# Band Tuning of Phosphorene Semiconductor via Floquet Theory

## TL;DR

This paper investigates the nonlinear optical response of graphene and phosphorene under intense electromagnetic fields using Floquet theory, highlighting the role of anisotropy and observing the Bloch-Siegert shift.

## Contribution

It introduces the application of Floquet theory to analyze the nonlinear optical behavior of phosphorene, emphasizing anisotropy effects and extending understanding beyond traditional resonance methods.

## Key findings

- Observation of Bloch-Siegert shift in graphene and phosphorene
- Numerical analysis showing anisotropy's impact on phosphorene's response
- Floquet theory effectively characterizes different fermionic systems

## Abstract

Graphene and phosphorene are monolayer of graphite and phosphorous, respectively. Graphene is completely relativistic (Dirac) fermionic system, but phosphorene is pseudorelativistic fermionic system. In phosphorene, electronic spectrum of phosphorene has a Dirac like (linear) band in one direction and Schrodinger like (parabolic) band in other direction. Conventional Rabi oscillations are studied by using rotating wave approximation in resonance case. The Floquet theory is an alternative way of study Rabi oscillations in off-resonance case and dominating in case of low energy physics. In this article, the nonlinear optical response of graphene and phosphorene studied under intense applied quantized electromagnetic field via Floquet theory. The Bloch-Siegert shift is observed for graphene and phosphorene. A numerical model is applied for justifying the role of anisotropy in phosphorene. Therefore, the Floquet theory can be utilized to characterize the different fermionic systems.