Versatile Floquet Weyl semimetal phases in an anisotropic Dirac system

Topological electronic states induced by periodic external fields such as laser light have attracted much attention [1]. Recently, it has been theoretically predicted that the time-reversal symmetry is broken by irradiating the three-dimensional Dirac semimetal with a circularly polarized laser, and the Floquet-Weyl semimetal state (FWSM) appears due to the chiral gauge field [2]. While it is well known that conventional Weyl semimetals can show anomalous Hall effect originating from the Berry curvature between the two Weyl points with opposite chirality, the topological natures and transport properties in the FWSM have not been detailed in a periodically driven system.

In this work, we study an effective model for paramagnetic Dirac semimetals hosting two spin-degenerated Dirac cones and investigate the consequence of the periodically driven system by the Floquet theory. We clarify that when the spin-orbit coupling is finite, the FWSM can be realized by splitting the Dirac points into two Weyl point pairs by circularly polarized irradiation. We also find several topological phase transitions with realignments and pair annihilations of the Weyl points by varying strength, frequency, and direction of the incident laser, which accompany the drastic changes of the anomalous Hall conductivity.

[1] T. Oka and H. Aoki, Phys. Rev. B 79, 081406(R) (2009). [2] S. Ebihara, K. Fukushima, and T. Oka, Phys. Rev. B 93, 155107 (2016).