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Physical Review B

Coherent and incoherent pairing instabilities and spin-charge separation in bipartite and nonbipartite nanoclusters: Exact results

ARMEN N. KOCHARIAN, Gayanath Fernando, Kalum Palandage, J. W. Davenport

Published Aug 21, 2008• 34 citations
Publisher

Abstract

Electron pairing and formation of various types of magnetic correlations for ensembles of small clusters of different geometries are studied with emphasis on tetrahedrons and square pyramids under variation of interaction strength, electron doping and temperature. These exact calculations of charge and spin collective excitations and pseudogaps yield intriguing insights into level crossing degeneracies, phase separation and condensation. Obtained coherent and incoherent pairings provide a route for possible superconductivity different from the conventional BCS theory. Criteria for spin-charge separation, reconciliation and recombination driven by interaction strength, next-nearest coupling and temperature are found. Resulting phase diagrams resemble a number of inhomogeneous, coherent and incoherent nanoscale phases seen recently in high-${T}_{c}$ cuprates, manganites and colossal magnetoresistive (CMR) nanomaterials.

DOI
10.1103/physrevb.78.075431

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Electron pairing and formation of various types of magnetic correlations for ensembles of small clusters of different geometries are studied with emphasis on tetrahedrons and square pyramids under variation of interaction strength, electron doping and temperature. These exact calculations of charge and spin collective excitations and pseudogaps yield intriguing insights into level crossing degeneracies, phase separation and condensation. Obtained coherent and incoherent pairings provide a route for possible superconductivity different from the conventional BCS theory. Criteria for spin-charge separation, reconciliation and recombination driven by interaction strength, next-nearest coupling and temperature are found. Resulting phase diagrams resemble a number of inhomogeneous, coherent and incoherent nanoscale phases seen recently in high-Tc{T}_{c}Tc​ cuprates, manganites and colossal magnetoresistive (CMR) nanomaterials.
Electron coherent and incoherent pairings and other types of correlations are studied exactly for the ensemble of small clusters with different geometries under variation of interaction strength, electron doping and temperature. Charge and spin collective excitations yield intriguing insights into level crossing degeneracies, phase separation and condensation. Criteria for spin-charge separation and recombination driven by interaction strength and temperature are found. Phase diagrams resemble a number of inhomogeneous, nanoscale phases and pseudogap regions seen recently in high TC cuprates, manganites, multiferroics and CMR nanomaterials.
Exact thermal studies of small (4-site and 8-site) Hubbard clusters with local electron repulsion yield intriguing insight into phase separation, charge-spin separation, pseudogaps, condensation, and, in particular, pairing fluctuations away from half-filling. These exact calculations, carried out in canonical and grand canonical ensembles, monitoring variations in temperature TTT and magnetic field hhh, show rich phase diagrams in a $T\ensuremath{-}\ensuremath{\mu}$ space consisting of pairing fluctuations and signatures of condensation. Corresponding electron pairing instabilities are seen when the on-site Coulomb interaction UUU is smaller than a critical value Uc(T){U}_{c}(T)Uc​(T) and they point to a possible electron pairing mechanism. The specific heat, magnetization, charge pairing, and spin pairing provide strong support for the existence of competing (paired and unpaired) phases near optimal doping in these clusters, and numerous similarities with experiments on high Tc{T}_{c}Tc​ superconductors are pointed out. In addition, these ideas may be linked to superconducting carbon nanotubes where a purely electronic mechanism could be responsible for superconductivity.
With the growing interest of unconventional superconductors, it is believed that these materials have spatial inhomogeneities accompanied with the separate pairing of electrons and subsequent condensation. In doped high-Tc cuprate superconductors, iron pnictide and telluride nanomaterials, above properties can be traced from both repulsive and attractive interactions of electrons. The principle differences and similarities of electron coherent and incoherent pairing instabilities are analyzed using ensembles of small clusters under variation of chemical potential (or doping), interaction strength, temperature and magnetic field. The exact calculations of quantum critical points, the charge and spin collective excitations, and corresponding critical transition temperatures display a common mechanism of phase separation transitions, condensation and formation of spatial inhomogeneities in various cluster geometries. The dependence of the gap function on position of the apical oxygen atom near its sign change due to its vibration provides a simple microscopic explanation of supermodulation of the coherent pairing gap in Bi2_{2}2​Sr2_{2}2​CaCu2_{2}2​O8+δ_{8+\delta }8+δ​ seen recently at atomic scale in the scanning tunneling microscopy experiments. Some features of band structures obtained using the local spin density approximation for FeTe will be also discussed.
An exact study of charge-spin separation, pairing fluctuations, and pseudogaps is carried out by combining the analytical eigenvalues of the four-site Hubbard clusters with the grand canonical and canonical ensemble approaches in a multidimensional parameter space of temperature (T)(T)(T), magnetic field (h)(h)(h), on-site interaction (U)(U)(U), and chemical potential $(\ensuremath{\mu})$. Our results, near the average number of electrons $⟨N⟩\ensuremath{\approx}3$, strongly suggest the existence of a critical parameter Uc(T){U}_{c}(T)Uc​(T) for the localization of electrons and a particle-hole binding (positive) gap ${\ensuremath{\Delta}}^{e\text{\ensuremath{-}}h}(T)>0$ at U>Uc(T)U>{U}_{c}(T)U>Uc​(T), with a zero temperature critical value, Uc(0)=4.584{U}_{c}(0)=4.584Uc​(0)=4.584. For U<Uc(T)U<{U}_{c}(T)U<Uc​(T), the particle-particle pair binding is found with a (positive) pairing gap ${\ensuremath{\Delta}}^{P}(T)>0$. The ground state degeneracy is lifted at U>Uc(T)U>{U}_{c}(T)U>Uc​(T) and the cluster becomes a Mott-Hubbard like insulator due to the presence of energy gaps at all (allowed) integer numbers $(1\ensuremath{\le}N\ensuremath{\le}8)$ of electrons. In contrast, for $U\ensuremath{\le}{U}_{c}(T)$, we find an electron pair binding instability at finite temperature near $⟨N⟩\ensuremath{\approx}3$, which manifests a possible pairing mechanism, a precursor to superconductivity in small clusters. Rigorous criteria for the existence of many-body Mott-Hubbard like particle-hole and particle-particle pairings, spin pairing, (spin) pseudogap, and (spin) antiferromagnetic critical crossover temperatures, at which the corresponding pseudogaps disappear, are also formulated. In particular, the resulting phase diagram consisting of charge and spin pseudogaps, antiferromagnetic correlations, hole pairing with competing hole-rich (⟨N⟩=2)(⟨N⟩=2)(⟨N⟩=2), hole-poor (⟨N⟩=4)(⟨N⟩=4)(⟨N⟩=4), and magnetic (⟨N⟩=3)(⟨N⟩=3)(⟨N⟩=3) regions in the ensemble of clusters near 1/8 filling closely resembles the phase diagrams and inhomogeneous phase separation recently found in the family of doped high-Tc{\mathrm{T}}_{\mathrm{c}}Tc​ cuprates.
The charge spin-separation, pseudogap formation and phase diagrams are studied in two and four site Hubbard clusters using analytical diagonalization and grand canonical ensemble method in a multidimensional parameter space of temperature, magnetic field, on-site Coulomb interaction (U≥0U\ge 0U≥0), and chemical potential. The numerically evaluated, exact expressions for charge and spin susceptibilities provide clear evidence for the existence of true gaps in the ground state and pseudogaps in a limited range of temperature. In particular, Mott-Hubbard type charge crossover, spin pseudogap and magnetic correlations with antiferromagnetic (spin) pseudogap structure for two and four site clusters closely resemble the pseudogap phenomena and the normal-state phase diagram in high Tc_cc​ superconductors. ~ ~
Pairing instabilities found from exact studies of repulsive Hubbard clusters with different topologies provide important insights into several many-body problems in condensed-matter physics. Electron charge and spin pairing instabilities in a multiparameter phase space, defined by temperature, magnetic field, and chemical potential, lead to properties that are remarkably similar to correlated inhomogeneous bulk (perovskite) systems such as the high-temperature superconductors and colossal-magnetoresistance materials. In particular, for small to moderate values of the on-site Coulomb repulsion UUU, the role of square-planar geometry is borne out for weak vertex coupling in an octahedron. These conditions are favorable to forming a Bose condensate in the region of instability near one hole off half filling while strong vertex coupling has a detrimental effect on such condensation. In addition, it is shown that magnetic flux can get trapped in stable minima at half-integral units of the flux quantum in hole-rich regions. For higher values of UUU, Nagaoka-type ferromagnetism is examined.