The Fermion Dynamical Symmetry Model

The Superconducting Critical Temperature

Two principles govern the critical temperature for superconducting transitions: (1) intrinsic strength of the pair coupling and (2) the effect of the many-body environments on the efficiency of that coupling. Most discussions take into account only the former, but we argue that the properties of unconventional superconductors are governed more often by the latter, through dynamical symmetry relating to normal and superconducting states. Differentiating these effects is essential to charting a path to the highest-temperature superconductors.

The Ground State of Monolayer Graphene in a Strong Magnetic Field

Experiments indicate that the ground state of graphene in a strong magnetic field exhibits spontaneous breaking of SU(4) symmetry. However, the nature of the corresponding emergent state is unclear because existing theoretical methods approximate the broken-symmetry solutions, yielding nearly-degenerate candidate ground states having different emergent orders. Resolving this ambiguity in the nature of the strong-field ground state is highly desirable, given the importance of graphene for both fundamental physics and technical applications. We have discovered a new SO(8) symmetry that recovers standard graphene SU(4) quantum Hall physics, but predicts two new broken-SU(4) phases and new properties for potential ground states. Our solutions are analytical; thus we capture the essential physics of spontaneously-broken SU(4) states in a powerful yet solvable model useful both in correlating existing data and in suggesting new experiments.