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We report a systematic study of low energy metastable states in van der Waals semimetals TiS2, TiSe2 and TiTe2 within the DFT theory by means the evolutionary search algorithm. We find a big difference between TiSe2, TiS2 and TiTe2 in low energy metastable states. While several metastable states exist in TiSe2 and TiS2, no low energy metastable states were found in TiTe2. We show that some of the obtained metastable states can be identified as charge density wave (CDW). We argue that existence of the low energy metastable phases indicates that emergence CDW as a ground state in these compounds., Comment: 13 pages, 5 figures

The interplay of orbital and spin degrees of freedom is the fundamental characteristic in numerous condensed matter phenomena, including high temperature superconductivity, quantum spin liquids, and topological semimetals. In iron-based superconductors (FeSCs), this causes superconductivity to emerge in the vicinity of two other instabilities: nematic and magnetic. Unveiling the mutual relationship among nematic order, spin fluctuations, and superconductivity has been a major challenge for research in FeSCs, but it is still controversial. Here, by carrying out 77Se nuclear magnetic resonance (NMR) measurements on FeSe single crystals, doped by cobalt and sulfur that serve as control parameters, we demonstrate that the superconducting transition temperature Tc increases in proportion to the strength of spin fluctuations, while it is independent of the nematic transition temperature Tnem. Our observation therefore directly implies that superconductivity in FeSe is essentially driven by spin fluctuations in the intermediate coupling regime, while nematic fluctuations have a marginal impact on Tc., Comment: 20 pages, 3 figures; includes supplementary materials (1 note and 3 figures)

We derive an S=1 spin polaron model which describes the motion of a single hole introduced into the S=1 spin antiferromagnetic ground state of Ca2RuO4. We solve the model using the self-consistent Born approximation and show that its hole spectral function qualitatively agrees with the experimentally observed high-binding energy part of the Ca2RuO4 photoemission spectrum. We explain the observed peculiarities of the photoemission spectrum by linking them to two anisotropies present in the employed model---the spin anisotropy and the hopping anisotropy. We verify that these anisotropies, and not the possible differences between the ruthenate (S=1) and the cuprate (S=1/2) spin polaron models, are responsible for the strong qualitative differences between the photoemission spectrum of Ca2RuO4 and of the undoped cuprates., Comment: 10 pages, 4 figures

We develop a theory of the phonon mediated Casimir interaction between two point-like impurities, which is based on the single impurity scattering T-matrix approach. Within this, we show that the Casimir interaction at $T = 0$ falls off as a power law with the distance between the impurities. We find that the power in the weak and in the unitary phonon-impurity scattering limits differs, and we relate the power law to the low-energy properties of the single impurity scattering T-matrix. In addition, we consider the Casimir interaction at finite temperature and show that at finite temperatures the Casimir interaction becomes exponential at large distances., Comment: 8 pages, 10 figures

The Casimir effect, a two-body interaction via vacuum fluctuations, is a fundamental property of quantum systems. In solid state physics it emerges as a long-range interaction between two impurity atoms via virtual phonons. In the classical limit for the impurity atoms in $D$ dimensions the interaction is known to follow the universal power-law $U(r)\sim r^{-D}$. However, for finite masses of the impurity atoms on a lattice, it was predicted to be $U(r)\sim r^{-2D-1}$ at large distances. We examine how one power-law can change into another with increase of the impurity mass and in presence of an external potential. We provide the exact solution for the system in one-dimension. At large distances indeed $U(r)\sim r^{-3}$ for finite impurity masses, while for the infinite impurity masses or in an external potential it crosses over to $U(r)\sim r^{-1}$ . At short distances the Casimir interaction is not universal and depends on the impurity mass and the external potential., Comment: 5+7 pages, 5+6 figures

The Hall effect is a powerful tool for investigating carrier type and density. For single-band materials, the Hall coefficient is traditionally expressed simply by $R_H^{-1} = -en$, where $e$ is the charge of the carrier, and $n$ is the concentration. However, it is well known that in the critical region near a quantum phase transition, as it was demonstrated for cuprates and heavy fermions, the Hall coefficient exhibits strong temperature and doping dependencies, which can not be described by such a simple expression, and the interpretation of the Hall coefficient for Fe-based superconductors is also problematic. Here, we investigate thin films of Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ with compressive and tensile in-plane strain in a wide range of Co doping. Such in-plane strain changes the band structure of the compounds, resulting in various shifts of the whole phase diagram as a function of Co doping. We show that the resultant phase diagrams for different strain states can be mapped onto a single phase diagram with the Hall number. This universal plot is attributed to the critical fluctuations in multiband systems near the antiferromagnetic transition, which may suggest a direct link between magnetic and superconducting properties in the BaFe$_2$As$_2$ system., Comment: Accepted for publication in Scientific Reports, 6 main figures plus Supplemental Information (8 figures)

We analyze the interplay between superconductivity and the formation of bound pairs of fermions (BCS-BEC crossover) in 2D models of interacting fermions with small Fermi energy EF and weak attractive interaction, which extends to energies well above EF. The 2D case is special because one has to distinguish between bound state formation and superconductivity already at weak coupling. We briefly review the situation in the one-band model and then consider two different two-band models: the one with a hole and an electron band, and the one with two electron bands. In each case we obtain the bound state energy 2 E0 for two fermions in a vacuum and solve the set of coupled equations for the pairing gaps and the chemical potentials to obtain the onset temperature of the pairing, Tins and the quasiparticle dispersion. We then compute the superfluid stiffness and obtain the actual Tc. We show that, at EF >> E0 the behavior of both two-band models is BCS-like in the sense that Tc almost coincides with Tins and both are much smaller than EF. At EF < E0, the two models behave differently: in the model with two electron bands, Tins ~E0/log(E0/EF) and Tc ~EF << Tins. In between Tins and Tc the system displays preformed pair behavior. In the model with a hole and an electron band, Tins ~ Tc and both remain finite at EF=0 The preformed pair behavior still exists in this model because Tc is numerically smaller than Tins. For both models we re-express Tins in terms of the fully renormalized two-particle scattering amplitude by extending to two-band case the method pioneered by Gorkov and Melik-Barkhudarov back in 1961. We apply our results to to Nb-doped SrTiO3 and to Fe-pnictides and Fe-chalcogenides, particularly to FeSe, in which superconducting gap is comparable to the Fermi energy., Comment: 25 pp, 14 figures, submitted to PRB

We consider an ordered ferromagnet in the vicinity of a T=0 transition into a paramagnet. We show that the free energy and the transverse and longitudinal static susceptibilities contain non-analyticities which destroy a continuous second-order transition. Depending on the parameters, the transition either becomes first-order, or occurs via an intermediate spiral phase., Comment: 4 pages, 3 figures

We study single-ion and exchange anisotropy effects in equal-spin $s_1$ tetramer single molecule magnets exhibiting $T_d$, $D_{4h}$, $D_{2d}$, $C_{4h}$, $C_{4v}$, or $S_4$ ionic point group symmetry. We first write the group-invariant quadratic single-ion and symmetric anisotropic exchange Hamiltonians in the appropriate local coordinates. We then rewrite these local Hamiltonians in the molecular or laboratory representation, along with the Dzyaloshinskii-Moriay (DM) and isotropic Heisenberg, biquadratic, and three-center quartic Hamiltonians. Using our exact, compact forms for the single-ion spin matrix elements, we evaluate the eigenstate energies analytically to first order in the microscopic anisotropy interactions, corresponding to the strong exchange limit, and provide tables of simple formulas for the energies of the lowest four eigenstate manifolds of ferromagnetic (FM) and anitiferromagnetic (AFM) tetramers with arbitrary $s_1$. For AFM tetramers, we illustrate the first-order level-crossing inductions for $s_1=1/2,1,3/2$, and obtain a preliminary estimate of the microscopic parameters in a Ni$_4$ from a fit to magnetization data. Accurate analytic expressions for the thermodynamics, electron paramagnetic resonance absorption and inelastic neutron scattering cross-section are given, allowing for a determination of three of the microscopic anisotropy interactions from the second excited state manifold of FM tetramers. We also predict that tetramers with symmetries $S_4$ and $D_{2d}$ should exhibit both DM interactions and multiferroic states, and illustrate our predictions for $s_1=1/2, 1$., Comment: 30 pages, 14 figures, submitted to Phys. Rev. B

For equal-spin $s_1$ tetramer single molecule magnets with ionic point groups $g=T_d, D_{4h}, D_{2d}, C_{4h}, C_{4v}$, and $S_4$, we write the group-invariant single-ion, Dzaloshinskii-Moriya, and symmetric anisotropic near-neighbor and next-nearest-neighbor exchange Hamiltonians using the respective local axial and azimuthal vector groups. The anisotropic exchange renormalized near-neighbor and next-nearest-neighbor isotropic exchange interactions are $\tilde{J}_g$ and $\tilde{J}_g'$. Using our exact, compact forms for the single-ion matrix elements, we evaluate the eigenstates of the full Hamiltonian to first order in the various interactions. There are two types of ferromagnetic (FM) and antiferromagnetic (AFM) tetramers. In Type I, $\tilde{J}_g'-\tilde{J}_g>0$, the tetramers act as two dimers with the maximal pair quantum numbers $s_{13}=s_{24}=2s_1$ at low temperature. Type II tetramers with $\tilde{J}_g'-\tilde{J}_g<0$ are frustrated, with minimal values of the pair quantum numbers $s_{13}$ and $s_{24}$ at low temperature. For both Type I and Type II AFM tetramers, we evaluate the first-order level-crossing inductions analytically for arbitary $s_1$, and illustrate the results for $s_1=1/2, 1, 3/2$. Accurate Hartree expressions for the thermodynamics, electron paramagnetic resonance (EPR) absorption and inelastic neutron scattering cross-section are given. A procedure to extract the effective microscopic parameters for Types I and II tetramers using EPR is given., Comment: 27 pages, 10 figures, submitted to Phys. Rev. B

We present a microscopic theory of single molecule magnets. From our exact single-ion spin matrix elements for four arbitrary spins, we study the single-ion anisotropy of equal spins exhibiting $T_d$, $D_{2d}$, or $C_{4v}$ molecular group symmetry. Each group generates site-dependent single-ion anisotropy. For weak anisotropy, accurate Hartree expressions for the magnetization, specific heat, electron paramagnetic resonance (EPR) absorption, and inelastic neutron scattering cross-section are given. For $D_{2d}$, azimuthal single-ion anisotropy leads to the observed Ni$_4$ EPR splittings., Comment: 4 pages, 2 figures, submitted to Phys. Rev. Lett

We present a model of equal spin $s_1$ dimer single molecule magnets. The spins within each dimer interact via the Heisenberg and the most general set of four quadratic anisotropic spin interactions with respective strengths $J$ and $\{J_j\}$, and with the magnetic induction ${\bf B}$. We solve the model exactly for $s_1=1/2, 1, 5/2$, and for antiferromagnetic Heisenberg couplings ($J<0$), present ${\bf M}({\bf B})$ curves at low $T$ for these cases. Low-$T$ $C_V({\bf B})$ curves for $s_1=1/2$ and electron paramagnetic susceptibility $\chi({\bf B},\omega)$ for $s_1=1$ are also provided. For weak anisotropy interactions, we employ a perturbative treatment, and show that the Hartree and extended Hartree approximations lead to reliable analytic results at low $T$ and large $B$ for these quantities and for the inelastic neutron scattering cross-section $S({\bf B}, {\bf q},\omega)$. Our results are discussed with regard to existing ${\bf M}({\bf B})$ experiments on $s_1=5/2$ Fe$_2$ dimer single molecule magnets, and suggest that one of them contains a substantial amount of single-ion anisotropy, without any sizeable global spin anisotropy. We urge further experiments of the above types on single crystals of Fe$_2$ and on some $s_=9/2$ [Mn$_4$]$_2$ dimers, in order to elucidate the precise values of the various microscopic interactions., Comment: 30 pages, 25 figures, submitted to Phys. Rev. B

We present an exactly solvable model of equal spin $s_1$ dimer single molecule magnets. The spins within each dimer interact via the Heisenberg and the most general quadratic global and local (single-ion) anisotropic spin interactions, and with the magnetic induction ${\bf B}$. For antiferromagnetic couplings and $s_1>1/2$, the low temperature $T$ magnetization ${\bm M}({\bm B})$ exhibits $2s_1$ steps of universal height and midpoint slope, the $s$th step of which occurs at the non-universal level-crossing magnetic induction $B_{s,s_1}^{\rm lc}(\theta,\phi)$, where $\theta,\phi$ define the direction of ${\bm B}$. The specific heat $C_V$ exhibits zeroes as $T\to0$ at these $B_{s,s_1}^{\rm lc}(\theta,\phi)$ values, which are equally surrounded by universal peak pairs as $T\to0$. The non-universal $B_{s,s_1}^{\rm lc}(\theta,\phi)$ values lead to a rich variety of magnetization plateau behavior, the structure and anisotropy of which depend upon the various global and local anisotropic spin interaction energies. We solve the model exactly for $s_1=1/2$, 1, and 5/2, and present ${\bm M}({\bm B})$ and $C_V({\bm B})$ curves at low $T$ for these cases. For weakly anisotropic dimers, rather simple analytic formulas for ${\bm M}({\bm B})$ and $C_V({\bm B})$ at arbitrary $s_1$ accurately fit the exact solutions at sufficiently low $T$ or large $B$. An expression for $B_{s,s_1}^{\rm lc}(\theta,\phi)$ accurate to second order in the four independent anisotropy energies is derived. Our results are discussed with regard to existing experiments on $s_1=5/2$ Fe$_2$ dimers, suggesting further experiments on single crystals of these and some $s_1=9/2$ Mn$_4$]$_2$ dimers are warranted., Comment: 22 pages, 26 figures, submitted to PRR

We calculate the static and dynamic properties of single crystal, single molecule magnets consisting of equal spin $S=1/2$ or 5/2 dimers. The spins in each dimer interact with each other via the Heisenberg exchange interaction and with the magnetic induction ${\bf B}$ via the Zeeman interaction, and interdimer interactions are negligible. For antiferromagnetic couplings, the static magnetization and specific heat exhibit interesting low temperature $T$ and strong ${\bf B}$ quantum effects. We calculate the frequency spectrum of the Fourier transform of the real part of the time autocorrelation function ${\cal C}_{11}(t)$ for arbitrary $T, {\bf B}$, and compare our results with those obtained for classical spins. We also calculate the inelastic neutron magnetic dynamical structure factor $S({\bf q},\omega)$ at arbitrary $T, {\bf B}$., Comment: 11 pages, 14 figures, submitted to Phys. Rev. B