Floquet Spectrum and Transport Through an Irradiated Graphene Ribbon (1106.0302v1)

Abstract: Graphene subject to a spatially uniform, circularly-polarized electric field supports a Floquet spectrum with properties akin to those of a topological insulator, including non-vanishing Chern numbers associated with bulk bands and current-carrying edge states. Transport properties of this system however are complicated by the non-equilibrium occupations of the Floquet states. We address this by considering transport in a two-terminal ribbon geometry for which the leads have well-defined chemical potentials, with an irradiated central scattering region. We demonstrate the presence of edge states, which for infinite mass boundary conditions may be associated with only one of the two valleys. At low frequencies, the bulk DC conductivity near zero energy is shown to be dominated by a series of states with very narrow anticrossings, leading to super-diffusive behavior. For very long ribbons, a ballistic regime emerges in which edge state transport dominates.

• The paper demonstrates that applying circularly polarized light to graphene ribbons generates a non-trivial Floquet spectrum with topological edge states.
• It uses a combination of analytical and numerical methods, including perturbative Schrödinger analysis and tight-binding simulations, to study transport characteristics.
• The findings reveal a shift from super-diffusive to ballistic transport as edge state conduction becomes dominant at low energies near anticrossings.

Overview of "Floquet Spectrum and Transport Through an Irradiated Graphene Ribbon"

This paper investigates the transport properties of graphene ribbons subjected to circularly polarized light, a scenario that results in a Floquet spectrum with characteristics reminiscent of topological insulators. The unique interplay of graphene's electronic properties and periodically driven systems underpins the main findings and implications of this paper.

The central focus is on the Floquet spectrum that emerges when a spatially uniform, circularly polarized electric field is applied to a graphene ribbon. This spectrum exhibits non-trivial topological properties, including non-zero Chern numbers and edge states, similar to those found in topological insulators. However, the non-equilibrium occupancy of these Floquet states presents challenges in understanding the transport properties, which this paper addresses. The authors analyze transport within a two-terminal setup, consisting of well-defined chemical potential leads connected through an irradiated graphene ribbon functioning as a scattering region.

Key Results and Analysis

• Edge States: The paper confirms the presence of edge states in the graphene ribbon, which, under infinite mass boundary conditions, are associated with a single valley of the two present in graphene's band structure. This results in a scenario where only one of the valleys supports edge conduction.
• Conductivity Behavior: At low frequencies, near zero energy, the DC conductivity is dictated by states near narrow anticrossings, resulting in super-diffusive transport behavior. This regime transitions into ballistic transport for sufficiently long ribbons, where edge states dominate conduction.
• Floquet Spectrum: The paper elucidates the structure of the Floquet spectrum, identifying how it reflects the folded band structure due to the periodic time dependence. The spectrum features small gaps at avoided crossings due to coupling between repeated bands, and these gaps influence the transmission and transport properties.

Methodology

The authors employ a mix of analytical and numerical methods. A time-dependent Schrödinger equation describes the system, facilitating the computation of the Floquet spectrum via perturbative methods and time discretization. Conductance through the irradiated region is calculated using a tight-binding model informed by the derived Floquet states, with consideration of boundary conditions and lead coupling.

Implications

The findings have noteworthy implications for understanding and exploiting the quantum coherent states in graphene under non-equilibrium conditions. The induced topological characteristics propose new avenues for realizing topological insulators through external driving, circumventing the need for intrinsic material properties like strong spin-orbit coupling, which is weak in graphene. This work suggests potential applications in developing novel electronic devices harnessing topological protection and robustness against disorder in two-dimensional materials.

Future Directions

The paper prompts several future research avenues:

• Optimal Control of Floquet States: Exploring the tunability of Floquet spectra using different field amplitudes and frequencies could optimize control over transport properties, possibly leveraging these effects for nanoscale electronic devices.
• Disorder and Edge State Dynamics: Further work is needed to robustly characterize the resistance of edge state transport to disorder, crucial for realistic implementation in devices.
• Exploring Other Two-Dimensional Materials: The methodology could be extended to paper other two-dimensional (2D) materials with intrinsic topological properties, providing a broader foundation for 2D topological electronics.

Thus, this paper makes significant contributions to the understanding of irradiated graphene systems, illuminating both theoretical frameworks and potential practical applications.