Proposed Realization and Signatures of Floquet Topological Superconductors and Insulators

As understood recently, a topological state may be generated dynamically in an otherwise normal combination of materials by a periodic driving force. These states can only occur when the system is driven out of equilibrium. A Floquet topological insulator can be realized, for example, in a two-dimensional system of Dirac fermions, such as graphene, irradiated by a circularly polarized laser [1]. It is characterized by steady state edge modes and \emph{two} separate integer-valued topological invariants. A Floquet topological superconductor, on the other hand, is characterized by two types of Floquet Majorana fermions---steady states of equal superposition of electrons and holes---with a period that is the same or twice that of the drive [2]. I introduce these concepts and present our recent theoretical work on the realization and detection of these Floquet topological states. First, I discuss how Floquet Majorana fermions can be realized in a highly tunable setup consisting of two coupled quantum dots and detected by a third probe dot [3]. More generally, Floquet Majorana fermions can be detected by measuring a quantized conductance sum rule over discrete values of lead bias differing by multiples of drive frequency [4]. This quantized sum rule is robust against weak disorder. Finally, I present an effective theory of Floquet topological insulators and use it to study their transport signature [5]. Remarkably, we find that disorder can enhance transport at certain Floquet topological transitions by several orders of magnitude. \\[4pt] [1] T. Oka, H. Aoki, Phys. Rev. B 79, 081406 (R) (2009).\\[0pt] [2] L. Jiang et al., Phys. Rev. Lett. 106, 220402 (2011).\\[0pt] [3] Y. Li, A. Kundu, F. Zhong, and B. Seradjeh, Phys. Phys. Rev. B 90, 121401(R) (2014).\\[0pt] [4] A. Kundu and B. Seradjeh, Phys. Rev. Lett. 111, 136402 (2013).\\[0pt] [5] A. Kundu, H. A. Fertig, and B. Seradjeh, Phys. Rev. Lett. (2014) in press; arXiv:1406.1490.