arXiv subjects

M. V. Sadovskii

Publications and source records attributed to M. V. Sadovskii.

At least 91 records · Page 5Linked to original sources

arXiv2003

Supeconductivity in the Pseudogap State in "Hot - Spots" Model: Ginzburg - Landau Expansion

We analyze properties of superconducting state (for both s-wave and d-wave pairing), appearing on the "background" of the pseudogap state, induced by fluctuations of "dielectric" (AFM(SDW) or CDW) short -- range order in the model of the Fermi surface with "hot spots". We present microscopic derivation of Ginzburg - Landau expansion, taking into account all Feynman diagrams of perturbation theory over electron interaction with this short - range order fluctuations, leading to strong electronic scattering in the vicinity of "hot spots". We determine the dependence of superconducting critical temperature on the effective width of the pseudogap and on correlation length of short - range order fluctuations. We also find similar dependences of the main characteristics of such superconductor close to transition temperature. It is shown particularly, that specific heat discontinuity at the transition temperature is significantly decreased in the pseudogap region of the phase diagram.

cond-mat.supr-con↗

arXiv2002

Optical Conductivity in a Two - Dimensional Model of the Pseudogap State

We consider a two-dimensional model of the pseudogap state, based on the scenario of strong electron scattering by fluctuations of ``dielectric'' (AFM, CDW) short-range order. We construct a system of recurrence equations both for one-particle Green's function and vertex part, describing electron interaction with an external field, which take into account all Feynman graphs for electron scattering by short-range order fluctuations. The results of detailed calculations of optical conductivity are presented for different geometries (topologies) of the Fermi surface, demonstrating both the effects of pseudogap formation and localization effects. These results are in qualitative agreement with experimental data obtained for high-temperature superconducting cuprates.

cond-mat.supr-con↗

arXiv2001

Superconductivity in an Exactly Solvable Model of the Pseudogap State: Absence of Self Averaging

We analyze the anomalies of superconducting state within a simple exactly solvable model of the pseudogap state, induced by fluctuations of ``dielectric'' short range order, for the model of the Fermi surface with ``hot'' patches. The analysis is performed for the arbitrary values of the correlation length xi_{corr} of this short range order. It is shown that superconducting energy gap averaged over these fluctuations is non zero in a wide temperature range above T_c - the temperature of homogeneous superconducting transition. This follows from the absence of self averaging of the gap over the random field of fluctuations. For temperatures T>T_c superconductivity apparently appears in separate regions of space (``drops''). These effects become weaker for shorter correlation lengths xi_{corr} and the region of ``drops'' on the phase diagram becomes narrower and disappears for xi_{corr}-->0, however, for the finite values of xi_{corr} the complete self averaging is absent.

cond-mat.supr-con↗

arXiv2001

Pseudogap in High - Temperature Superconductors

This review describes the main experimental facts and a number of theoretical models concerning the pseudogap state in high - temperature superconductors. On the phase diagram of HTSC - cuprates the pseudogap state is observed in the region of current carrier concentrations less than optimal and leads to a number of anomalies of electronic properties. These pseudogap anomalies apparently are due to fluctuations of antiferromagnetic short - range order developing as system moves towards antiferromagnetic region on the phase diagram. Electron interaction with these fluctuations leads to anisotropic renormalization of electronic spectrum and non - Fermi liquid behavior on certain parts of the Fermi surface. We also discuss some simple theoretical models describing basic properties of the pseudogap state, including the anomalies of superconducting state due to pseudogap renormalization of electronic spectrum.

cond-mat.supr-con↗

arXiv2000

Superconductivity in the Pseudogap State due to Fluctuations of Short-Range Order

We analyze the anomalies of superconducting state (s and d-wave pairing) in a simple model of pseudogap state, induced by fluctuations of short - range order (e.g. antiferromagnetic), based on the model Fermi surface with "hot patches". We derive a system of recursion relations for Gorkov's equations which take into account all diagrams of perturbation theory for electron interaction with fluctuations of short-range order. Then we find superconducting transition temperature and gap behavior for different values of the pseudogap width and correlation lengths of short-range order fluctuations. In a similar approximation we derive the Ginzburg-Landau expansion and study the main physical characteristics of a superconductor close to the transition temperature, both as functions of the pseudogap width and correlation length of fluctuations. Results obtained are in qualitative agreement with a number of experiments on underdoped HTSC-cuprates.

cond-mat.supr-con↗

arXiv1999

Models of the Pseudogap State in Cuprates

We review a certain class of ("nearly") exactly solvable models of electronic spectrum of two-dimensional systems with fluctuations of short range order of "dielectric" (e.g. antiferromagnetic) or "superconducting" type, leading to the formation of anisotropic pseudogap state on certain parts of the Fermi surface. The models are based on recurrence procedure for one- and two-electron Green's functions which takes into account of all Feynman diagrams in perturbation series with the use of the approximate Ansatz for higher-order terms in this series. These models can be applied to calculation of spectral density, density of states and conductivity in the normal state, as well as to calculation of some properties of superconducting state.

cond-mat.supr-con↗

arXiv1999

Superconductivity in a Toy Model of the Pseudogap State

We analyze superconducting state (both s and d - wave) in a simple exactly solvable model of pseudogap state, induced by short - range order fluctuations (e.g. antiferromagnetic), which is based upon model Fermi - surface with "hot patches". It is shown that superconducting energy gap averaged over these fluctuations is non zero even for the temperatures larger than mean - field T_c of superconducting transition in a sample as a whole. For temperatures T>T_c superconductivity apparently exists within separate regions ("drops"). We study the spectral density and the density of states and demonstrate that superconductivity signals itself in these already for T>T_c, while at T_c itself nothing special happens from this point of view. These anomalies are in qualitative agreement with a number experiments on underdoped cuprates.

cond-mat.supr-con↗

arXiv1999

Superconductivity and Localization

We present a review of theoretical and experimental works on the problem of mutual interplay of Anderson localization and superconductivity in strongly disordered systems. We start with brief discussion of modern aspects of localization theory including the basic concept of scaling, self-consistent theory and interaction effects. After that we analyze disorder effects on Cooper pairing and superconducting transition temperature as well as Ginzburg-Landau equations for superconductors which are close to the Anderson transition. A necessary generalization of usual theory of ``dirty'' superconductors is formulated which allows to analyze anomalies of the main superconducting properties close to disorder-induced metal-insulator transition. Under very rigid conditions superconductivity may persist even in the localized phase (Anderson insulator).Strong disordering leads to considerable reduction of superconducting transition temperature T_{c} and to important anomalies in the behavior of the upper critical field H_{c2}. Fluctuation effects are also discussed. In the vicinity of Anderson transition inhomogeneous superconductivity appears due to statistical fluctuations of the local density of states. We briefly discuss a number of experiments demonstrating superconductivity close to the Anderson transition both in traditional and high-T_{c} superconductors. In traditional systems superconductivity is in most cases destroyed before metal-insulator transition. In case of high-T_{c} superconductors a number of anomalies show that superconductivity is apparently conserved in localized phase before it is suppressed by strong enough disorder.

cond-mat.dis-nn↗

arXiv1999

Ginzburg-Landau Expansion in a Toy Model of Superconductor with Pseudogap

We propose a toy model of electronic spectrum of two-dimensional system with ``hot-patches'' on the Fermi surface, which leads to essential renormalization of spectral density (pseudogap). Within this model we derive Ginzburg-Landau expansion for both s-wave and d-wave Cooper pairing and analyze the influence of pseudogap formation on the basic properties of superconductors.

cond-mat.supr-con↗

arXiv1999

Optical Conductivity in a Simple Model of Pseudogap State in Two-Dimensional System

We present calculation of optical conductivity in a simple model of electronic spectrum of two-dimensional system with "hot patches" on the Fermi surface, leading to non Fermi-liquid renormalization of the spectral density (pseudogap) on these patches. It is shown that this model qualitatively reproduces basic anomalies of optical experiments in the pseudogap state of copper oxides.

cond-mat.supr-con↗

arXiv1998

Models of the Pseudogap State of Two-Dimensional Systems

We analyze a number of ``nearly exactly'' solvable models of electronic spectrum of two-dimensional systems with well-developed fluctuations of short range order of ``dielectric'' (e.g. antiferromagnetic) or ``superconducting'' type, which lead to the formation of anisotropic pseudogap state on certain parts of the Fermi surface. We formulate a recurrence procedure to calculate one-electron Green's function which takes into account all Feynman diagrams in perturbation series and is based upon the approximate Ansatz for higher-order terms in this series. Detailed results for spectral densities and density of states are presented. We also discuss some important points concerning the justification of our Ansatz for higher-order contributions.

cond-mat.supr-con↗

arXiv1997

Ginzburg-Landau Expansion and the Slope of the Upper Critical Field in Superconductors with Anisotropic Normal Impurity Scattering

Ginzburg-Landau expansion for superconductors with anisotropic $s-$ and $d-$wave pairing is derived in the presence of anisotropic normal impurity scattering which makes $d-$pairing state more stable under disordering. It is demonstrated that the slope of the upper critical field $|dH_{c2}/dT|_{T_{c}}$ in superconductors with $d-$wave pairing has nonlinear dependence on disorder, i.e. for the low anisotropic scattering rate it drops rather fast with concentration of normal impurities, but as anisotropy of scattering increases it features initial nonlinear growth, approaches a maximum and drops again, vanishing at the critical impurity concentration. In superconductors with anisotropic $s-$wave pairing $|dH_{c2}/dT|_{T_{c}}$ grows, approaching the known asymptotic behavior, characteristic of usual isotropic case irrespective to the scattering anisotropy.

cond-mat.supr-con↗

arXiv1997

Combinatorics of Feynman Diagrams for the Problems with Gaussian Random Field

The algorithm to calculate the generating function for the number of ``skeleton'' diagrams for the irreducible self-energy and vertex parts is derived for the problems with Gaussian random fields. We find an exact recurrence relation determining the number of diagrams for any given order of perturbation theory, as well as its asymptotics for the large order limit. These results are applied to the analysis of the problem of an electron in the Gaussian random field with the ``white-noise'' correlation function. Assuming the equality of all ``skeleton'' diagrams for the self-energy part in the given order of perturbation theory, we construct the closed integral equation for the one-particle Green's function, with its kernel defined by the previously introduced generating function. Our analysis demonstrate that this approximation gives the qualitatively correct form of the localized states ``tail'' in the density of states in the region of negative energies and is apparently quite satisfactory in the most interesting region of strong scattering close to the former band-edge, where we can derive the asymptotics of the Green's function and density of states in the limit of very strong scattering.

cond-mat.dis-nn↗

arXiv1996

Disorder Effects in Superconductors with Anisotropic Pairing: From Cooper Pairs to Compact Bosons

In the weak coupling BCS-approximation normal impurities do not influence superconducting T_{c} in significant manner in case of isotropic s-wave pairing. However, in case of d-wave pairing these are strongly pair-breaking. This fact is in rather strong contradiction with many experiments on disordered high-T_{c} superconductors assuming the d-wave nature of pairing in these systems. With the growth of electron attraction within the Cooper pair the system smoothly crosses over from BCS-pairs to compact Boson picture of superconductivity. As pairing strength grows and pairs become compact significant deviations from universal Abrikosov-Gorkov dependence of T_{c} on disorder appear in case of d-wave pairing with superconducting state becoming more stable than in the weak coupling case. As high-T_{c} superconductors are actually in the intermediate region with Cooper pairs size of the order of few interatomic lengths, these results can explain the relative stability of d-wave pairing under rather strong disordering.

cond-mat.supr-con↗

arXiv1996

Superconductivity Suppression Close to the Metal-Insulator Transition in Strongly Disordered Systems

On the basis of the recently proposed self-consistent theory of metal- insulator transition in strongly disordered systems, taking into account interaction effects, we study transition temperature $T_{c}$ suppression in disordered superconductors for the wide disorder interval --- from weakly disordered metal up to Anderson insulator, induced by "Coulomb pseudogap" formation in the density of states. It is shown that for a number of systems this theory provides rather satisfactory fit of experimental data.

cond-mat.supr-con↗

arXiv1995

Ginzburg-Landau Expansion and the Slope of the Upper Critical Field in Disordered Superconductors with Anisotropic Pairing

It is demonstrated that the slope of the upper critical field $|dH_{c2}/dT|_{T_{c}}$ in superconductors with $d$-wave pairing drops rather fast with concentration of normal impurities, while in superconductors with anisotropic $s$-wave pairing $|dH_{c2}/dT|_{T_{c}}$ grows, and in the limit of strong disorder is described by the known dependences of the theory of ``dirty'' superconductors. This allows to use the measurements of $H_{c2}$ in disordered superconductors to discriminate between these different types of pairing in high-temperature and heavy-fermion superconductors.

cond-mat↗

arXiv1994

Self-Consistent Theory of Metal Insulator Transitions in Disordered Systems

Self-consistent theory of electron localization in disordered systems is generalized for the case of interacting electrons. We propose and critically compare a number of possible self-consistency schemes which take into account the lowest perturbation theory contributions over the interaction. Depending on self-consistency scheme we can obtain either the continuous metal-insulator transition or that with the minimal metallic conductivity. Within the continuous transition approach we calculate the frequency dependence of generalized diffusion coefficient both for metallic and insulating phases. We also consider interaction renormalization of the single-electron density of states which demonstrates the growth of the effective pseudogap as system goes from metal to insulator.

cond-mat↗

arXiv1994

Josephson Effect in Superconductors with Odd-Gap Pairing

It is shown that the Josephson current in $S-I-S$---geometry is zero, if one or both superconductors possess the gap odd over $p-p_{F}$. For the odd-frequency pairing the Josephson current is zero in case of the tunneling between the traditional and odd-gap superconductor and is finite for the tunneling between two odd-gap superconductors.

cond-mat↗