@article{ISI:000432962700007,
 abstract = {We study the Floquet phase diagram of two-dimensional Dirac materials
such as graphene and the onedimensional (1D) spin-1/2 XY model in a
transverse field in the presence of periodic time-varying terms in their
Hamiltonians in the lowdrive frequency (omega) regimewhere standard
1/omega perturbative expansions fail. For graphene, such periodic
time-dependent terms are generated via the application of external
radiation of amplitude A(0) and time period T = 2 pi/omega, while for
the 1D XY model, they result from a two-rate drive protocol with a
time-dependent magnetic field and nearest-neighbor couplings between the
spins. Using the adiabatic-impulse method, whose predictions agree
almost exactly with the corresponding numerical results in the
low-frequency regime, we provide several semianalytic criteria for the
occurrence of changes in the topology of the phase bands (eigenstates of
the evolution operator U) of such systems. For irradiated graphene, we
point out the role of the symmetries of the instantaneous Hamiltonian
H(t) and the evolution operator U behind such topology changes. Our
analysis reveals that at low frequencies, topology changes of irradiated
graphene phase bands may also happen at t = T/3 and 2T/3 (apart from t =
T) showing the necessity of analyzing the phase bands of the system for
obtaining its phase diagrams. We chart out the phase diagrams at t =
T/3, 2T/3, and T, where such topology changes occur, as a function of
A(0) and T using exact numerics, and compare them with the prediction of
the adiabatic-impulse method. We show that several characteristics of
these phase diagrams can be analytically understood from results
obtained using the adiabatic-impulse method and point out the crucial
contribution of the high-symmetry points in the graphene Brillouin zone
to these diagrams. We study the modes that can appear at the edges of a
finite-width strip of graphene and show that the change in the number of
such modes agrees with the change in the Chern number of bulk graphene
as we go across a phase band crossing. Finally, we study the 1D XY model
with a two-rate driving protocol. After studying the symmetries of the
system, we use the adiabatic-impulse method and exact numerics to study
its phase band crossing which occurs at t = T/2 and k = pi/2. We also
study the end modes generated by such a drive and show that there can be
anomalous modes whose Floquet eigenvalues are not equal to +/- 1. We
suggest experiments to test our theory.},
 article-number = {205415},
 author = {Mukherjee, Bhaskar and Mohan, Priyanka and Sen, Diptiman and Sengupta,
K.},
 doi = {10.1103/PhysRevB.97.205415},
 eissn = {2469-9969},
 issn = {2469-9950},
 journal = {PHYSICAL REVIEW B},
 month = {MAY 11},
 number = {20},
 orcid-numbers = {Mohan, Priyanka/0000-0003-1358-5194},
 researcherid-numbers = {Mohan, Priyanka/AAF-1731-2019},
 times-cited = {8},
 title = {Low-frequency phase diagram of irradiated graphene and a periodically
driven spin-1/2 XY chain},
 unique-id = {ISI:000432962700007},
 volume = {97},
 year = {2018}
}