Hierarchy of Floquet gaps and edge states for driven honeycomb lattices

Electromagnetic driving in a honeycomb lattice can induce gaps and topological edge states with a structure of increasing complexity as the frequency of the driving lowers. While the high frequency case is the most simple to analyze we focus on the multiple photon processes allowed in the low frequency regime to unveil the hierarchy of Floquet edge-states. In the case of low intensities an analytical approach allows us to derive effective Hamiltonians and address the topological character of each gap in a constructive manner. At high intensities we obtain the net number of edge states, given by the winding number, with a numerical calculation of the Chern numbers of each Floquet band. Using these methods, we find a hierarchy that resembles that of a Russian nesting doll. This hierarchy classifies the gaps and the associated edge states in different orders according to the electron-photon coupling strength. For large driving intensities, we rely on the numerical calculation of the winding number, illustrated in a map of topological phase transitions. The hierarchy unveiled with the low energy effective Hamiltonians, alongside with the map of topological phase transitions discloses the complexity of the Floquet band structure in the low frequency regime. The proposed method for obtaining the effective Hamiltonian can be easily adapted to other Dirac Hamiltonians of two dimensional materials and even the surface of a 3D topological insulator.Comment: Phys. Rev. A 91, 04362

Taurus

The purpose of this project was to gather information about the stars and objects in the constellation Taurus. This is a project for the Natural Sciences Poster Session at Parkland College

Tuning laser-induced bandgaps in graphene

Could a laser field lead to the much sought-after tunable bandgaps in graphene? By using Floquet theory combined with Green's functions techniques, we predict that a laser field in the mid-infrared range can produce observable bandgaps in the electronic structure of graphene. Furthermore, we show how they can be tuned by using the laser polarization. Our results could serve as a guidance to design opto-electronic nano-devices.Comment: 4 pages, 3 figures, to appear in Applied Physics Letter

Non-perturbative laser effects on the electrical properties of graphene nanoribbons

The use of Floquet theory combined with a realistic description of the electronic structure of illuminated graphene and graphene nanoribbons is developed to assess the emergence of non-adiabatic and non-perturbative effects on the electronic properties. Here, we introduce an efficient computational scheme and illustrate its use by applying it to graphene nanoribbons in the presence of both linear and circular polarization. The interplay between confinement due to the finite sample size and laser-induced transitions is shown to lead to sharp features on the average conductance and density of states. Particular emphasis is given to the emergence of the bulk limit response.Comment: 14 pages, 8 figures, to appear in J. Phys.: Condens. Matter, special issue on "Ultrafast and nonlinear optics in carbon nanomaterials

Laser-induced effects on the electronic features of graphene nanoribbons

We study the interplay between lateral confinement and photon-induced processes on the electronic properties of illuminated graphene nanoribbons. We find that by tuning the device setup (edges geometries, ribbon width and polarization direction), a laser with frequency {\Omega} may either not affect the electronic structure, or induce bandgaps or depletions at \hbar {\Omega}/2, and/or at other energies not commensurate with half the photon energy. Similar features are also observed in the dc conductance, suggesting the use of the polarization direction to switch on and off the graphene device. Our results could guide the design of novel types of optoelectronic nano-devices.Comment: 4 pages, 3 figure