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In this study, we analyze the dielectric function of high-Tc cuprates as a function of doping level, taking into account the full energy band dispersion within the CuO$_2$ monolayer. In addition to the conventional two-dimensional (2D) gapless plasmon mode, our findings reveal the existence of three anomalous branches within the plasmon spectrum. Two of these branches are overdamped modes, designated as hyperplasmons, and the third is an almost one-dimensional plasmon mode (1DP). We derive an analytic expression for dynamic part of the response function. Furthermore, we investigated the effect of the doping on these modes. Our analysis demonstrates that in the doping level range close to the optimal doping level, the properties of all three modes undergo a significant transformation.

The studies of a number of systems treated in terms of an inhomogeneous (spatially separated) Fermi-Bose mixture with superconducting clusters or droplets of the order parameter in a host medium with unpaired normal states are reviewed. A spatially separated Fermi-Bose mixture is relevant to superconducting BaKBiO3 bismuth oxides. Droplets of the order parameter can occur in thin films of a dirty metal, described in the framework of the strongly attractive two-dimensional Hubbard model at a low electron density with a clearly pronounced diagonal disorder. The Bose-Einstein condensate droplets are formed in mixtures and dipole gases with an imbalance in the densities of the Fermi and Bose components. The Bose-Einstein condensate clusters also arise at the center or at the periphery of a magnetic trap involving spin-polarized Fermi gases. Exciton and plasmon collapsing droplets can emerge in the presence of the exciton-exciton or plasmon-plasmon interaction. The plasmon contribution to the charge screening in MgB2 leads to the formation of spatially modulated inhomogeneous structures. In metallic hydrogen and metal hydrides, droplets can be formed in shock-wave experiments at the boundary of the first-order phase transition between the metallic and molecular phases. In a spatially separated Fermi-Bose mixture arising in an Aharonov-Bohm interference ring with a superconducting bridge in a topologically nontrivial state, additional Fano resonances may appear and collapse due to the presence of edge Majorana modes in the system., Comment: 18 pages, 10 figures, submitted to JETP Lett

We discuss the properties of topologically nontrivial superconducting phases and the conditions for their realization in condensed matter, and the principles for identifying Majorana bound states (MBSs). Along with the well-known Kitaev chain and superconducting nanowire (SW) models with spin-orbit coupling in an external magnetic field, we discuss models of quasi-2D materials in which MBSs are realized in the presence of noncollinear spin ordering. For finite-length SWs, we demonstrate a cascade of quantum transitions occurring with a change in the magnetic field, accompanied by a change in the fermion parity of the ground state. The corresponding anomalous behavior of the magnetocaloric effect can be used as a tool for identifying MBSs. We devote considerable attention to the analysis of the transport characteristics of devices that contain topologically nontrivial materials. The results of studying the conductance of an Aharonov-Bohm ring whose arms are connected by an SW are discussed in detail. An important feature of this device is the appearance of Fano resonances in the dependence of conductance on the magnetic field when the SW is in a topologically nontrivial phase. We establish a relation between the characteristics of such resonances and the spatial structure of the lowest-energy SW state. The conditions for the occurrence of an MBS in the phase of the coexistence of chiral $d+id$ superconductivity and 120-degree spin ordering are determined in the framework of the $t-J-V$ model on a triangular lattice. We take electron-electron interactions into account in discussing the topological invariants of low-dimensional superconducting materials with noncollinear spin ordering. The formation of Majorana modes in regions with an odd value of a topological $\mathbb{Z}$ invariant is demonstrated. The spatial structure of these excitations in the Hubbard fermion ensemble is determined., Comment: 114 pages, 31 figures

We consider the nanoscale electronic phase separation in a wide class of different materials, mostly in strongly correlated electron systems. The phase separation turns out to be quite ubiquitous manifesting itself in different situations, where the itineracy of charge carriers competes with their tendency toward localization. The latter is often related to some specific type of magnetic ordering, e.g. antiferromagnetic in manganites and low-spin states in cobaltites. The interplay between the localization-induced lowering of potential energy and metallicity (which provides the gain in the kinetic energy) favors an inhomogeneous ground state such as nanoscale ferromagnetic droplets in an antiferromagnetic insulating background. The present review article deals with the advances in the subject of electronic phase separation and formation of different types of nanoscale ferromagnetic (FM) metallic droplets (FM polarons or ferrons) in antiferromagnetically ordered (AFM), charge-ordered (CO), or orbitally-ordered (OO) insulating matrices, as well as the colossal magnetoresistance (CMR) effect and tunneling electron transport in the nonmetallic phase-separated state of complex magnetic oxides. It also touches upon the compounds with spin-state transitions, inhomogeneous phase-separated state in strongly correlated multiband systems, and electron polaron effect. A special, attention is paid to the systems with the imperfect Fermi surface nesting such as chromium alloys, iron-based pnictides, and AA stacked graphene bilayers., Comment: 135 pages, 72 figures, submitted to Physics Reports

The properties of a two-dimensional low density (n<<1) electron system with strong onsite Hubbard attraction U>W (W is the bandwidth) in the presence of a strong random potential V uniformly distributed in the range from -V to +V are considered. Electronic hoppings only at neighboring sites on the square lattice are taken into account, thus W=8t. The calculations were carried out for a lattice of 24x24 sites with periodic boundary conditions. In the framework of the Bogoliubov - de Gennes approach we observed an appearance of inhomogeneous states of spatially separated Fermi-Bose mixture of Cooper pairs and unpaired electrons with the formation of bosonic droplets of different size in the matrix of the unpaired normal states We observed a decrease in the droplet size (from larger droplets to individual bielectronic pairs) when we decrease the electron density at fixed values of the Hubbard attraction and random potential. The obtained results are important for the construction of the gross phase diagram and understanding of the nature of the phase transition between superconducting, normal metallic and localized states in quasi-2D (thin) film of a dirty metal. In a more practical sense it is interesting also for the experimental implementation of superconducting qubits on quantum circuits with high impedances in granular superconductors., Comment: 14 pages, 10 figures, 30 references

One of the main features of the Majorana state, which attracts a considerable current interest to these excitations in solid-state systems, is related to its nonlocal character. It is demonstrated that the direct consequence of such nonlocality is the collapse of the Fano resonance manifesting itself in the conductance of an asymmetric interference device, the arms of which are connected by a one-dimensional topological superconductor. In the framework of the spinless model, it is shown that the predicted effect is associated with an increase in the multiplicity of the degeneracy of the zero-energy state of the structure arising at a specific case of the Kitaev model. Such an increase leads to the formation of a bound state in the continuum., Comment: 6 pages, 4 figures

We consider an expansion of the strongly interacting superfluid Fermi gas in a vacuum, assuming absence of the trapping potential, in the so-called unitary regime (see, for instance, \cite{pitaevskii2008superfluid}) when the chemical potential $\mu \propto \hbar^2n^{2/3}/m$ where $n$ is the density of the Bose-Einstein condensate of Cooper pairs of fermionic atoms. In low temperatures, $T\to 0$, such expansion can be described in the framework of the Gross-Pitaevskii equation (GPE). Because of the chemical potential dependence on the density, $\sim n^{2/3}$, the GPE has additional symmetries, resulting in the existence of the virial theorem \cite% {vlasov1971averaged}, connecting the mean size of the gas cloud and its Hamiltonian. It leads asymptotically at $t\to\infty$ to the gas cloud expansion, linearly growing in time. We study such asymptotics, and reveal the perfect match between the quasi-classical self-similar solution and the asymptotic expansion of the non-interacting gas. This match is governed by the virial theorem, derived through utilizing the Talanov transformation \cite{talanov1970focusing}, which was first obtained for the stationary self-focusing of light in media with a cubic nonlinearity due to the Kerr effect. In the quasi-classical limit, the equations of motion coincide with 3D hydrodynamics for the perfect monoatomic gas with $\gamma=5/3$. Their self-similar solution describes, on the background of the gas expansion, the angular deformities of the gas shape in the framework of the Ermakov--Ray--Reid type system., Comment: 14 pages, 5 figures

We consider a quasi-one-dimensional model of a two-component Fermi gas at zero temperature on one, two and three-leg attractive-U Hubbard ladders. We construct the grand canonical phase diagram of a two-component spin-polarized gas. We find that the structure of the phase diagram of the attractive-U Hubbard model for two and three leg ladders significantly differs q from the structure of the phase diagram of a single chain. We argue that the single chain model is a special case, and that multichain ladders display qualitative features of the 1D-to-3D crossover, observed in experiments with trapped ultracold gases.

Taking into account an inner structure of the arms of the Aharonov-Bohm ring (AB ring) we have analyzed the transport features related to the topological phase transition which is induced in a superconducting wire (SC wire) with strong spin-orbit interaction (SOI). The SC wire acts as a bridge connecting the arms. The in-plane magnetic-field dependence of linear-response conductance obtained using the nonequilibrium Green's functions in the tight-binding approximation revealed the Breit-Wigner and Fano resonances (FRs) if the wire is in the nontrivial phase. The effect is explained by the presence of two interacting transport channels in the system. As a result, the FRs are attributed to bound states in continuum (BSCs). The BSC lifetime is determined by both hopping parameters between subsystems and the SC-wire properties. It is established that the FR width and position are extremely sensitive to the type of the lowest-energy excitation in the SC wire, the Majorana or Andreev bound state (MBS or ABS, respectively). Moreover, it is shown that in the specific case of the AB ring, the T-shape geometry, the FR disappears for the transport via the MBS and the conductance is equal to one quantum. It doubles in the local transport regime. On the contrary, in the ABS case the local conductance vanishes. The influence of the mean-field Coulomb interactions and diagonal disorder in the SC wire on the FR is investigated., Comment: 12 pages, 9 figures

The description of quantum transport in a quadruple quantum-dot structure (QQD) is proposed taking into account the Coulomb correlations and nonzero bias voltages. To achieve this goal the combination of nonequilibrium Green's functions and equation-of-motion technique is used. It is shown that the anisotropy of kinetic processes in the QQD leads to negative differential conductance (NDC). The reason of the effect is an interplay of the Fano resonances which are induced by the interdot Coulomb correlations. Different ways to increase the peak-to-valley ratio related to the observed NDC are discussed., Comment: 13 pages, 4 figures

Physics of many-body systems where particles are restricted to move in two spatial dimensions is challenging and even controversial: On one hand, neither long-range order nor Bose condensation may appear in infinite uniform 2D systems at finite temperature, on the other hand this does not prohibit superfluidity or superconductivity. Moreover, 2D superconductors, such as cuprates, are among the systems with highest critical temperatures. Ultracold atoms are a platform for studying 2D physics. Uniquely to other physical systems, quantum statistics may be completely changed in an ultracold gas: an atomic Fermi gas may be smoothly crossed over into a gas of Bose molecules (or dimers) by tuning interatomic interactions. We review recent experiments where such crossover has been demonstrated as well as critical phenomena in the Fermi-to-Bose crossover. We also present simple theoretical models describing the gas at different points of the crossover and compare the data to these and more advanced models., Comment: Review for J. Phys.: Cond. Matt

A quadruple quantum-dot (QQD) cell is proposed as a spin filter. The transport properties of the QQD cell were studied in linear response regime on the basis of the equations of motion for retarded Green's functions. The developed approach allowed us to take into account the influence of both intra- and interdot Coulomb interactions on carriers' spin polarization. It was shown that the presence of the insulating bands in the conductance due to the Coulomb correlations results in the emergence of spin-polarized windows (SPWs) in magnetic field leading to the high spin polarization. We demonstrated the SPWs can be effectively manipulated by gate fields and considering the hopping between central dots in both isotropic and anisotropic regimes., Comment: 4 pages, 7 figures

We present analytical and numerical investigation of spectral and transport properties of a quadruple quantum-dot (QQD) structure which is one of the popular low-dimensional systems in the context of fundamental quantum physics study, future electronic applications and quantum calculations. The density of states, occupation numbers and conductance of the structure were analyzed using the nonequilibrium Green's functions in the tight binding approach and the equation-of-motion method. In particular the anisotropy of hopping integrals and on-site electron energies as well as the effects of the finite intra- and interdot Coulomb interactions were investigated. It was found out that the anisotropy of the kinetic processes in the system leads to the Fano-Feshbach asymmetrical peak. We demonstrated that the conductance of QQD device has a wide insulating band with steep edges separating triple-peak structures if the intradot Coulomb interactions are taken into account. The interdot Coulomb correlations between the central QDs result in the broadening of this band and the occurrence of an additional band with low conductance due to the Fano antiresonances. It was shown that in this case the conductance of the anisotropic QQD device can be dramatically changed by tuning the anisotropy of on-site electron energies., Comment: 21 pages, 25 figures

Magnetic properties of single crystals of Mn$_{1-x}$Fe$_x$Si solid solutions with $x < 0.2$ are investigated by pulsed field technique in magnetic fields up to 50 T. It is shown that magnetization of Mn$_{1-x}$Fe$_x$Si in the paramagnetic phase follows power law $M(B) \sim B^\alpha$ with the exponents $\alpha \sim 0.33-0.5$, which starts above characteristic fields $B_c \sim 1.5-7$ T depending on the sample composition and lasts up to highest used magnetic field. Analysis of magnetization data including SQUID measurements in magnetic fields below 5 T suggests that this anomalous behavior may be likely attributed to the formation of a field-induced Griffiths phase in the presence of spin-polaron effects., Comment: to be published in JETP Letters

We discuss the mechanisms of unconventional superconductivity and superfluidity in 3D and 2D fermionic systems with purely repulsive interaction at low densities. We construct phase diagrams of these systems and find the areas of the superconducting state in free space, as well as on the lattice in the framework of the Fermi-gas model with hard-core repulsion, the Hubbard model, the Shubin-Vonsovsky model, and the $t-J$ model. We demonstrate that the critical superconducting temperature can be greatly increased in the spin-polarized case or in a two-band situation already at low densities. The proposed theory is based on the Kohn-Luttinger mechanism or its generalizations and explains or predicts anomalous $p$-, $d$-, and $f$-wave pairing in various materials, such as high-temperature superconductors, the idealized monolayer and bilayer of doped graphene, heavy-fermion systems, layered organic superconductors, superfluid $^3$He, spin-polarized $^3$He mixtures in $^4$He, ultracold quantum gases in magnetic traps, and optical lattices., Comment: 38 pages, 19 figures

The effect of the long-range Coulomb interaction on the realization of the Kohn-Luttinger superconductivity in idealized monolayer doped graphene is studied. It is shown that the allowance for the Kohn-Luttinger renormalizations up to the second order in perturbation theory in the on-site Hubbard interaction inclusively, as well as the intersite Coulomb interaction significantly affects the competition between the superconducting phases with the $f$-wave, $p+ip$-wave and $d + id$-wave symmetries of the order parameter. It is shown that the account for the Coulomb repulsion of electrons located at the next-nearest neighboring atoms in such a system changes qualitatively the phase diagram and enhances the critical superconducting temperature., Comment: 6 pages, 3 figures. Submitted to the Special Issue of "Journal of Low Temperature Physics" "Recent Progress in Low Temperature Physics - NT37"

The effect of the intersite and interplane Coulomb interactions between the Dirac fermions on the formation of the Kohn-Luttinger superconductivity in bilayer doped graphene is studied disregarding the effects of the van der Waals potential of the substrate and both magnetic and non-magnetic impurities. The phase diagram determining the boundaries of superconductive domains with different types of symmetry of the order parameter is built using the extended Hubbard model in the Born weak-coupling approximation with allowance for the intratomic, interatomic, and interlayer Coulomb interactions between electrons. It is shown that the Kohn-Luttinger polarization contributions up to the second order of perturbation theory in the Coulomb interaction inclusively and an account for the long-range intraplane Coulomb interactions significantly affect the competition between the superconducting $f-$, $p+ip-$, and $d+id-$wave pairings. It is demonstrated that the account for the interplane Coulomb interaction enhances the critical temperature of the transition to the superconducting phase., Comment: 10 pages, 7 figures

The effect of Coulomb interaction in an ensemble of Dirac fermions on the formation of superconducting pairing in monolayer and bilayer doped graphene is studied using the Kohn-Luttinger mechanism disregarding the Van der Waals potential of the substrate and impurities. The electronic structure of graphene is described using the Shubin-Vonsovsky model taking into account the intratomic, interatomic, and interlayer (in the case of bilayer graphene) Coulomb interactions between electrons. The Cooper instability is determined by solving the Bethe-Saltpeter integral equation. The renormalized scattering amplitude is obtained with allowance for the Kohn-Luttinger polarization contributions up to the second order of perturbation theory in the Coulomb interaction. It plays the role of effective interaction in the Bethe-Salpeter integral equation. It is shown that the allowance for the Kohn-Luttinger renormalizations as well as intersite Coulomb interaction noticeably affects the competition between the superconducting phases with the $f-$wave and $d + id-$wave symmetries of the order parameter. It is demonstrated that the superconducting transition temperature for an idealized graphene bilayer with significant interlayer Coulomb interaction between electrons is noticeably higher than in the monolayer case., Comment: 10 pages, 7 figures

We present a review of theoretical investigations into the Kohn-Luttinger nonphonon superconductivity mechanism in various 3D and 2D repulsive electron systems described by the Fermi-gas, Hubbard, and Shubin-Vonsovsky models. Phase diagrams of the superconducting state are considered, including regions of anomalous $s$-, $p$-, and $d$-wave pairing. The possibility of a strong increase in the superconducting transition temperature $T_c$ even for a low electron density is demonstrated by analyzing the spin-polarized case or the two-band situation. The Kohn-Luttinger theory explains or predicts superconductivity in various materials such as heterostructures and semimetals, superlattices and dichalcogenides, high-$T_c$ superconductors and heavy-fermion systems, layered organic superconductors, and ultracold Fermi gases in magnetic traps. This theory also describes the anomalous electron transport and peculiar polaron effects in the normal state of these systems. The theory can be useful for explaining the origin of superconductivity and orbital currents (chiral anomaly) in systems with the Dirac spectrum of electrons, including superfluid $^3$He-A, doped graphene, and topological superconductors., Comment: 18 pages, 11 figures

The problem of Cooper instability is studied by implementing the Kohn-Luttinger mechanism in the framework of the Shubin-Vonsowsky model taking into account the intersite Coulomb interactions within the first and second coordination spheres. It is shown that the Kohn-Luttinger renormalization for the effective interaction in the second-order terms of perturbation theory, as well as the inclusion of intersite hoppings in the second and third coordination spheres, significantly affects the interplay between the superconducting phases with $d_{xy}$-, $p$-, $s$-, and $d_{x^2-y^2}$-wave symmetries of the order parameter., Comment: 7 pages, 6 figures

Idealized graphene monolayer is considered neglecting the van der Waals potential of the substrate and the role of the nonmagnetic impurities. The effect of the long-range Coulomb repulsion in an ensemble of Dirac fermions on the formation of the superconducting pairing in a monolayer is studied in the framework of the Kohn-Luttinger mechanism. The electronic structure of graphene is described in the strong coupling Wannier representation on the hexagonal lattice. We use the Shubin-Vonsowsky model which takes into account the intra- and intersite Coulomb repulsions of electrons. The Cooper instability is established by solving the Bethe-Salpeter integral equation, in which the role of the effective interaction is played by the renormalized scattering amplitude. The renormalized amplitude contains the Kohn-Luttinger polarization contributions up to and including the second-order terms in the Coulomb repulsion. We construct the superconductive phase diagram for the idealized graphene monolayer and show that the Kohn-Luttinger renormalizations and the intersite Coulomb repulsion significantly affect the interplay between the superconducting phases with $f-$, $d+id-$, and $p+ip-$wave symmetries of the order parameter., Comment: 9 pages, 5 figures

In Chapter 11 we present Fermi-gas approach for the search of s-wave and p-wave superfluidity in three-dimensional solutions of He-3 in He-4 and in He-3 submonolayers. In Chapter 13 on the basis of the anisotropic and isotropic t-J models we study spin-charge separation and confinement in ladder systems and in high-Tc superconductors., Comment: In preparation for Springer-Verlag

In Chapter 1 we start with general Landau scheme of the conservation laws for the hydrodynamics of classical liquids and superfluids. On the basis of Landau scheme we consider hydrodynamics of rotating superfluids with large number of vortices. We study different regimes of slow and fast rotations. In Chapter 4 we consider complicated and yet unresolved problem of chiral anomaly in superfluid 3He-A and present two competing approaches. The first one is based on supersymmetric hydrodynamics, another one on the formal analogy with Dirac equation in QED. In Chapters 6 and 7 we study composed fermions and bosons which correspond to the different bound states consisting of two fermions, two bosons and fermion and boson in ultracold quantum gasses and mixtures. We also elucidate the exact solutions of the Skorniakov-Ter-Martirosian integral equations. We present the basic ideas of Nozieres-Schmitt Rink and Legget theory on BCS-BEC crossover in quantum gasses and construct the phase diagrams for the s-wave and p-wave pairings. In Chapters 9 and 10 we discuss non-phonon mechanisms of superconductivity of the Kohn-Luttinger type for different models in 3D and 2D electron systems at low densities including Fermi-gas, Hubbard and Shubin-Vonsovsky models. We complete the superconductive phase-diagrams of p-wave and d-wave pairing and discuss the possibility to increase Tc already at low density. In Chapters 15 and 16 the mechanisms of electron nanoscale phase-separation in manganite-type oxide materials are analyzed. The instability of magnetic (or charge) homogeneous ordering towards the formation of droplet structures (magnetic polarons) is predicted for a wide parameter range on the phase-diagram. The transport properties of these materials in the phase-separated state are also discussed., Comment: Manuscript in preparation for publication in Springer-Verlag

In the large variety of models such as 3D and 2D Fermi-gas model with hard-core repulsion, 3D and 2D Hubbard model, and Shubin-Vonsovsky model we demonstrate the possibility of triplrt p-wave pairing at low electron density. We show that the critical temperature of the p-wave pairing can be strongly increased in a spin-polarized case or in a two-band situation already at low density and reach experimentally observable values of (1-5)K. We also discuss briefly d-wave pairing and high-Tc superconductivity with Tc~100K which arises in the t-J model in the range of parameters realistic for cuprates., Comment: 12 pages 11 figures, accepted for publication in Journal of Superconductivity and Novel Magnetism, based on invited talks on Ginzburg conference in Zvenigorod and Vortex VII conference in Rhodes, 2011

We search for anomalous normal and superconductive behavior in the two-band Hubbard model with one narrow band. We analyze the influence of electron-polaron effect and Altshuler-Aronov effect on effective mass enhancement and scattering times of heavy and light components in the clean case. We find anomalous behavior of resistivity at high temperatures $T>W_{h}^{*}$ both in 3D and 2D situation. The SC instability in the model is governed by enhanced Kohn-Luttinger effect for p-wave pairing of heavy electrons via polarization of light electrons., Comment: 8 pages, 4 figures, accepted for publication in Journal of Superconductivity and Novel Magnetism, based on the invited talk on Stripes XI Conference in Rome, July 2011

We analyze superconducting instabilities in 3D and 2D extended Hubbard model with Coulomb repulsion between electrons on neighboring sites in the limit of low electron density ($n_{el} \rightarrow 0$) on simple cubic (square) lattice. We show that in a realistic strong-coupling case $U\gg V\gg W$ ($U$ and $V$ are the onsite and the intersite Coulomb repulsions, $W$ the bandwidth) the main SC instability corresponds to the p-wave pairing and in the leading order is correctly described by the equations obtained earlier in the absence of the intersite Coulomb interaction V=0., Comment: 6 pages, 4 figures, accepted for JETP Letters

We search for marginal Fermi-liquid behavior in the two-band Hubbard model with one narrow band. We consider the limit of low electron densities in the bands and strong intraband and interband Hubbard interactions. We analyze the influence of electron polaron effect and other mechanisms of mass-enhancement (related to momentum dependence of the self-energies) on effective mass and scattering times of light and heavy components in the clean case (electron - electron scattering and no impurities). We find the tendency towards phase-separation (towards negative partial compressibility of heavy particles) in a 3D case for large mismatch between the densities of heavy and light bands in a strong coupling limit. We also observe that for low temperatures and equal densities the resistivity in a homogeneous state R(T) ~ T^2 - behaves in a Fermi-liquid fashion both in 3D and 2D cases. For temperatures higher then effective bandwidth for heavy electrons T > Wh* the coherent behavior of heavy component is totally destroyed. The heavy particles move diffusively in the surrounding of light particles. At the same time the light particles scatter on the heavy ones as if on immobile (static) impurities. In this regime the heavy component is marginal, while the light one is not. The resistivity goes on saturation for T > Wh* in the 3D case. In 2D the resistivity has a maximum and localization tail due to weak - localization corrections of Altshuler - Aronov type. Such behavior of resistivity in 3D could be relevant for some uranium-based heavy-fermion compounds like UNi2Al3 and in 2D for some other mixed-valence compounds possibly including the layered manganites. We also consider briefly the superconductive (SC) instability in the model. The leading instability is towards p-wave pairing and is governed by enhanced Kohn - Luttinger mechanism of SC at low electron density., Comment: 37 pages, 9 figures, accepted for JETP

We solve the Leggett equations for the BCS - BEC crossover in the three dimension resonance p-wave superfluid with the symmetry of the A1 - phase. We calculate the sound velocity, the normal density, and the specific heat for the BCS-domain (\mu > 0), BEC-domain (\mu < 0), and close to important point \mu = 0 in 100% polarized case. We find the indications of quantum phase - transition close to the point \mu(T = 0) = 0. Deep in the BCS and BEC-domains the crossover ideas of Leggett and Nozieres, Schmitt-Rink work pretty well. We discuss the spectrum of orbital waves, the paradox of intrinsic angular momentum and complicated problem of chiral anomaly in the BCS A1 - phase at T = 0. We present two different approaches to a chiral anomaly: one based on supersymmetric hydrodynamics, another one on the formal analogy with the Dirac equation in quantum electrodynamics. We evaluate the damping of nodal fermions due to different decay processes in superclean case at T = 0 and find that we are in a ballistic regime \omega\tau >> 1. We propose to use aerogel or nonmagnetic impurities to reach hydrodynamic regime \omega\tau<< 1 at T = 0. We discuss the concept of the spectral flow and exact cancellations between time-derivatives of anomalous and quasiparticle currents in the equation for the total linear momentum conservation. We propose to derive and solve the kinetic equation for the nodal quasiparticles both in the hydrodynamic and in the ballistic regimes to demonstrate this cancellation explicitly. We briefly discuss the role of the other residual interactions different from damping and invite experimentalists to measure the spectrum and damping of orbital waves in A-phase of 3He at low temperatures., Comment: 14 pages, 10 figures

We consider the 2D Hubbard model in the strong-coupling case (U>>W) and at low electron density (nd^2<<1). We find an antibound state as a pole in the two-particle T-matrix. The contribution of this pole in the self-energy reproduces a two-pole structure in the dressed one-particle Green-function similar to the Hubbard-I approximation. We also discuss briefly the Engelbrecht-Randeria mode which corresponds to the pairing of two holes below the bottom of the band for U>>W and low electron density. Both poles produce non-trivial corrections to Landau Fermi-liquid picture already at low electron density but do not destroy it in 2D, Comment: 15 pages, accepted for Sov. Low. Temp. Phys

We analyze the possibility of the nanoscale phase separation manifesting itself in the formation of ferromagnetic (FM) polarons (FM droplets) in the general situation of doped anisotropic three- and two-dimensional antiferromagnets. In these cases, we calculate the shape of the most energetically favorable droplets. We show that the binding energy and the volume of a FM droplet in the three-dimensional (3D) case depend only upon two universal parameters $\bar{J} =(J_x + J_y + J_z)S^2$ and $t_{eff} =(t_xt_yt_z)^{1/3}$, where $\bar{J}$ and $t_{eff}$ are effective antiferromagnetic (AFM) exchange and hopping integrals, respectively. In the two-dimensional (2D) case, these parameters have the form $\bar{J} =(J_x + J_y)S^2$ and $t_{eff} =(t_xt_y)^{1/2}$. The most favorable shape of a ferromagnetic droplet corresponds to an ellipse in the 2D case and to an ellipsoid in the 3D case., Comment: 6 pages, 1 figure, RevTeX

We perform a detailed study of the collective mode across the whole BEC-BCS crossover in fermionic gases at zero temperature, covering the whole range of energy beyond the linear regime. This is done on the basis of the dynamical BCS model. We recover first the results of the linear regime in a simple form. Then specific attention is payed to the non linear part of the dispersion relation and its interplay with the continuum of single fermionic excitations. In particular we consider in detail the merging of collective mode into the continuum of single fermionic excitations. This occurs not only on the BCS side of the crossover, but also slightly beyond unitarity on the BEC side. Another remarkable feature is the very linear behaviour of the dispersion relation in the vicinity of unitarity almost up to merging with the continuum. Finally, while on the BEC side the mode is quite analogous to the Bogoliubov mode, a difference appear at high wavevectors. On the basis of our results we determine the Landau critical velocity in the BEC-BCS crossover which is found to be largest close to unitarity. Our investigation has revealed interesting qualitative features which would deserve experimental exploration as well as further theoretical studies by more sophisticated means., Comment: 21 pages

The structure of bound magnetic polarons in an antiferromagnetic matrix is studied in the framework of two-dimensional (2D) and three-dimensional (3D) Kondo-lattice models in the double exchange limit (J_H >> t). The conduction electron is bound by a nonmagnetic donor impurity and forms a ferromagnetic core of the size about the electron localization length (bound magnetic polaron). We find that the magnetic polaron produces rather long-range extended spin distortions of the antiferromagnetic background around the core. In a wide range of distances, these distortions decay as 1/r^2 and 1/r^4 in 2D and 3D cases, respectively. In addition, the magnetization of the core is smaller than its saturation value. Such a magnetic polaron state is favorable in energy in comparison to usually considered one (saturated core without extended distortions)., Comment: 7 pages, 5 figures, submitted to Phys. Rev. B; v.2 contains the changes introduced according to comments of the PRB Referees

We investigate within a self-consistent theory the molecular instabilities arising in the normal state of a homogeneous degenerate Fermi gas, covering the whole BEC-BCS crossover. These are the standard instability for molecular formation, the BCS instability which corresponds to the formation of Cooper pairs and the related Bose-Einstein instability. These instabilities manifest themselves in the properties of the particle-particle vertex, which we calculate in a ladder approximation. To find the critical temperatures corresponding to these various instabilities, we handle the properties of the interacting Fermi gas on the same footing as the instabilities by making use of the same vertex. This approximate treatment is shown to be quite satisfactory in a number of limiting situations where it agrees with known exact results. The results for the BCS critical temperature and for the BE condensation are found to be in fair agreement with earlier results. The threshold for formation of molecules at rest undergoes a sizeable shift toward the BEC side, due to quantum effects arising from the presence of the degenerate Fermi gas. This should make its experimental observation fairly easy. This shift remains important at least up to temperatures comparable to the Fermi energy of the gas.

We present an exact diagrammatic approach for the problem of dimer-dimer scattering in 3D for dimers being a resonant bound state of two fermions in a spin-singlet state, with corresponding scattering length $a_F$. Applying this approach to the calculation of the dimer-dimer scattering length $a_B$, we recover exactly the already known result $a_B=0.60 a_F$. We use the developed approach to obtain new results in 2D for fermions as well as for bosons. Namely, we calculate bound state energies for three $bbb$ and four $bbbb$ resonantly interacting bosons in 2D. For the case of resonant interaction between fermions and bosons we calculate exactly bound state energies of the following complexes: two bosons plus one fermion $bbf$, two bosons plus two fermions $bf_{\uparrow}bf_{\downarrow}$, and three bosons plus one fermion $bbbf$., Comment: 10 pages, 9 figures

Starting from the assumption that ferromagnetically correlated regions exist in manganites even in the absence of long-range magnetic order, we construct a model of charge transfer due to the spin-dependent tunnelling of charge carriers between such regions. This model allows us to analyze the temperature and magnetic field dependence of resistivity, magnetoresistance, and magnetic susceptibility of phase-separated manganites in the temperature range corresponding to non-metallic behavior. The comparison of theoretical and experimental results reveals the main characteristics of the phase-separated state., Comment: 18 pages, 12 figures, submitted to Journal of Experimental and Theoretical Physics (Zh. Eksp. Teor. Fiz., v.125 (2), 2004)

We study the possibility of nanoscale phase separation in manganites in the framework of the double exchange model. The homogeneous canted state of this model is proved to be unstable toward the formation of small ferromagnetic droplets inside an antiferromagnetic insulating matrix. For the ferromagnetic polaronic state we analyze the quantum effects related to the tails of electronic wave function and a possibility of electron hopping in the antiferromagnetic background. We find that these effects lead to the formation of the threshold for the polaronic state., Comment: 10 pages, 2 figures, invited talk on the workshop on Strongly Correlated Electrons in New Materials (SCENM02), Loughborough (UK). submitted to Journal of Physics A: Mathematical and General

We consider a model of Fermi-Bose mixture with strong hard-core repulsion between particles of the same sort and attraction between particles of different sorts. In this case, besides the standard anomalous averages of the type $$; $$ and $$, a pairing between fermion and boson of the type $bc$ is possible. This pairing corresponds to a creation of composite fermions in the system. At low temperatures and equal densities of fermions and bosons composite fermions are further paired in quartets. Our investigations are important for high-$T_c$ superconductors and in connection with recent observation of weakly bound dimers in magnetic traps at ultralow temperatures., Comment: 7 pages, 2 figures

We present a phase diagram for a dilute two-dimensional Bose-gas on a lattice. For one sort of boson we consider a realistic case of the van der Waals interaction between particles with a strong hard-core repulsion $U$ and a van der Waals attractive tail $V$. For $V< 2 t $, $t$ being a hopping amplitude, the phase diagram of the system contains regions of the usual one-particle Bose-Einstein condensation (BEC). However for $V>2t$ we have total phase separation on a Mott-Hubbard Bose solid and a dilute Bose gas. For two sorts of structureless bosons described by the two band Hubbard model an s-wave pairing of the two bosons of different sort $ \neq 0$ is possible. The results we obtained should be important for different Bose systems, including submonolayers of $^4$He, excitons in semiconductors, Schwinger bosons in magnetic systems and holons in HTSC. In the HTSC case a possibility of two-holon pairing in the slave-bosons theories of superconductivity can restore a required charge $2e$ of a Cooper pair., Comment: 10 pages, 2 figures

High order perturbation theory corrections to the superfluid transition temperature in a weakly interacting Fermi gas with repulsive interaction are calculated. This involves calculating the contributions of third and fourth order diagrams in the gas parameter and taking into account effects of retardation. The contributions from both second, third and fourth orders result in the effective attraction in p-wave channel. It is shown that the critical temperature is mainly determined by second and third orders terms of perturbation theory. The dependence of the critical temperature on an external magnetic field is found. We discuss possible applications of the results to the diluted 3He-4He mixtures and trapped neutral-atom Fermi gases., Comment: The version of the paper (JETP 90 (2000) 861) with author proofs, which were not taken into account in translated journal publication. 21 pages, 12 figures

A simple model is proposed to calculate resistivity, magnetoresistance, and noise spectrum in non-metallic phase-separated manganites containing small metallic droplets (magnetic polarons). The system is taken to be far from the percolation transition into a metallic state. It is assumed that the charge transfer occurs due to electron tunneling from one droplet to another through the insulating medium. As a result of this tunneling, the droplets acquire or lose extra electrons forming metastable two-electron and empty states. In the framework of this model, explicit expressions for dc conductivity and noise power of the system are derived. It is shown that the noise spectrum has 1/f form in the low-frequency range., Comment: 6 pages, 1 fugure included

A new scenario for superconductivity in the bismuthates based on the concept of a spatially separated Fermi-Bose mixture is proposed. In the framework of this scenario we qualitatively explain the insulator-metal transition and the nature of the superconductivity which occur in Ba_{1-x}K_xBiO_3 under doping by K. We also analyze briefly an applicability of this scenario for the high-Tc superconductors. In conclusion some additional experiments required to elucidate more precisely the nature of the superconductivity in the bismuthates are discussed., Comment: 10 pages, 4 figures

A simple model of charge ordering is considered. It is shown explicitly that at any deviation from half-filling ($n \neq 1/2$) the system is unstable with respect to phase separation into charge ordered regions with $n = 1/2$ and metallic regions with smaller electron or hole density. Possible structure of this phase-separated state (metallic droplets in a charge-ordered matrix)is discussed. The model is extended to account for the strong Hund-rule onsite coupling and the weaker intersite antiferromagnetic exchange. An analysis of this extended model allows us to determine the magnetic structure of the phase-separated state and to reveal the characteristic features of manganites and other substances with charge ordering., Comment: 9 pages, revtex

We calculate the one-electron spectral function of the attractive-U Hubbard model in two dimensions. We work in the intermediate coupling and low density regime and evaluate analytically the self-energy. The results are obtained in a framework based on the self-consistent T-matrix approximation. We also calculate the chemical potential of the bound pairs as a function of temperature. On the basis of this calculation we analyze the low-temperature resistivity and specific heat in the normal state of this system. We compare our results with recent beautiful tunneling experiments in the underdoped regime of HTSC-materials., Comment: 2 pages, LT22 Conference paper, phbauth and elsart style files included

We predict a possibility of triplet Cooper pairing in a Fermi-gas of neutral particles in a confined geometry of magnetic traps at ultra-low temperatures. We evaluate a superfluid transition temperature and analyze the difference between pairing in free space and in confined geometry. We also consider in details a case of fermionic 6Li., Comment: 2 pages, LT22 Conference paper, phbauth and elsart style files included

The critical temperature of a superfluid phase transition in a Fermi gas with repulsive interaction is found. The influence of a magnetic field on the transition is analyzed. The estimates for the critical temperature for a trapped gas of $^6$Li atoms and $^3$He--$^4$He mixtures are presented., Comment: 2 pages, 1 figure, LT22 Conference paper, phbauth and elsart style files included