arXiv subjects

M. Yu. Kagan

Publications and source records attributed to M. Yu. Kagan.

At least 37 records · Page 2Linked to original sources

arXiv2015

Anomalous superconductivity and superfluidity in repulsive fermion systems

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.

cond-mat.supr-con↗

arXiv2015

Kohn-Luttinger superconductivity in monolayer and bilayer semimetals with the Dirac spectrum

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.

cond-mat.supr-con↗

arXiv2014

The Kohn-Luttinger effect and anomalous pairing in new superconducting systems and graphene

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.

cond-mat.supr-con↗

arXiv2014

Effect of long-range interactions on the Kohn-Luttinger mechanism of the Cooper instability in the Shubin-Vonsowsky model

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.

cond-mat.supr-con↗

arXiv2014

The Kohn-Luttinger superconductivity in idealized doped graphene

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.

cond-mat.supr-con↗

arXiv2013

Modern trends in Superconductivity and Superfluidity. Chapters 11, 13

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.

cond-mat.supr-con↗

arXiv2012

Modern trends in Superconductivity and Superfluidity. Selected Chapters

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.

cond-mat.supr-con↗

arXiv2011

Superconductivity in repulsive Fermi-systems at low density

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.

cond-mat.supr-con↗

arXiv2011

Anomalous resistivity and the electron-polaron effect in the two-band Hubbard model with one narrow band

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.

cond-mat.str-el↗

arXiv2011

Triplet p-wave superconductivity in low-density extended Hubbard model with Coulomb repulsion

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.

cond-mat.supr-con↗

arXiv2011

Manifestation of the Upper Hubbard band in the 2D Hubbard model at low electron density

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

cond-mat.str-el↗

arXiv2011

BCS - BEC crossover and quantum hydrodynamics in p-wave superfluids with a symmetry of the A1 - phase

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 (μ> 0), BEC-domain (μ< 0), and close to important point μ= 0 in 100% polarized case. We find the indications of quantum phase - transition close to the point μ(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 ωτ>> 1. We propose to use aerogel or nonmagnetic impurities to reach hydrodynamic regime ωτ<< 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.

cond-mat.quant-gas↗

arXiv2011

Anomalous resistivity and the origin of a heavy mass in the two-band Hubbard model with one narrow band

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.

cond-mat.str-el↗

arXiv2006

Small-scale phase separation in doped anisotropic antiferromagnets

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.

cond-mat.str-el↗

arXiv2006

A new type of bound magnetic polaron state: the formation of long-range spin distortions

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).

cond-mat.str-el↗

arXiv2006

Collective mode of homogeneous superfluid Fermi gases in the BEC-BCS crossover

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.

cond-mat.other↗

arXiv2005

Bound states of three and four resonantly interacting particles

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 $bbbf$.

cond-mat.str-el↗

arXiv2005

Self-consistent theory for molecular instabilities in a normal degenerate Fermi gas in the BEC-BCS crossover

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.

cond-mat.other↗