Quantization Phenomena of critical Hamiltonians in 2D systems

TL;DR

This review discusses recent advances in understanding quantization phenomena in 2D materials using a generalized tight-binding model that considers multiple interactions and structures, revealing unique Landau level behaviors.

Contribution

It introduces a comprehensive tight-binding approach to analyze complex quantization phenomena in emergent 2D materials, including effects of multi-orbital, spin-orbital, and external fields.

Findings

Unique magnetic quantization in layered systems like black phosphorus and MoS2

Identification of orbital-, spin-, and valley-dependent Landau levels

Theoretical predictions confirmed by experimental measurements

Abstract

This review work addresses the recent advances in solving more comprehensive Hamiltonians. The generalized tight-binding model is developed to investigate the feature-rich quantization phenomena in emergent 2D materials. The mutli-orbital bondings, the spin-orbital interactions, the various geometric structures, and the external fields are taken into consideration simultaneously. Specifically, the IV-group layered systems, black phosphorus and MoS$_{2}$ exhibit the unique magnetic quantization. This is clearly indicated in three kinds of Landau levels (LLs), the orbital-, spin- and valley-dependent LL groups, the abnormal LL energy spectra, and the splitting, crossing and anticrossing behaviors. A detailed comparison with the effective-mass model is made. Some theoretical predictions have been confirmed by the experimental measurements.