Abstract
Anyons have recently received great attention due to their promising application in topological quantum computation. The best validated system that enjoys the anyonic excitations are the Laughlin states. The quasi-particles in Laughlin states are neither fermions nor bosons but possess the discrete statistical angle θ = π/m, with m being an integer. Here we report a possible realization of the universal Abelian anyons, whose statistical angle can be tuned continuously by external parameters and can take any arbitrary values interpolating θ = 0 and θ = π. The proposed setup is the surface state of a three dimensional topological insulator driven by an amplitude-modulated circularly-polarized light. It is found that the external field leads to a particular Floquet phase, which is a two-spatial-dimensional analogy of the Weyl semimetal phase in the Floquet first Brillouin zone. The chiral anomaly of this phase results in a U(1) Chern-Simons gauge theory with a tunable Floquet Chern number. Owing to this underlying gauge field theory, the irradiated surface of topological insulator constitutes a promising platform for the observation of the universal anyons.
Highlights
Anyons have recently received great attention due to their promising application in topological quantum computation
It is found that the external field leads to a particular Floquet phase, which is a two-spatial-dimensional analogy of the Weyl semimetal phase in the Floquet first Brillouin zone
In order to do so, we recall the effective gauge field theory describing the electromagnetic response of the Chern insulator[2], which is very similar to Eq (3)
Summary
Anyons have recently received great attention due to their promising application in topological quantum computation. The special feature of the Floquet phases is that the periodically driven system can absorb and emit photons, forming Floquet bands denoted by different photon numbers n This effectively enlarges the “spacetime” by introducing a fictitious dimension to the undriven phase, and provides a possibility for the two dimensional (2D) driven system to exhibit the chiral anomaly. The PWSM possesses the chiral anomaly, which leads to a U(1) Chern-Simons gauge field theory with a tunable coefficient C This differs from the conventional Chern-Simons action of the integer and fractional quantum Hall state in the sense that it predicts two novel topological behaviors: the universal anyon excitations and the tunable quantum anomalous Hall (QAH) effect
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