Mechanical Deformation Effects on Floquet-driven Graphene Systems 

Static and dynamic stimuli can independently access intertwined degrees of freedom, allowing for the generation and control of novel states of matter. For example, strain engineering has emerged as a key method for modifying graphene's properties. Static strain profiles can induce pseudomagnetic fields that alter hopping parameters, and create scalar potentials, allowing for precise control over charge carrier dynamics. Analogously, subjecting a graphene sheet to circularly polarized light -a dynamic effect-, leads to the formation of topological gaps and the emergence of the anomalous Hall effect. In this work, we consider a graphene membrane irradiated with a monochromatic light source and subjected to a static Gaussian-shaped deformation. To address this space-time dependent system, we utilize the Floquet formalism to treat time-periodicity. By considering the high-frequency approximation, we derive an effective stroboscopic Hamiltonian for irradiated graphene and obtain the real-space Green's functions governing the system. We then include the strain-induced gauge field in the effective Hamiltonian, and we consider a wide Gaussian deformation as a perturbation effect on the membrane. Solving the Lippmann–Schwinger equation in the first-Born approximation, we obtain the local density of states (LDOS). We present a complete description of the effects of irradiation on sublattice and valley polarizations through the analysis of valley and sublattice-polarized LDOS.