Phase fluctuations and Non-Fermi Liquid Properties of 2D Fermi-system with attraction

The effect of static fluctuations in the phase of the order parameter on the normal and superconducting properties of a 2D system with attractive four-fermion interaction has been studied. Analytic expressions for the fermion Green function, its spectral density and the density of states are derived. The resultant single-particle Green function clearly demonstrates non-Fermi liquid behavior. The results show that as the temperature increases through the 2D critical temperature the width of the quasiparticle peaks broadens significantly. At the same time one retains the gap in quasiparticle spectrum. The spectral density for the dynamical fluctuations can also be obtained. Clearly the dynamical fluctuations fill the gap giving the observed pseudogap behaviour.Comment: 4 pages, LaTeX; invited paper presented at New^3SC-2, Las Vegas, USA, 199

Pseudogap phase formation in the crossover from Bose-Einstein condensation to BCS superconductivity in low dimensional systems

A phase diagram for a 2D metal with variable carrier density has been studied using the modulus-phase representation for the order parameter in a fully microscopic treatment. This amounts to splitting the degrees of freedom into neutral fermion and charged boson degrees of freedom. Although true long range order is forbidden in two dimensions, long range order for the neutral fermions is possible since this does not violate any continuous symmetry. The phase fluctuations associated with the charged degrees of freedom destroy long range order in the full system as expected. The presence of the neutral order parameter gives rise to new features in the superconducting condensate formation in low dimensional systems. The resulting phase diagram contains a new phase which lies above the superconducting (here Berezinskii-Kosterlitz-Thouless) phase and below the normal (Fermi-liquid) phase. We identify this phase with the pseudogap phase observed in underdoped high-$T_{c}$ superconducting compounds above their critical temperature. We also find that the phase diagram persists even in the presence of weak 3-dimensionalisation.Comment: 4 pages, LaTeX; invited paper presented at New^3SC-1, Baton Rouge, USA, 1998. To be published in Int.J.Mod.Phys.

Transport Spectroscopy of the Field Induced Cascade of Lifshitz Transitions in YbRh2Si2

A series of strong anomalies in the thermoelectric power is observed in the heavy fermion compound YbRh$_2$Si$_2$ under the effect of magnetic field varying in the range from 9.5~T to 13~T. We identify these features with a sequence of topological transformations of the sophisticated Fermi surface of this compound, namely a cascade of Lifshitz topological transitions. In order to undoubtedly attribute these anomalies to the specific topological changes of the Fermi surface, we employ the renormalized band method. Basing on its results we suggest a simplified model consisting of the large peripheral Fermi surface sheet and the number of continuously appearing (disappearing) small "voids" or "necks". We account for the multiple electron scattering processes between various components of the Fermi surface, calculate the corresponding scattering times, and, finally, find the magnetic field dependence of the Seebeck coefficient. The obtained analytical expression reproduces reasonably the observed positions of the maxima and minima as well as the overall line shapes and allows us to identify the character of corresponding topological transformations.Comment: 7 pages, 6 figure, to appear in J. Phys. Soc. Jp

Persistence of pseudogap formation in quasi-2D systems with arbitrary carrier density

The existence of a pseudogap above the critical temperature has been widely used to explain the anomalous behaviour of the normal state of high-temperature superconductors. In two dimensions the existence of a pseudogap phase has already been demonstrated in a simple model. It can now be shown that the pseudogap phase persists even for the more realistic case where coherent interlayer tunneling is taken into account. The effective anisotropy is surprisingly large and even increases with increasing carrier density.Comment: 17 pages, LaTeX, 1 EMTeX figure; extended versio

Effective action approach and Carlson-Goldman mode in d-wave superconductors

We theoretically investigate the Carlson-Goldman (CG) mode in two-dimensional clean d-wave superconductors using the effective ``phase only'' action formalism. In conventional s-wave superconductors, it is known that the CG mode is observed as a peak in the structure factor of the pair susceptibility $S(\Omega, \mathbf{K})$ only just below the transition temperature T_c and only in dirty systems. On the other hand, our analytical results support the statement by Y.Ohashi and S.Takada, Phys.Rev.B {\bf 62}, 5971 (2000) that in d-wave superconductors the CG mode can exist in clean systems down to the much lower temperatures, $T \approx 0.1 T_c$. We also consider the manifestations of the CG mode in the density-density and current-current correlators and discuss the gauge independence of the obtained results.Comment: 23 pages, RevTeX4, 12 EPS figures; final version to appear in PR

Phase Fluctuations and Pseudogap Phenomena

This article reviews the current status of precursor superconducting phase fluctuations as a possible mechanism for pseudogap formation in high-temperature superconductors. In particular we compare this approach which relies on the two-dimensional nature of the superconductivity to the often used $T$-matrix approach. Starting from simple pairing Hamiltonians we present a broad pedagogical introduction to the BCS-Bose crossover problem. The finite temperature extension of these models naturally leads to a discussion of the Berezinskii-Kosterlitz-Thouless superconducting transition and the related phase diagram including the effects of quantum phase fluctuations and impurities. We stress the differences between simple Bose-BCS crossover theories and the current approach where one can have a large pseudogap region even at high carrier density where the Fermi surface is well-defined. The Green's function and its associated spectral function, which explicitly show non-Fermi liquid behaviour, is constructed in the presence of vortices. Finally different mechanisms including quasi-particle-vortex and vortex-vortex interactions for the filling of the gap above $T_c$ are considered.Comment: 129 pages, Elsart, 28 EPS figures; Physics Reports, in press. Authors related information under "http://nonlin.bitp.kiev.ua/~sharapov/superconductivity.html