context of the global Torelli theorem for hyperk\"aler manifolds. We show that they are Finsler and explicitly describe their Finsler norms. To achieve this goal we consider a class of distance functions (called here sub-conic metrics) that slightly generalize sub-Riemann metrics. The main technical result is the statement that every sub-conic metric is sub-Finsler. The content and methods of the paper lie within basic metric geometry. The complex geometrical background and motivation are isolated in the appendix., Comment: 32 pages, comments are welcome

The aim of this note is to share the observation that the set of elementary operations of Turing on lattice knots can be reduced to just one type of simple local switches., Comment: 8 pages, comments are welcome

Electronic ordering is prevalent in correlated systems, which commonly exhibit competing interactions. Here, we use x-ray diffraction to show that the charge density wave transition temperature of FeGe increases with pressure and evolves towards a $\sqrt{3}\times\sqrt{3}$ periodic lattice modulation, $\mathbf{q}$$^*$=$\left(\frac{1}{3}\ \frac{1}{3}\ \frac{1}{2}\right)$. In the pressure interval between 4$<$$p$$<$12 GPa both orders coexist and the spatial extent of the $\sqrt{3}\times\sqrt{3}$ order at high pressure becomes nearly long-range, $\sim$30 unit cells, while the correlation length of the 2$\times$2 phase remains shorter-ranged. The $\sqrt{3}\times\sqrt{3}$ phase is the ground state above 15 GPa, consistent with harmonic DFT calculations that predict a dimerization induced $\sqrt{3}\times\sqrt{3}$ order without phonon softening. The pressure dependence of the integrated intensities of $\mathbf{q}$$_\mathrm{CDW}=\left(\frac{1}{2}\ 0\ \frac{1}{2}\right)$ and $\mathbf{q}$$^*$ indicates a competition between the 2$\times$2 and $\sqrt{3}\times\sqrt{3}$ and demonstrates that the ground state of FeGe is characterized by a rich landscape of metastable/fragile phases. We discuss possible scenarios based on an order-disorder transformation and the formation of Friedel oscillations.

The intrinsic frustrated nature of a kagome lattice is amenable to the realization of exotic phases of matter, such as quantum spin liquids or spin ices, and more recently the multiple-$\mathrm{\textbf{q}}$ charge density waves (CDW) in the kagome metals. Despite intense efforts to understand the mechanism driving the electronic modulations, its origin is still unknown and hindered by competing interactions and intertwined orders. Here, we identify a dimerization-driven 2D hexagonal charge-diffuse precursor in the antiferromagnetic kagome metal FeGe and demonstrate that the fraction of dimerized/undimerized states is the relevant order parameter of the multiple-$\mathrm{\textbf{q}}$ CDW of a continuous phase transition. The pretransitional charge fluctuations with propagation vector $\mathrm{\textbf{q}=\textbf{q}_M}$ at T$_{\mathrm{CDW}}$$<$T$<$T$^*$(125 K) are anisotropic, hence holding a quasi-long-range bond-orientational order. The broken translational symmetry emerges from the anisotropic diffuse precursor, akin to the Ising scenario of antiferromagnetic triangular lattices. The temperature and momentum dependence of the critical scattering show parallels to the stacked hexatic $\mathrm{B}$-phases reported in liquid crystals and transient states of CDWs and highlight the key role of the topological defect-mediated melting of the CDW in FeGe.

EuAl$_4$ is a rare earth intermetallic in which competing itinerant and/or indirect exchange mechanisms give rise to a complex magnetic phase diagram, including a centrosymmetric skyrmion lattice. These phenomena arise not in the tetragonal parent structure but in the presence of a charge density wave (CDW), which lowers the crystal symmetry and renormalizes the electronic structure. Microscopic knowledge of the corresponding atomic modulations and their driving mechanism is a prerequisite for a deeper understanding of the resulting equilibrium of electronic correlations and how it might be manipulated. Here, we use synchrotron single-crystal X-ray diffraction, inelastic X-ray scattering, and lattice dynamics calculations to clarify the origin of the CDW in EuAl$_4$. We observe a broad softening of a transverse acoustic phonon mode that sets in well above room temperature and, at $T_\mathrm{CDW}=142$ K, freezes out in an atomic displacement mode described by the superspace group $Immm(00\gamma)s00$. In the context of previous work, our observation is a clear confirmation that the CDW in EuAl$_4$ is driven by electron-phonon coupling. This result is relevant for a wider family of BaAl$_4$ and ThCr$_2$Si$_2$-type rare-earth intermetallics known to combine CDW instabilities and complex magnetism.

The topology of electronic and phonon band structures of graphene is well studied and known to exhibit a Dirac cone at the K point of the Brillouin zone. Here, we applied inelastic x-ray scattering (IXS) along with $\textit{ab initio}$ calculations to investigate phonon topology in graphite, the 3D analogue of graphene. We identified a pair of modes that form a very weakly gapped linear anticrossing at the K point that can be essentially viewed as a Dirac cone approximant. The IXS intensity in the vicinity of the quasi-Dirac point reveals a harmonic modulation of the phonon spectral weight above and below the Dirac energy, which was previously proposed as an experimental fingerprint of the nontrivial topology. We illustrate how the topological winding of IXS intensity can be understood in terms of atomic displacements, and highlight that the intensity winding is not in fact sensitive in telling quasi- and true Dirac points apart.

We study risk processes with level dependent premium rate. Assuming that the premium rate converges, as the risk reserve increases, to the critical value in the net-profit condition, we obtain upper and lower bounds for the ruin probability. In contrast to existing in the literature results, our approach is purely probabilistic and based on the analysis of Markov chains with asymptotically zero drift., Comment: 37 pages. arXiv admin note: text overlap with arXiv:1612.01592

We've studied the B800 part of Rhodoblastus acidophilus light-harvesting complex (LH2) by several quantum chemical techniques based on the density functional theory (DFT) and determined the specific method and a minimal reliable model suitable for further studies of the LH2. In addition to bacteriochlorophyll a molecules, the minimal model includes two $\alpha$ and one $\beta$ chain amino acids. Within the model, we are able to reproduce the contribution of the B800 ring of nine bacteriochlorophyll a molecules to the near infrared $Q_y$ absorption band. We also discuss the use of hybrid DFT calculations for precise energy and optical estimations and DFT-based tight binding (DFTB) method for the large-scale calculations. Crucial importance of Hartree-Fock exchange interaction for the correct description of B800 peak position was shown., Comment: 11 pages + supplementary materials (2 pages)

We investigate phonon lifetimes in VO2 single crystals. We do so in the metallic state above the metal-insulator transition (MIT), where strong structural fluctuations are known to take place. By combining inelastic X-ray scattering and Raman spectroscopy, we track the temperature dependence of several acoustic and optical phonon modes up to 1000 K. Contrary to what is commonly observed, we find that phonon lifetimes decrease with decreasing temperature. Our results show that pre-transitional fluctuations in the metallic state give rise to strong electron-phonon scattering that onsets hundreds of degrees above the transition and increases as the MIT is approached. Notably, this effect is not limited to specific points of reciprocal space that could be associated with the structural transition.

In order to characterize in detail the charge density wave (CDW) transition of 1$T$-VSe$_2$, its electronic structure and lattice dynamics are comprehensively studied by means of x-ray diffraction, angle resolved photoemission (ARPES), diffuse and inelastic x-ray scattering (IXS), and state-of-the-art first principles density functional theory calculations. Resonant elastic x-ray scattering (REXS) does not show any resonant enhancement at either V or Se K-edges, indicating that the CDW peak describes a purely structural modulation of the electronic ordering. ARPES identifies (i) a pseudogap at T$>$T$_{CDW}$, which leads to a depletion of the density of states in the $ML-M'L'$ plane at T$<$T$_{CDW}$, and (ii) anomalies in the electronic dispersion reflecting a sizable impact of phonons on it. A diffuse scattering precursor, characteristic of soft phonons, is observed at room temperature (RT) and leads to the full collapse of the low-energy phonon ($\omega_1$) with propagation vector (0.25 0 -0.3) r.l.u. We show that the frequency and linewidth of this mode are anisotropic in momentum space, reflecting the momentum dependence of the electron-phonon interaction (EPI), hence demonstrating that the origin of the CDW is, to a much larger extent, due to the momentum dependence EPI with a small contribution from nesting. The pressure dependence of the $\omega_1$ soft mode remains nearly constant up to 13 GPa at RT, with only a modest softening before the transition to the high-pressure monoclinic $C2/m$ phase. The wide set of experimental data are well captured by our state-of-the art first-principles anharmonic calculations with the inclusion of van der Waals (vdW) corrections in the exchange-correlation functional. The description of the electronics and dynamics of VSe$_2$ reported here adds important pieces of information to the understanding of the electronic modulations of TMDs.

Physics of high-$T_c$ superconducting cuprates is obscured by the effect of strong electronic correlations. One way to overcome the problem is to seek for an exact solution at least within the small cluster and expand it to the whole crystal. Such an approach is in the heart of the cluster perturbation theory (CPT). Here we develop CPT for the dynamic spin and charge susceptibilities (spin-CPT and charge-CPT), within which the correlation effects are explicitly taken into account by the exact diagonalization. We apply spin-CPT and charge-CPT to the effective two-band Hubbard model for the cuprates obtained from the three-band Emery model and calculate one- and two-particle correlation functions, namely, spectral function and spin and charge susceptibilities. Doping dependence of the spin susceptibility was studied within spin-CPT and CPT-RPA that is the CPT generalization of the random phase approximation (RPA). Both methods produce the low energy response at four incommensurate wave vectors in qualitative agreement to the results of the inelastic neutron scattering on overdoped cuprates., Comment: 14 pages, 8 figures

The long range electronic modulations recently discovered in the geometrically frustrated kagome lattice have opened new avenues to explore the effect of correlations in materials with topological electron flat bands. The observation of the lattice response to the emergent new phases of matter, a soft phonon mode, has remained elusive and the microscopic origin of charge density waves (CDWs) is still unknown. Here, we show, for the first time, a complete melting of the ScV$_ 6$Sn$_ 6$ (166) kagome lattice. The low energy phonon with propagation vector $\frac{1}{3} \frac{1}{3} \frac{1}{2}$ collapses at 98 K, without the emergence of long-range charge order, which sets in with a propagation vector $\frac{1}{3} \frac{1}{3} \frac{1}{3}$. The CDW is driven (but locks at a different vector) by the softening of an overdamped phonon flat plane at k$_z$=$\pi$. We observe broad phonon anomalies in momentum space, pointing to (1) the existence of approximately flat phonon bands which gain some dispersion due to electron renormalization, and (2) the effects of the momentum dependent electron-phonon interaction in the CDW formation. Ab initio and analytical calculations corroborate the experimental findings to indicate that the weak leading order phonon instability is located at the wave vector $\frac{1}{3} \frac{1}{3} \frac{1}{2}$ of a rather flat collapsed mode. We analytically compute the phonon frequency renormalization from high temperatures to the soft mode, and relate it to a peak in the orbital-resolved susceptibility, obtaining an excellent match with both ab initio and experimental results, and explaining the origin of the approximately flat phonon dispersion. Our data report the first example of the collapse of a softening of a flat phonon plane and promote the 166 compounds of the kagome family as primary candidates to explore correlated flat phonon-topological flat electron physics., Comment: 10 pages, 4 figures

We derive subexponential tail asymptotics for the distribution of the maximum of a compound renewal process with linear component and of a L\'evy process, both with negative drift, over random time horizon $\tau$ that does not depend on the future increments of the process. Our asymptotic results are uniform over the whole class of such random times. Particular examples are given by stopping times and by $\tau$ independent of the processes. We link our results with random walk theory.

The nature of the charge density wave phases in the kagome metal compound AV$_3$Sb$_5$ has raised many questions and their origin is still under debate. Here, we combine diffuse scattering (DS) and inelastic x-ray scattering (IXS) to identify a 3-dimensional (3D) precursor of the charge order with propagation vector (0.5 0 0.5), which condenses into a 3D-CDW through a first order phase transition. The quasi-elastic critical scattering indicates that the dominant contribution to the diffuse precursor is the elastic central peak without phonon softening. However, the inelastic spectra show a small broadening of the Einstein-type phonon mode on approaching the phase transition. Our results point to the situation where the Fermi surface instability at the \textit{L} point is of order-disorder type with a critical growth of quasi-static domains. The results go beyond the classical weak-coupling Peierls transition dynamics and are discussed within models including strong-electron phonon coupling and non-adiabaticity.