Exotic Topological States Of Matter Induced By Periodic Driving

Topological phases which are represented by topological insulators,topological superconductors and topological semimetals have aroused extensive research interest.From the perspective of fundamental physics,it breaks through the symmetry breaking mechanism in traditional phase transitions and can also enrich the paradigm of condensed matter physics.From the perspective of technology application,topological states of matter and their simulation in optical systems and acoustic systems are also breeding many revolutionary new devices and provide a rich material treasure house for today’s booming quantum technology.Novel topological quantum matters including non-Hermitian topological states,higher order topological superconductor and semimetal continue to enrich the family of topological states of matter.At the same time,the research of novel devices needs efficient control ways.Explorations of physical systems supporting exotic topological features and of efficient control ways to these features are not only a mainstream of condensed-matter physics,but also a demand of quantum technologies.On the other hand,development of ultrafast optics has aroused interest in periodically driven quantum phases which are represented by exotic states of matter induced by light.It successfully extends the energy band engineering in quantum materials to the Floquet engineering of non-equilibrium systems and offers us a new way to explore exotic topological phases by adding the time-periodicity as an extra control dimension of the energy band in the system.Based on these developments,we have done the following works.In the first part,we have investigated the topological insulators in periodically driven non-Hermitian systems.Topological insulators are special states of matter that have a bulk band gap like an ordinary insulator but have protected conducting states on their edge or surface.According to the principle of bulk-boundary correspondence of this kind of state: the existence of boundary states is dictated by the topology of bulk states.Non-Hermitian topological insulators have diverse applications in invisible media,laser,and sensor,so how to regulate these topological states of matter is very meaningful.Floquet engineering provides a new means for generating and reulating novel non-Hermitian topological insulators.Previously,it was found that non-Hermitian topological insulators violate bulk-boundary correspondence due to the skin effect,so it is not possible to define non-Hermitian topological insulators by using the well developed theory in Hermitian system,how to define non-Hermitian topological insulators induced by periodic driving is even more an unsolved problem.We propose a scheme to retrieve the bulkboundary correspondence and establish a complete description of the topological phases of the periodically driven non-Hermitian system.The key point is to restore the chiral symmetry of the periodically driven systems by the proposed appropriate similarity transformations.Taking the non-Hermitian Su-Schrieffer-Heeger model as an example,many intriguing topological insulators absent in static systems have been discovered,such as exotic non-Hermitian topological phases of widely tunable numbers of edge states and Floquet topological Anderson insulator.Then the study of one-dimensional(1D)periodically driven non-Hermitian systems can also be extended to the case of second-order topological insulators both for 2D and3 D systems.It is found that rich exotic non-Hermitian second order topological insulators with a widely tunable number of 0D corner states and 1D hinge states and a coexistence of the first-and second-order topological insulators are induced by the periodic driving.It lays the foundation for developing topological devices using the advantages of both first-and second-order non-Hermitian topological insulators.In the second part,we have investigated topological semimetals in periodically driven non-Hermitian systems.As frontier research area in quantum materials,topological semimetals are characterized by topologically protected band touching point or line at the Fermi level,and their chiral anomaly has important applications in technological innovation.It was revealed that the non-Hermiticity can transform a Weyl semimetal into a Weyl-exceptional-ring semimetal.However,this belief is from the systems without skin effect.We investigate the nonHermitian Weyl semimental and its Floquet engineering in a system with skin effect.We retrieve the bulk-boundary correspondence and establish a complete description of topological semimetals of the periodically driven non-Hermitian system.It is interesting to find that the skin effect invalidates the general belief that the non-Hermiticity could convert the Weyl points into exceptional rings.We discover that exotic non-Hermitian topological matters,e.g.,a composite phase of Weyl semimetal and topological insulator with the coexisting Fermi arc and chiral boundary states,a widely tunable Hall conductivity with multiple quantized plateaus,and a Weyl semimetal with anomalous Fermi arcs formed by the crossing of gapped bound state,are induced by the periodic driving and the non-Hermiticity.These results demonstrate the important role of periodic driving in exploring and regulating novel non-Hermitian topological semimetals.In the third part,we have investigated the periodic-driving induced topological phase in a two-band odd-parity superconductor system.Topological superconductor successfully simulates the mysterious Majorana Fermion in a condensedmatter system and also holds a promising application in realizing quantum computation.The recently discovered second-order topological superconductors open up a new avenue toward topological quantum computation.The hybridization of different orders of topological superconductors is attractive because it facilitates the simultaneous utilization of their respective advantages.However,previous studies found that they cannot coexist in one system due to their substantial different features in the energy spectrum at the boundaries.We here propose a Floquetengineering scheme to generate a 2D hybrid-order topological superconductors in an odd-parity superconductor system.Exotic hybrid-order phases exhibiting the coexisting gapless chiral edge states and gapped Majorana corner states not only in two different quasienergy gaps but also in one single quasienergy gap are created by the periodic driving.The generalization of this scheme to the 3D odd-parity superconductor system with space-time inversion symmetry has led us to discover a second-order superconducting Dirac semimetal featured with the coexisting of surface and hinge Majorana Fermi arcs.These freely controllable novel states of matter cannot be realized in a static system.In summary,the discovery of a large number of novel topological states greatly enriches the family of topological states.Correspondingly,we have established the description of periodically driven topological states of matter.Finally,our result demonstrates that Floquet engineering supplies us a new controllable way to explore novel topological phases,which is useful in exploring their application.