Abstract
We consider asymmetric and symmetric dimerized two-leg ladders, comprising of four different lattice points per unit cell, illuminated by circularly polarized light. In the asymmetric dimerized ladder case, rungs are not perpendicular to the ladder’s legs whereas the rungs are perpendicular to the legs for the symmetric one. Using the Floquet theory, we obtain an effective Hamiltonian to study topological properties of the systems. Depending on the dimerization strength and driving amplitude, it is shown that topologically protected edge states manifest themselves not only as a zero-energy band within the gap between conduction and valence band but also as finite-energy curved bands inside the gap of subbands. The latter one can penetrate into bulk states and hybridize with the bulk states revealing hybridized Floquet topological metal phase with delocalized edge states in the asymmetric ladder case. However, in the symmetric ladder, the finite-energy edge states while remaining localized can coexist with the extended bulk states manifesting Floquet topological metal phase.
Highlights
By varying θ, the values of inverse participation ratio (IPR) of edge states change significantly in transition from topological insulator phase, where the edge states are within gapped states, to the hybridized Floquet topological metal phase originating from breaking of the exchange symmetry Υ in the asymmetric ladder case
We found that there exist zero- and finite-energy edge states in the asymmetric ladder case, whereas the symmetric ladder hosts only the finite-energy ones
For asymmetric ladder, when the finite-energy edge states are within the bulk ones, due to the absence of exchange symmetry, these two types of states having the same energy and quantum number would hybridize together providing the hybridized Floquet topological metal states
Summary
J j atlwehnghedseu,tr2preep=Xsepu(r†et//1)′lcljot=iwisvetethrly+ec.heTδalhetinceftoharrotoantpshpyaeimnnjntgmhiheeunitnlreaiitrtcigcolieaneldsl(.dacte1l(ror′e)nawatgnhiodtehnrtee2)(′a)orsauptrne1erg=iasntototrrf2ato=(hfinesttulea+brdl)adδuttetnriacintaerdcXeetlt1′l(3wh=aohnpitdc2p′ hti=4n c.gaWtsn−aebloceδnhtegofiotothhrseeesrytu1Amp=pmoerertB2t′arn=itcydpltaleod−)wdoδeenrrt where δt = δ0 cos θ is the dimerization strength with θ and δ0 being a cyclical parameter varying from 0 to 2π continuously and dimerization amplitude, respectively. For both asymmetric and symmetric cases, we choose t3 = t4 = t + δt. Hamiltonian (1) can be periodic in time H(t) = H(t + T) through Peierls substitution tij
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