Pseudo-spin Skyrmions in the Phase Diagram of Cuprate Superconductors

Abstract : Topological states of matter are at the root of some of the most fascinating phenomena in condensed matter physics. Here we argue that skyrmions in the pseudo-spin space related to an emerging SU(2) symmetry enlighten many mysterious properties of the pseudogap phase in under-doped cuprates. We detail the role of the SU(2) symmetry in controlling the phase diagram of the cuprates, in particular how a cascade of phase transitions explains the arising of the pseudogap, superconducting and charge modulation phases seen at low temperature. We specify the structure of the charge modulations inside the vor-tex core below $T_c$ , as well as in a wide temperature region above $T_c$ , which is a signature of the skyrmion topological structure. We argue that the underlying SU(2) symmetry is the main structure controlling the emergent complexity of excitations at the pseudogap scale $T^*$. The theory yields a gapping of a large part of the anti-nodal region of the Brillouin zone, along with $q = 0$ phase transitions, of both nematic and loop currents characters.