Floquet–Polaron-Driven Modulation of Optical Conductivity for Quantum Nanosensing in 8- <i>Pmmn</i> Borophene

We present a unified theoretical framework that integrates Floquet engineering with polaron theory to investigate the optical response of 8-Pmmn borophene under off-resonant, circularly polarized light. A Floquet Hamiltonian, constructed within the framework of polaron theory, is combined with the Kubo approach to establish a unified formalism for analyzing the optical response. This framework examined light–matter or electron–phonon interactions independently; this work combines both effects within a self-consistent Floquet–Kubo–polaron formalism. The Floquet Hamiltonian, constructed in the polaronic representation, is incorporated into the Kubo formalism to quantitatively assess how electron–phonon coupling modifies the Floquet-driven optical conductivity. The choice of 8-Pmmn borophene is crucial because its intrinsically tilted and anisotropic Dirac cones enable directional control of Floquet-induced gaps and phonon coupling strengths. Our results reveal that surface optical phonons from the substrate cause direction-dependent damping and anisotropic suppression of the optical conductivity, effects absent in conventional Floquet-only models. This framework establishes 8-Pmmn borophene as a model platform for dynamically tunable optoelectronic and quantum-sensing applications.