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In this work, we study the extended Falicov-Kimball model at half-filling within the Hartree-Fock approach (HFA) (for various crystal lattices) and compare the results obtained with the rigorous ones derived within the dynamical mean field theory (DMFT). The model describes a system, where electrons with spin-$\downarrow$ are itinerant (with hopping amplitude $t$), whereas those with spin-$\uparrow$ are localized. The particles interact via on-site $U$ and intersite $V$ density-density Coulomb interactions. We show that the HFA description of the ground state properties of the model is equivalent to the exact DMFT solution and provides a qualitatively correct picture also for a range of small temperatures. It does capture the discontinuous transition between ordered phases at $U=2V$ for small temperatures as well as correct features of the continuous order-disorder transition. However, the HFA predicts that the discontinuous boundary ends at the isolated-critical point (of the liquid-gas type) and it does not merge with the continuous boundary. This approach cannot also describe properly a change of order of the continuous transition for large $V$ as well as various metal-insulator transitions found within the DMFT., Comment: 13 pages, 7 figures; pdfReVTex class. This is the Accepted Manuscript version (author created) of an article accepted for publication in J. Phys.: Condens. Matter. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The article has been published on a gold open access basis under a CC BY 3.0 licence

Topological insulators are characterized by the existence of band inversion and the possibility of the realization of surface states. Doping with a magnetic atom, which is a source of the time-reversal symmetry breaking, can lead to realization of novel magneto-electronic properties of the system. In this paper, we study effects of substitution by the transition metal ions (Mn, Fe, Co and Ni) into Bi$_{2}$Se$_{3}$ on its electric properties. Using the ab inito supercell technique, we investigate the density of states and the projected band structure. Under such substitution the shift of the Fermi level is observed. We find the existence of nearly dispersionless bands around the Fermi level associated with substituted atoms, especially, in the case of the Co and Ni. Additionally, we discuss the modification of the electron localization function as well as charge and spin redistribution in the system. Our study shows a strong influence of the transition metal--Se bond on local modifications of the physical properties. The results are also discussed in the context of the interplay between energy levels of the magnetic impurities and topological surface states., Comment: 13 pages, 8 figures

We analyze the influence of a local pairing on the quantum interference in nanoscopic systems. As a model system we choose the double quantum dot coupled to one metallic and one superconducting electrode in the T-shape geometry. The analysis is particularly valuable for systems containing coupled objects with considerably different broadening of energy levels. In such systems, the scattering of itinerant electrons on a discrete (or narrow) energy level gives rise to the Fano-type interference. Systems with induced superconducting order, along well understood Fano resonances, exhibit also another features on the opposite side of the Fermi level. The lineshape of these resonances differs significantly from their reflection on the opposite side of the Fermi level, and their origin was not fully understood. Here, considering the spin-polarized tunneling model, we explain a microscopic mechanism of a formation of these resonances and discuss the nature of their uncommon lineshapes. We show that the anomalous Fano profiles originate solely from the pairing of nonscattered electrons with scattered ones. We investigate also the interplay of each type of resonances with the Kondo physics and discuss the resonant features in differential conductivity., Comment: 16 pages, 7 figures; wlscirep pdfLaTeX class. This is author-created e-print version of the article published in Scientific Reports

Compounds with a tetragonal ThCr$_{2}$Si$_{2}$-type structure are characterized by the possibility of the isostructural phase transition from the tetragonal phase to the collapsed tetragonal phase induced by the external pressure. An example of a compound with such a phase transition is KFe$_{2}$As$_{2}$, which belongs to the family of the iron-based superconductors. In this paper, we investigate the effects of the phase transition on the structural, electronic, and dynamical properties of this compound. Performing the ab initio calculations, we reproduce the dependence of the lattice constants on pressure and analyze the changes of the inter-atomic distances in the tetragonal and collapsed tetragonal phases. Using the tight binding model with maximally localized Wannier orbitals, we calculate and discuss the influence of pressure on the electronic band structure as well as on the shape of the Fermi surface. We found a precursor of the phase transition in the form of enhancement of overlapping between two Wannier orbitals of As atoms. In order to better understand the superconducting properties of KFe$_{2}$As$_{2}$, we study the orbital-projected Cooper pairs susceptibility as a function of pressure. We found a decrease of susceptibility with the increasing pressure in a good qualitative agreement with experimental observation. The structural transition also influences the phonon spectrum of KFe$_{2}$As$_{2}$, which exhibits pronounced changes induced by pressure. Some phonon modes related with the vibrations of Fe and As atoms show an anomalous, nonmonotonic dependence on pressure close to the phase transition., Comment: 14 figures, 17 pages

The extended Falicov-Kimball model is analyzed exactly for finite temperatures ($T\geq0$) in the limit of large dimensions. Onsite and intersite density-density interactions $U$ and $V$ are included in the model. Using the dynamical mean field theory formalism on the Bethe lattice we find rigorously the temperature dependent density of states (DOS) at half-filling. At $T=0$ the system is ordered to form the checkerboard pattern and the DOS has the gap $\Delta(\varepsilon_F) > 0$ at the Fermi level, if only $U\neq 0$ or $V\neq 0$. If $U <0$ or $U > 2V$, two additional subbands develop inside the principal energy gap. They become wider with increasing $T$ and at a certain $U$- and $V$-dependent temperature $T_{MI}$ they join with each other at $\varepsilon_F$. Since above $T_{MI}$ the DOS is positive at $\varepsilon_F$, we interpret $T_{MI}$ as the transformation temperature from insulator to metal. Moreover, we show that if $V\lesssim 0.54$ then $T_{MI}=0$ at two quasi-quantum critical points $U_{cr}^{\pm}$ (one positive and the other negative), whereas for $V\gtrsim 0.54$ there is only one negative $U^-_{cr}$. Having calculated the temperature dependent DOS we study thermodynamic properties of the system starting from its free energy and then we construct the phase diagrams in the variables $T$ and $U$ for a few values of $V$. Our calculations give that inclusion of the intersite coupling $V$ causes the finite temperature phase diagrams to become asymmetric with respect to a change of sign of $U$. On these phase diagrams we detected stability regions of eight different kinds of ordered phases, where both charge-order and antiferromagnetism coexists (five of them are insulating and three are conducting) and three different nonordered phases (two of them are insulating and one is conducting). Moreover, both continuous and discontinuous transitions between various phases were found., Comment: 16 pages, 13 figures, 78 references; pdfReVTeX; submitted to Physical Review B. Changes: corrected typos, added Fig. 11 and its discussion in Section III B 4, added several references, results unchanged

Ultracold fermionic gases in optical lattices give a great opportunity for creating different types of novel states. One of them is phase separation induced by a trapping potential between different types of superfluid phases. The core-shell structures, occurring in systems with a trapping potential, are a good example of such separations. The types and the sequences of phases which emerge in such structures can depend on spin-imbalance, shape of the trap and on-site interaction strength. In this work, we investigate the properties of such structures within an attractive Fermi gas loaded in the optical lattice, in the presence of the trapping potential and their relations to the phase diagram of the homogeneous system. Moreover, we show how external and internal parameters of the system and parameters of the trap influence their properties. In particular, we show a possible occurrence of the core-shell structure in a system with a harmonic trap, containing the BCS and FFLO states. Additionally, we find a spatial separation of two superfuild states in the system, one in the BCS limit as well as the other one in the tightly bound local pairs (BEC) regime., Comment: 6 figures, 11 pages

The spin-orbit coupling can lead to exotic states of matter and unexpected behavior of the system properties. In this paper, we investigate the influence of spin-orbit coupling induced by proximity effects on a monolayer of superconductor (with s-wave or d-wave pairing) placed on an insulating bulk. We show that the critical temperatures $T_{c}$ of the superconducting states can be tuned by the spin-orbit coupling both in the case of on-site and inter-site pairing. Moreover, we discuss a possibility of changing the location of the maximal $T_{c}$ from the half-filling into the underdoped or overdoped regimes., Comment: 11 pages, 9 figures

The extended Falicov-Kimball model is analyzed exactly in the ground state at half filling in the limit of large dimensions. In the model the on-site and the intersite density-density interactions between all particles are included. We determined the model's phase diagram and found a discontinuous transition between two different charge-ordered phases. Our analytical calculations show that the ground state of the system is insulating for any nonzero values of the interaction couplings. We also show that the dynamical mean-field theory and the static broken-symmetry Hartree-Fock mean-field approximation give the same results for the model at zero temperature. In addition, we prove using analytical expressions that at infinitesimally small, but finite, temperatures the system can be metallic., Comment: 10 pages, 7 figures, 72 references; pdf-ReVTeX class; submitted to Physical Review B

The phenomenon associated with inhomogeneous distribution of electron density is known as a charge ordering. In this work, we study the zero-bandwidth limit of the extended Hubbard model, which can be considered as a simple effective model of charge ordered insulators. It consists of the on-site interaction $U$ and the intersite density-density interactions $W_1$ and $W_2$ between nearest-neighbors and next-nearest neighbors, respectively. We derived the exact ground state diagrams for different lattice dimensionalities and discuss effects of small finite temperatures in the limit of high dimensions. In particular, we estimated the critical interactions for which new ordered phases emerge (laminar or stripe and four-sublattice-type). Our analysis show that the ground state of the model is highly degenerated. One of the most intriguing finding is that the nonzero temperature removes these degenerations., Comment: 13 pages, 8 figures, ReVTex, submitted to Physical Review E

The paper is devoted to a study of superconducting properties of population-imbalanced fermionic mixtures in quasi-one dimensional optical lattices. The system can be effectively described by the attractive Hubbard model with the Zeeman magnetic field term. We investigated the ground state phase diagram of the model as a function of the chemical potential and the magnetic field. The ground state of the system exhibits the conventional BCS-type superconductivity as well as the unconventional so-called Fulde-Ferrell-Larkin-Ovchinnikov state, in which the total momentum of Cooper pairs is non-zero. We determine the orders of transitions as well as the behavior of order parameters with a change of the model parameters., Comment: 6 pages, 4 figures; submitted to Journal of Superconductivity and Novel Magnetism

In this paper we determine the phase diagrams (for $T=0$ as well as $T>0$) of the Penson-Kolb-Hubbard model for two dimensional square lattice within Hartree-Fock mean-field theory focusing on investigation of superconducting phases and possibility of the occurrence of the phase separation. We obtain that the phase separation, which is a state of coexistence of two different superconducting phases (with $s$-wave and $\eta$-wave symmetries), occurs in define range of the electron concentration. In addition, increasing temperature can change the symmetry of the superconducting order parameter (from $\eta$-wave into $s$-wave). The system considered exhibits also an interesting multicritical behaviour including bicritical points., Comment: 8 pages, 6 figures, ReVTeX, minor changes in text, proper list of authors given

In this work we focus on the study of phase separation in the zero-bandwidth extended Hubbard with nearest-neighbors intersite Ising-like magnetic interactions $J$ and on-site Coulomb interactions $U$. The system has been analyzed by means of Monte Carlo simulations (in the grand canonical ensemble) on two dimensional square lattice (with $N=L\times L =400$ sites) and the results for $U/(4J)=2$ as a function of chemical potential and electron concentration have been obtained. Depending on the values of interaction parameters the system exhibits homogeneous (anti-)ferromagnetic (AF) or non-ordered (NO) phase as well as phase separation PS:AF/NO state. Transitions between homogeneous phases (i.e. AF-NO transitions) can be of first or second order and the tricritical point is also present on the phase diagrams. The electron compressibility $K$ is an indicator of the phase separation and that quantity is of particular interest of this paper., Comment: 4 pages, 3 figures; pdf-ReVTeX; updated references; presented at The European Conference PHYSICS OF MAGNETISM 2014 (PM'14), June 23-27, 2014, Poznan, Poland; submitted to Acta Physica Polonica A

The extended Hubbard model in the zero-bandwidth limit is studied. The effective Hamiltonian consists of (i) on-site $U$ interaction and intersite (ii) density-density interaction $W$ and (iii) Ising-like magnetic exchange interaction $J$ (between the nearest-neighbors). We present rigorous (and analytical) results obtained within the transfer-matrix method for 1D-chain in two particular cases: (a) $W=0$ and $n=1$; (b) $U\rightarrow+\infty$ and $n=1/2$ ($W\neq 0$, $J\neq 0$). We obtain the exact formulas for the partition functions which enables to calculate thermodynamic properties such as entropy, specific heat ($c$), and double occupancy per site. In both cases the system exhibits an interesting temperature dependence of $c$ involving a characteristic two-peak structure. There are no phase transitions at finite temperatures and the only transitions occur in the ground state., Comment: 4 pages, 2 figures; pdf-ReVTeX; updated references; presented at The European Conference PHYSICS OF MAGNETISM 2014 (PM'14), June 23-27, 2014, Poznan, Poland; submitted to Acta Physica Polonica A

In this paper the two dimensional extended Hubbard model with intersite magnetic Ising-like interaction in the atomic limit is analyzed by means of the classical Monte Carlo method in the grand canonical ensemble. Such an effective simple model could describe behavior of insulating (anti)ferromagnets. In the model considered the Coulomb interaction ($U$) is on-site and the magnetic interactions in $z$-direction ($J>0$, antiferromagnetic) are restricted to nearest-neighbors. Simulations of the model have been performed on a square lattice consisting of $N=L\times L=400$ sites ($L=20$) in order to obtain the full phase diagram for $U/(4J)=1$. Results obtained for on-site repulsion ($U>0$) show that, apart from homogeneous non-ordered (NO) and ordered magnetic (antiferromagnetic, AF) phases, there is also a region of phase separation (PS: AF/NO) occurrence. We present a phase diagram as well as some thermodynamic properties of the model for the case of $U/(4J)=1$ (and arbitrary chemical potential and arbitrary electron concentration). The AF-NO transition can be second-order as well as first-order and the tricritical point occurs on the diagram., Comment: 5 pages, 4 figures, pdf-ReVTeX, presented at 16th National School of Superconductivity: Unconventional superconductivity and strongly correlated systems, Zakopane, Poland, October 7-12, 2013, submitted to Acta Physica Polonica A

The effects of a single non-magnetic impurity on superconducting states in the Penson-Kolb-Hubbard model have been analyzed. The investigations have been performed within two steps: (i) the homogeneous system is analysed using the Bogoliubov transformation, whereas (ii) the inhomogeneous system is investigated self-consistent Bogoliubova-de Gennes equations (by exact diagonalization and the kernel polynomial method). We analysed both signs of pair hopping, which correspond to s-wave and $\eta$-wave superconductivity. Our results show that an enhancement of the local superconducting gap at the impurity-site occurs for both cases. We obtained that Cooper pairs are scattered (at the impurity site) into the states which are from the neighborhoods of the states, which are commensurate ones with the crystal lattice. Additionally, in the $\eta$-phase there are peaks in the local-energy gap (in momentum space), which are connected with long-range oscillations in the spatial distribution of the energy gap, superconducting order parameter as well as effective pairing potential. Our results can be contrasted with the experiment and predicts how to experimentally differentiate these two different symmetries of superconducting order parameter by scanning tunneling microscopy technique., Comment: 11 pages, 4 figures

We present the analysis of paramagnetic effects of magnetic field ($B$) (Zeeman term) in the zero-bandwidth limit of the extended Hubbard model for arbitrary chemical potential $\mu$ and electron density $n$. The effective Hamiltonian considered consists of the on-site interaction $U$ and the intersite charge exchange term $I$, determining the hopping of electron pairs between nearest-neighbour sites. The model has been analyzed within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation (rigorous in the limit of infinite dimensions $d\rightarrow+\infty$). In this report we focus on metastable phases as well as phase separated (PS) states involving superconducting (SS) and nonordered (NO) phases and determine their ranges of occurrence for $U/I_0=1.05$ ($I_0=zI$) in the presence of magnetic field $B\neq0$. Our investigations of the general case for arbitrary $U/I_0$ show that, depending on the values of interaction parameters (for fixed $n$), the PS state can occur in higher fields than the homogeneous SS phase (field-induced PS). Moreover, a first-order SS-NO transition occurs between metastable phases and these metastable phases can exist inside the regions of the PS state stability. Such behaviour is associated with the presence of tricritical line on the phase diagrams of the system., Comment: 6 pages, 3 figures; pdf-ReVTeX; presented at 16th National School of Superconductivity: Unconventional superconductivity and strongly correlated systems, Zakopane, Poland, October 7-12, 2013; submitted to Acta Physica Polonica A