Higher-order Topological Semimetals In Periodically Driven Systems

The discovery of quantum Hall effect revealed novel state of matter that can-not be described by Landau’s symmetry breaking theory.It introduced the concept of topology to condensed matter physics for the first time and enriched the frame-work of condensed matter physics.Afterwards,various topological phases have sprung up.The most famous one is topological insulators.Being called first-order topological insulator,it is featured by the presence of d-1-dimensional gapless boundary states in the d-dimensional bulk-insulator system.It can usually be char-acterized by a dipole moment.In recent years,with the generalization of the dipole moments to the quadrupole and octopole moments,another type of state of matter called higher-order topological insulators has appeared.What is completely differ-ent from the previous ones is that they have d-n-dimensional boundary states.For example,a second-order topological insulator has zero-dimensional corner states and one-dimensional hinge states in two-dimensional and three-dimensional sys-tems,respectively.People also found that material exhibited the feature of Weyl semimetals and Dirac semimetals by stacking two-dimensional topological insu-lators along a specific direction.These semimetals have topologically protected double or quadruple degenerate energy band touching points and surface Fermi arcs.As the surface Fermi arc expands to the lower-dimensional hinge Fermi arc,higher-order topological semimetals have also come into people’s vision.The emergence of these novel topological states has continuously enriched the research of topological physics.Whether it is the understanding of matter or the experiments related to spe-cific practical applications,obtaining rich topological phases and having flexible modulation methods are the consistent pursuit of researchers.But for static sys-tems,fixed parameters are difficult to control,material topological properties are severely restricted,and the robustness of the system topological properties is not strong enough.To solve these problems,we introduced Floquet engineering as a versatile tool in quantum-state control.It refers to the protocol of controlling the states of matter by use of periodic driving.It has been revealed that periodic driv-ing can make the system emerge rich topological features.It not only can realize topological phases with a widely tunable number of boundary states,but also can realize many exotic topological phases totally absent in the static system.How-ever,there is still not a complete description of higher-order topological semimetal systems,and it is not clear on what that innovations can periodic driving bring to higher-order topological semimetal systems.Addressing on these questions,we will investigate the Floquet engineering to higher-order topological semimetal.In this work,we first establish a complete description of topological phase transition in periodically driven three-dimensional crystalline system.The con-dition of topological phase transition is analytically derived for such periodically driven four-band model.Secondly,novel Floquet higher-order Dirac semimetal phases which shows the coexistence of higher-order nodal loops and higher-order Dirac points are created by periodically driving the lattice hopping parameters.Compared with the static case,the Dirac-type semimetal induced by the periodic driving not only has the same topological charge for the adjacent Dirac points such that they exhibit robustness,but also allows the number of hinge Fermi arcs con-necting a pair of Dirac points with same topological charges be widely tunable.Then,by adding perturbations,which break the time-reversal symmetry,Floquet higher-order Weyl semimetals with both first-order and higher-order Weyl points,surface Fermi arcs,and hinge Fermi arcs are realized.These coexistence endows the system rich k_z-dependent topological phases,which can be any combination of two-dimensional band insulators,Chern insulators,and second-order topological insulators.Via the quasienergy spectrum and topological invariants,the complete topological description of the periodically driven system are given.Our results en-rich the family of higher-order topological phases and provide a feasible scheme for experimentalists to design novel higher-order topological semimetals.