Quadratic band touching points and flat bands in two-dimensional topological Floquet systems

Abstract

In this work we theoretically study, using Floquet-Bloch theory, the influence of circularly and linearly polarized light on two-dimensional band structures with Dirac and quadratic band touching points, and flat bands, taking the nearest neighbor hopping model on the kagome lattice as an example. We find circularly polarized light can invert the ordering of this three band model, while leaving the flat-band dispersionless. We find a small gap is also opened at the quadratic band touching point by 2-photon and higher order processes. By contrast, linearly polarized light splits the quadratic band touching point (into two Dirac points) by an amount that depends only on the amplitude and polarization direction of the light, independent of the frequency, and generally renders dispersion to the flat band. The splitting is perpendicular to the direction of the polarization of the light. We derive an effective low-energy theory that captures these key results. Finally, we compute the frequency dependence of the optical conductivity for this 3-band model and analyze the various interband contributions of the Floquet modes. Our results suggest strategies for optically controlling band structure and interaction strength in real systems.

9 pages, 5 figures

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• Floquet-engineering topological transitions in a twisted transition metal dichalcogenide homobilayer
• Isolated flat bands in an interlocking-circles lattice
• Floquet theory of photoinduced topological phase transitions in the organic salt $\alpha$-(BEDT-TTF)${}_2$I${}_3$ irradiated with elliptically polarized light
• Persistence of the flat band in a kagome magnet with dipolar interactions
• Predicted Photo-Induced Topological Phases in Organic Salt $\alpha$-(BEDT-TTF)${}_2$I${}_3$
• Orbital-selective thermalization plateau in the mass imbalanced Hubbard model
• Magnetic Order in Laser-Irradiated Kagome Antiferromagnets