Skyrmion-like textures in superconductors with competing orders

Abstract

Vortex cores in a superconductor can develop structure and manifest competing orders. In strong magnetic fields, the inter-vortex distance can become short enough for vortex cores to overlap, giving rise to long ranged textures. We show that spin orbit coupling (SOC) can modify the interaction between vortex cores to give rise to undulating competing order fields. We illustrate this using the SO(3) theory of competing orders, wherein superconductivity and a scalar order form a threecomponent vector field. We consider a spherical surface with a radial magnetic flux that creates two vortices. We find stationary solutions where both vortex cores develop competing order in (a) the same sense, and (b) opposite senses. The latter represents a topologically stable vector configuration analogous to a single skyrmion. Its free energy is lowered when SOC is introduced, making it the ground state beyond a threshold SOC strength. We study this physics on the two dimensional plane using the attractive Hubbard model with Rashba SOC. Here, charge density wave (CDW) order competes with superconductivity. We find phases with long ranged, but spatially modulated, CDW order where the average CDW moment vanishes. In a wide range of parameters, CDW loses its rigidity as SOC lowers the energy cost for domain wall formation. We discuss consequences for systems such as the cuprates where charge order develops without a sharp diffraction peak. arXiv:1903.11053v1 [cond-mat.supr-con]

Fermion-fermion interaction driven instability and criticality of quadratic band crossing systems with the breaking of time-reversal symmetry

“…Consequently, we come to a conclusion that the leading instability is directly associated with the phase transition from QBCP semimetal to CDW state under the influence of fermion-fermion couplings in the 2D QBCP materials sited on the kagomé lattice without time-reversal symmetry. It is worth pointing out that this result is basically in agreement with recent works on analogous compounds [109][110][111][112] . This suggests that the CDW state is another winner driven by fermion-fermion interactions in the 2D QBCP materials besides quantum anomalous Hall and quantum spin Hall sates in its checkerboard-lattice counterpart with time-reversal symmetry 48,51 .…”

The attractive Hubbard model as an $SO(3)$ system of competing phases: supersolid order and its thermal melting

“…Based on this observation, it was conjectured that these two models were equivalent. This conjecture was supported by further studies 29,30 . In this article, we establish this equivalence by way of a rigorous mapping.…”