Computing Floquet quasienergies in finite and extended systems: Role of electromagnetic and quantum-geometric gauges

Abstract

We present an approach to compute the Floquet quasienergy spectrum of time-periodic systems. The method allows to characterize the light-matter interaction in finite and extended structures by carefully addressing the resolution of the position operator. In periodic systems we discuss the role of the quantum-geometric gauge freedom of Bloch states and employ a Wannier-based scheme to compute the required matrix elements. As a consequence, the method is accurate and applicable to a broad range of systems, from atoms and molecules to cold atomic gases and materials described by density functional theory, as well as model systems. We demonstrate the applicability of the approach by studying two cases: a particle trapped in a one-dimensional box and the semiconducting material BC${}_2$N. We employ the first example to provide a numerical proof of the invariance of the Floquet quasienergy spectrum with respect to the choice of electromagnetic gauge. The analysis of BC${}_2$N then serves to illustrate the physical effects described by the quasienergies, such as multiphoton resonances, and their expected range of occurrence in real materials in terms of external electric field and frequency of the drive pulse.

16 pages, 6 figures

References in corpus (10)

• Quantum ESPRESSO toward the exascale
• Topological characterization of periodically-driven quantum systems
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Nonthermal pathways to ultrafast control in quantum materials
• Spectral and Fermi surface properties from Wannier interpolation
• Coherent control of dressed matter waves
• Buildup and dephasing of Floquet-Bloch bands on subcycle time scales
• Correspondence between a shaken honeycomb lattice and the Haldane model
• Floquet formulation of the dynamical Berry-phase approach to non-linear optics in extended systems
• Topological Phase Diagram of Optimally Shaken Honeycomb Lattices: A Dual Perspective from Stroboscopic and Non-Stroboscopic Floquet Hamiltonians

Cited by in corpus (1)

• First-principle based Floquet engineering of solids in the velocity gauge