SU(4) Model of High-Temperature Superconductivity: Manifestation of Dynamical Symmetry in Cuprates

Abstract

The mechanism that leads to high-temperature superconductivity in cuprates remains an open question despite intense study for nearly two decades. Here, we introduce an SU(4) model for cuprate systems having many similarities to dynamical symmetries known to play an important role in 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) 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. It is demonstrated that with a slightly broken SO(5) but under constraint of the parent SU(4) symmetry, the model is capable of describing the rich physics that is crucial in explaining why cuprate systems that are antiferromagnetic Mott insulators at half filling become superconductors through hole doping.

Coexistence of spin density wave, d-wave singlet and staggered π-triplet superconductivity

“…Similar π operators were introduced in the past, i.e. by Yang Sun et al in an SU (4) model for HTC superconductivity [20], but, to our knowledge were first discussed by Psaltakis et al [10].…”

SO(4) FLEX+DMFT formalism with SU(2)$\otimes$SU(2)-symmetric impurity solver for superconductivity in the repulsive Hubbard model

“…Along with the advances of the above-mentioned numer-ical toolboxes, the phenomenologies approaches in terms of competing and/or synergistic order parameters based on generalizations of the Ginzburg-Landau (GL) theory have been developed for providing insights into various phases. Such approaches introduce the order parameters of the system based on symmetry considerations [32][33][34][35][36][37] . In the GL theory, the respected symmetries of the relevant order parameters indeed govern the diversity of the associated phase diagram.…”

“…Specifically, inspired by the phenomenological SU(4) theory of superconductivity 33,34,38 , here we extend the slaveboson decomposition to capture (i) the bipartite nature of the AF and d-wave SC phase, along with…”