# Diverse quantization phenomena in layered materials

## TL;DR

This paper reviews diverse quantization phenomena in layered 2D materials, highlighting their unique electronic and optical properties, theoretical models, and experimental confirmations across various systems like graphene, silicene, phosphorene, and topological insulators.

## Contribution

It provides a comprehensive overview of quantization effects in layered materials, integrating theoretical models with experimental results, and exploring a wide range of 2D systems and their unique behaviors.

## Key findings

- Distinct quantization phenomena observed in various layered 2D materials.
- Theoretical models align well with high-resolution experimental measurements.
- Unique electronic and optical properties depend on stacking and structural configurations.

## Abstract

The diverse quantization phenomena in 2D condensed-matter systems, being due to a uniform perpendicular magnetic field and the geometry-created lattice symmetries, are the focuses of this book. They cover the diversified magneto-electronic properties, the various magneto-optical selection rules, the unusual quantum Hall conductivities, and the single- and many-particle magneto-Coulomb excitations. The rich and unique behaviors are clearly revealed in few-layer graphene systems with the distinct stacking configurations, the stacking-modulated structures, and the silicon-doped lattices, bilayer silicene/germanene systems with the bottom-top and bottom-bottom buckling structures, monolayer and bilayer phosphorene systems, and quantum topological insulators. The generalized tight-binding model, the static and dynamic Kubo formulas, and the random-phase approximation, are developed/modified to thoroughly explore the fundamental properties and propose the concise physical pictures. The different high-resolution experimental measurements are discussed in detail, and they are consistent with the theoretical predictions.