Graphene irradiated by a circularly polarized laser has been predicted to be a Floquet topological insulator showing a laser-induced quantum Hall effect. A circularly polarized laser also drives the system out of equilibrium resulting in non-thermal electron distribution functions that strongly affect transport properties. Results are presented for the Hall conductance for two different cases. One is for a closed system such as a cold-atomic gas where transverse drift due to non-zero Berry curvature can be measured in time of flight measurements. For this case the effect of a circularly polarized laser that has been switched on suddenly is studied. The second is for an open system coupled to an external reservoir of phonons. While for the former, the Hall conductance is far from the quantized limit, for the latter, coupling to a sufficiently low temperature reservoir of phonons is found to produce effective cooling, and thus an approach to the quantum limit, provided the frequency of the laser is large as compared to the band-width. For laser frequencies comparable to the band-width, strong deviations from the quantum limit of conductance is found even for a very low temperature reservoir, with the precise value of the Hall conductance determined by a competition between reservoir induced cooling and the excitation of photo-carriers by the laser. For the closed system, the electron distribution function is determined by the overlap between the initial wavefunction and the Floquet states which can result in a Hall conductance which is opposite in sign to that of the open system.

Motivated by recent pump-probe spectroscopies, we study the effect of phonon dissipation and potential cooling on the nonequilibrium distribution function in a Floquet topological state. To this end, we apply a Floquet kinetic equation approach to study two dimensional Dirac fermions irradiated by a circularly polarized laser, a system which is predicted to be in a laser induced quantum Hall state. We find that the initial electron distribution shows an anisotropy with momentum dependent spin textures whose properties are controlled by the switching-on protocol of the laser. The phonons then smoothen this out leading to a non-trivial isotropic nonequilibrium distribution which has no memory of the initial state and initial switch-on protocol, and yet is distinct from a thermal state. An analytical expression for the distribution at the Dirac point is obtained that is relevant for observing quantized transport.

Results are presented for the optical Hall conductivity of a Floquet topological insulator (FTI) for an ideal closed quantum system, as well as an open system in a nonequilibrium steady-state with a reservoir. The steady-state, even for the open system, is strongly dependent on the topological phase of the FTI, with certain phases showing a remarkable near-cancellation from pockets of Berrycurvature of opposite signs, leading to a suppressed low-frequency Hall conductivity, that also shows an anomalous temperature dependence, by increasing as the temperature of the reservoir is increased. Such a behavior is in complete contrast to heating, and arises because of a strong modification of the effective system-reservoir coupling by the laser. The Berry curvature of the Floquet modes is time-dependent, and its frequency components are found to control the main features of the high-frequency Hall conductivity.

Different para-substituted meso-tetraphenylporphyrins (H2T(4-X)PP, X = H, Cl, CH3, CH(CH3)2, OCH3) react with various molar ratios of tetracyanoethylene (TCNE) in dichloromethane or benzene and produce only the 1 : 2 molecular complex, (TCNE)2H2T(4-X)PP. The remarkable agreement between the corresponding 1H, 13C solution (CDCl3) NMR resonances of the porphyrin moiety in these complexes with those of tetraphenylporphyrin dication, H4TPP2+, and also the strong resemblance between their UV-vis spectra and the spectra of the related diprotonated porphyrins indicates similar out-of-plane distorted porphyrin core structure in all of them. Based on these close spectral correspondences among the various molecular complexes and the related diprotonated porphyrins, and also consideration of the known structure of H4TPP2+Cl2- species, it is proposed that the two TCNEs in (TCNE)2H2T(4-X)PP complexes are bonded from above and below the mean porphyrin plane to the lone electron pairs of the pyrrolenine nitrogens of the porphyrins.Spectral data (13C, IR) of the bonded TCNEs in the molecular complexes seem to be most consistent with the interaction of an acceptor π* orbital centered at a CN group of the TCNEs with the porphyrin core nitrogen donors.

Results are presented for the occupation probabilities and current densities of bulk and edge states of half-filled graphene in a cylindrical geometry, and irradiated by a circularly polarized laser. It is assumed that the system is closed, and that the laser has been switched on as a quench. Laser parameters corresponding to some representative topological phases are studied: one where the Chern number of the Floquet bands equals the number of chiral edge modes, a second where anomalous edge states appear in the Floquet Brillouin zone boundaries, and a third where the Chern number is zero, yet topological edge states appear at the center and boundaries of the Floquet Brillouin zone. Qualitative differences are found for the high frequency off-resonant and low frequency on-resonant laser with edge states arising due to resonant processes occupied with a high effective temperature, whereas edge states arising due to off-resonant processes occupied with a low effective temperature. For an ideal half-filled system where only one of the bands in the Floquet Brillouin zone is occupied and the other empty, particle-hole and inversion symmetry of the Floquet Hamiltonian implies zero current density. However the laser switch-on protocol breaks the inversion symmetry, resulting in a net cylindrical sheet of current density at steady-state. Due to the underlying chirality of the system, this current density profile is associated with a net charge imbalance between the top and bottom of the cylinders.

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