Floquet topological superconductivity induced by chiral many-body interaction

<jats:title>Abstract</jats:title><jats:p>Non-equilibrium engineering is becoming a seminal way for realising novel quantum phases that are unimaginable in equilibrium. In particular, Floquet theory applied to quantum mechanics revealed that we can even control the band topology in semimetallic/insulating systems, while the straightforward application to topological superconductivity fails for typical superconductors because the supercondicting gap function does not couple to the electromagnetic field in a direct manner. Here we show that we can overcome this difficulty by taking account of correlation effects. Namely, we study how a <jats:italic>d</jats:italic>-wave superconductivity is changed when illuminated by circularly-polarised light (CPL) in the repulsive Hubbard model in the strong-coupling regime. We adopt the Floquet formalism for the Gutzwiller-projected effective Hamiltonian with the time-periodic Schrieffer-Wolff transformation. We find that CPL induces a topological superconductivity with a <jats:italic>d</jats:italic> + <jats:italic>i</jats:italic><jats:italic>d</jats:italic> pairing, which arises from the chiral spin coupling and the three-site term generated by the CPL. The latter term remains significant even for low frequencies and low intensities of the CPL. This is clearly reflected in the obtained phase diagram against the laser intensity and temperature for various frequencies red-detuned from the Hubbard <jats:italic>U</jats:italic>, with the transient dynamics also examined. The phenomenon revealed here can open a novel, dynamical way to induce a topological superconductivity.</jats:p>