SU(4) model of high-temperature superconductivity and antiferromagnetism

Abstract

We present an SU (4) model of high-temperature superconductivity having many similarities to dynamical symmetries known to play an important role in microscopic nuclear structure physics and in elementary particle physics. Analytical solutions in three dynamical symmetry limits of this model are found: an SO(4) limit associated with antiferromagnetic order; an SU (2) × SO(3) limit that may be interpreted as a d-wave pairing condensate; and an SO(5) limit that may be interpreted as a doorway state between the antiferromagnetic order and the superconducting order. The model suggests a phase diagram in qualitative agreement with that observed in the cuprate superconductors. The relationship between the present model and the SO(5) unification of superconductivity and antiferromagnetic order proposed by Zhang is discussed.There are compelling arguments that the mechanism leading to high-temperature superconductivity does not correspond to ordinary BCS s-wave pairing. Although experimental evidence implicates singlet (hole) pairs as the carriers of the supercurrent, the interaction leading to the formation of the singlet pairs appears not to be the traditional lattice phonon mechanism underlying the BCS theory, but rather seems to be a collective electronic interaction. Furthermore, the pairing gap is anisotropic, with nodes in the k x -k y plane strongly suggestive of dwave hybridization in the 2-particle wavefunctions, and the mechanism responsible for superconductivity in the cuprates is thought to be closely related to the unusual antiferromagnetic (AF) insulator properties of their normal states.Contrary to the case for BCS superconductors, the formation of Cooper pairs and the formation of a superconducting (SC) condensate of those pairs in high-T c compounds may be distinct, with pair formation corresponding to a higher temperature scale than the condensation of the pairs into the SC state. That is, there appear to be at least two distinct energy scales associated with the formation of the high-temperature SC state. This is reminiscent of grand unified theories in elementary particle physics, where qualitatively different physical phases result from a hierarchy of symmetry breakings occurring on different energy (temperature) scales. This finds its most natural explanation in a Lie group structure that is broken spontaneously (and perhaps explicitly) down to subgroups at different characteristic energy scales. I. DYNAMICS AND SYMMETRIESSuch observations argue strongly for a theory based on continuous symmetries of the dynamical system that is capable of describing more sophisticated pairing than found in the simple BCS picture (which is described by a single complex order parameter), and capable of unifying different collective modes and phases on a equivalent footing. Then such fundamentally different physics as antiferromagnetic order and superconductivity can emerge from the same effective Hamiltonian as concentration variables (e.g., doping parameters) are varied. A. Fermion Dynamical SymmetriesFor approxim...

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“…Comparing with Figs. 1(a)-1(d) suggests a strong analogy, with pairing playing a similar role in both cases, and nuclear quadrupole deformation being the analog of condensedmatter antiferromagnetic correlations (an analogy that is elaborated in [18]). …”

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“…The most powerful means of implementing this space truncation is to identify dynamical symmetries expressed through Lie algebras and associated Lie groups [16][17][18][19][20][21][22][23][24][25][26][27]. Such methods have been applied extensively in nuclear [16,24], elementary particle [25], molecular [26], and condensed matter physics [18].…”

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