Topological States Of Matter Induced By Periodic Driving

It is one of the main contents of condensed matter physics that how to classify and explore novel topological states of matter.A topological insulator is a material with nontrivial topological order that behaves as an insulator in its interior but whose surface contains conducting states,meaning that electrons can only move along the surface of the material.As a new topological state of matter,topological insulator has been aroused a wide attention because of its similarity to the quantum Hall states of matter.It was found that,to gain a complete correspondence between fractional quantum Hall effect and fractional topological insulator in lattice system,one must have the flat energyband with topologically nontrivial surface states.Therefore,how to generate the topologically nontrivial flat band attracts much attention in recent years.The conventional methods focus on to fabricate the specific long-range interactions and multi-layer structure in material to achieve the flat band.Those methods challenge greatly the state-of-art of experiments.We intend to generate topologically nontrivial flat band in the system without such long-range interactions and multi-layer structure by using of periodic driving.First,we introduce the works to generate the large-Chern-number topological insulator states and fractional Chern insulator states by periodic driving.The topological insulator,whose transpose current is proportional to the Chern number,with a widely controllable large Chern number has potential applications in electronic devices.The previous works found that such large-Chern-number topological phases exist in the long-rang correlated static systems.Using periodic driving,we can generate the large-Chern-number topological insulator states in the system with only short-range interactions involved.It is the action to generate vast touching points in energy spectrum by the periodic driving which results in such achievement.We also can generate a ferromagnetic Floquet fractional Chern insulator state at 7/12 total filling in a graphene by applying a circularly polarized light.Via above two instances,we want to reveal the distinguished role played by periodic driving in topological phase transition: Periodic driving can not only realize the topological phases not accessible for the static system in the same setting,but also generate novel topological phases with no analogy in its static system.Second,we adopt the periodic driving to realize the topologically nontrivial band with higher flatness ratio ?/W,which is the essential condition for quantum anomalous fractional Hall effect and fractional Chern insulator.We find that the time-reversal symmetry is broken and effective long-range interaction are induced by the periodic driving.It makes the driven system produce a series of touching points in the energy spectrum.The topological phase transition characterized by the closing and reopening in the Floquet quasienergy spectrum is occurred by changing the parameters of the periodic driving.At the same time,flatness ratio of energy band can be dramatically enhanced by the periodic driving.Taking N3 Haldane model and BHZ model for two general instances,we realize the topologically nontrivial states of matter with higher flatness ratio ?/W=25.25 and ?/W=15.91,respectively.Comparing with the corresponding static system,the advantage of Floquet system is the enhancement to the flatness ratio and the change to the topological property of energyband.Our result of the flat band induced by periodic driving supplies a novel method to simulate fractional Hall effect in lattice system.The novel topological states of matter induced by periodic driving revealed in our work enrich the physics of topological phase transition in conventional static systems.It implies that the periodic driving opens new avenue to synthesize artificially extremal topological states of matter.Its merit is to introduce a new control dimension,i.e.time,into the system,which supplies a new key to explore the physics of the relevant systems with a high controllability.