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arXiv:cond-mat/9901224 · Physical review. B, Condensed matter

Bound pair states beyond the condensate for Fermi systems below Tc: The pseudogap as a necessary condition

Alexander Yu. Cherny, Arkady A Shanenko

Published Jul 1, 1999• 5 citations
arXivHTMLPDF

Abstract

As is known, the ${1/q}^{2}$ theorem of Bogoliubov asserts that the mean density of the fermion pair states with the total momentum q obeys the inequality ${n}_{q}>~{C/q}^{2}(\stackrel{\ensuremath{\rightarrow}}{q}0)$ in the case of the Fermi system taken at nonzero temperature and in the superconducting state provided the interaction term of its Hamiltonian is locally gauge invariant. With the principle of correlation weakening it is proved in this paper that the reason for the mentioned singular behavior of ${n}_{q}$ is the presence of the bound states of particle pairs with nonzero total momenta. Thus, below the temperature of the superconducting phase transition there always exist the bound states of the fermion couples beyond the pair condensate. If the pseudogap observed in the normal phase of the high-${T}_{c}$ superconductors is stipulated by the presence of the electron bound pairs, then the derived result suggests, in a model-independent manner, that the pseudogap survives below ${T}_{c}.$

DOI
10.1103/physrevb.60.1276

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As is known, the 1/q2{1/q}^{2}1/q2 theorem of Bogoliubov asserts that the mean density of the fermion pair states with the total momentum q obeys the inequality nq> C/q2(q\ensuremath→0){n}_{q}>~{C/q}^{2}(\stackrel{\ensuremath{\rightarrow}}{q}0)nq​> C/q2(q\ensuremath→​0) in the case of the Fermi system taken at nonzero temperature and in the superconducting state provided the interaction term of its Hamiltonian is locally gauge invariant. With the principle of correlation weakening it is proved in this paper that the reason for the mentioned singular behavior of nq{n}_{q}nq​ is the presence of the bound states of particle pairs with nonzero total momenta. Thus, below the temperature of the superconducting phase transition there always exist the bound states of the fermion couples beyond the pair condensate. If the pseudogap observed in the normal phase of the high-Tc{T}_{c}Tc​ superconductors is stipulated by the presence of the electron bound pairs, then the derived result suggests, in a model-independent manner, that the pseudogap survives below Tc.{T}_{c}.Tc​.
A weak-coupling scenario wherein bosonic preformed electron pairs emerge upon cooling from two-electron correlations can explain the pseudogap phase consisting of segments where a Bogoliubov-like energy-momentum relation gapped spectrum alternates with a normal ungapped one. Bose–Einstein condensation (BEC) of preformed pairs interacting with the background fermions leads to either - or -wave-like superconducting gaps, the result being sensitive to the magnitude of the total number density of pairs at which BEC occurs and becomes possible already for a moderately anisotropic -wave pairing of fermions repelling each other via isotropic coulombic forces. The present model is compatible with the coexistence of pseudogap and of superconductivity phenomena.
Bosonization of Cooper pairs and novel Bose-liquid superconductivity and superfluidity in high-TcT_cTc​ cuprates and other systems
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The purpose of this work is twofold.In the first part we describe superfluidity/superconductivity as an emergent phenomenon resulting from two-body correlations in presence of the Bose-Einstein condensation of particles.We briefly discuss the underlying mechanism for bosons as well as fermion pairs and illustrate various realizations of superfluidity emphasizing the recent examples.In the second part we study the glassy liquid of incoherent pairs which might exist above the transition temperature T c in the underdoped regime of cuprate superconductors.In particular, we explore the angular variation of pseudogap within two-dimensional version of the boson-fermion model using for a quantitative analysis the projective method.We find that above T c the pseudogap closes first near the nodal areas restoring there pieces (arcs) of the Fermi surface whereas remaining parts of the large Fermi surface around the antinodal points are still absent due to incoherent pairs.Upon increasing temperature the length of the Fermi arcs enlarges because the superconducting correlations are gradually suppressed.An intriguing death of Fermi surface can thus be closely related to the Bogoliubov quasiparticles whose existence in the pseudogap state has been predicted by us and confirmed recently by the angle resolved photoemission spectroscopy measurements on Bi 2 Sr 2 CaCu 2 O 8 and La 1.895 Sr 0.105 CuO 4 compounds.
A model of a Fermi liquid with the fermion condensate (FC) is applied to the consideration of quasiparticle excitations in high-temperature superconductors, in their superconducting and normal states. Within our model the appearance of the fermion condensate presents a quantum phase transition that separates the regions of normal and strongly correlated electron liquids. Beyond the phase transition point the quasiparticle system is divided into two subsystems, one containing normal quasiparticles and the other---fermion condensate localized at the Fermi surface and characterized by almost dispersionless single-particle excitations. In the superconducting state the quasiparticle dispersion in systems with FC can be presented by two straight lines, characterized by effective masses MFC∗{M}_{\mathrm{FC}}^{*}MFC∗​ and ML∗,{M}_{L}^{*},ML∗​, respectively, and intersecting near the binding energy, which is of the order of the superconducting gap. This same quasiparticle picture persists in the normal state, thus manifesting itself over a wide range of temperatures as new energy scales. Arguments are presented that fermion systems with FC have features of a ``quantum protectorate'' [R. B. Laughlin and D. Pines, Proc. Natl. Acad. Sci. U.S.A. 97, 28 (2000); P. W. Anderson, cond-mat/0007185 (unpublished); cond-mat/0007287 (unpublished)].
The origin of the pseudogap behavior, found in many high-TcT_cTc​ superconductors, remains one of the greatest puzzles in condensed matter physics. One possible mechanism is fermionic incoherence, which near a quantum critical point allows pair formation but suppresses superconductivity. Employing quantum Monte Carlo simulations of a model of itinerant fermions coupled to ferromagnetic spin fluctuations, represented by a quantum rotor, we report numerical evidence of pseudogap behavior, emerging from pairing fluctuations in a quantum-critical non-Fermi liquid. Specifically, we observe enhanced pairing fluctuations and a partial gap opening in the fermionic spectrum. However, the system remains non-superconducting until reaching a much lower temperature. In the pseudogap regime the system displays a gap-filling rather than gap-closing behavior, consistent with experimental observations. Our results provide the first unambiguous lattice model realization of a pseudogap state in a strongly correlated system, driven by superconducting fluctuations.