Floquet engineering magnetism and superconductivity in the square-lattice Hubbard model

We study the interplay of magnetic order and superconductivity in the square-lattice Hubbard model under periodic driving with circularly polarized light. Formulating diagrammatic techniques based on the random-phase approximation in terms of Floquet Green's functions, allows us to analyze fluctuation-driven unconventional pairing for weak to moderate interactions. The interplay of repulsive interactions and photoassisted hopping of electrons gives rise to a rich magnetic phase diagram featuring an antiferromagnetic-to-ferromagnetic transition prior to a Floquet Lifshitz transition. Close to the antiferromagnetic transition, topological <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>d</a:mi> <a:mo>+</a:mo> <a:mi>i</a:mi> <a:mi>d</a:mi> </a:mrow> </a:math> -wave superconductivity prevails in the phase diagram for a wide range of drive parameters. At intermediate- to high-frequency driving near the Floquet Lifshitz transition, superconducting orders are tuned from spin-singlet <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>d</b:mi> </b:math> -wave to spin-triplet <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>p</c:mi> </c:math> -wave character, providing an effective protocol for Floquet engineering topological superconductivity.