Fermion dynamical symmetry and strongly-correlated electrons: A comprehensive model of high-temperature superconductivity

Abstract

We review application of the SU(4) model of strongly-correlated electrons to cuprate and iron-based superconductors. A minimal self-consistent generalization of BCS theory to incorporate antiferromagnetism on an equal footing with pairing and strong Coulomb repulsion is found to account systematically for the major features of high-temperature superconductivity, with microscopic details of the parent compounds entering only parametrically. This provides a systematic procedure to separate essential from peripheral, suggesting that many features exhibited by the high-T c data set are of interest in their own right but are not central to the superconducting mechanism. More generally, we propose that the surprisingly broad range of conventional and unconventional superconducting and superfluid behavior observed across many fields of physics results from the systematic appearance of similar algebraic structures for the emergent effective Hamiltonians, even though the microscopic Hamiltonians of the corresponding parent states may differ radically from each other.

The Superconducting Critical Temperature

“…The same SU(4) symmetry requiring the undoped ground state to be an AF Mott insulator implies that this state is fundamentally unstable against condensing Cooper pairs when doped [31,33]. This results in a quantum phase transition (QPT) to be discussed more extensively below, and implies a rapid transition to a superconducting state upon doping, as observed for data in Figure 4.…”

“…Hence, charge transport is suppressed at half band-filling and the undoped ground state is a Mott insulator. Moreover, this state has SU(4) ⊃ SO(4) dynamical symmetry and the matrix elements of an AF Néel state [23,24,33]. Thus, the undoped SU(4) ground state is an AF Mott insulator, just as observed for cuprates.…”

“…The best fit is for the smooth dependence of G 0 and χ on the doping P shown in the inset of Figure 4, but the basic features survive if these parameters are held constant with doping (see Ref. [33]). Thus, the cuprate phase diagram is a consequence of SU(4) symmetry correlating emergent d-wave singlet pairing and antiferromagnetism; it depends only parametrically on microscopic details such as pairing formfactors.…”

“…This reduces SO(8) to a 15-generator subgroup SU(4), with generators representing AF, spin-singlet and spin-triplet bondwise pairs, spin, and charge operators; explicit forms for the operators and their commutation relations are given in Refs. [23,33]. Three dynamical symmetry chains have exact solutions and correspond (through their matrix elements) to physical states thought to be relevant for cuprate doped and undoped states: We will now document concisely in Section 3 that this microscopic approach gives a remarkably good description of a broad range of cuprate phenomena with minimal assumptions, and then use the validated SU(4) theory to discuss SC transition temperatures in Section 4.…”

“…Based on the dynamical symmetry considerations described above, we have constructed an SU(4) model of emergent high-temperature superconductivity, which is doc-umented in a series of publications [23][24][25][26][27][28][29][30][31][32] and a comprehensive review [33]. Here we collect in one place a unified set of physical implications for this SU(4) dynamical symmetry, unobscured by technical detail.…”