Introduction

In this chapter, the background of all germanene-related materials is introduced in detail. This book is mainly focused on the first-principles simulations and their close relations with the phenomenological models, in which both approaches are thoroughly consistent under the quasiparticle framework. The former is capable of providing the enough information in evaluating whether the reliable former could be well established under the unusual crystal symmetries and complicated orbital hybridizations. The detailed comparisons between theoretical predictions and examined results are illustrated thoroughly in each chapter, covering the various merits and drawbacks of experimental observations. Both numerical simulations and model calculations are strong required to explore the diverse phenomena due to the natural and/or artificial operations. The long-term theoretical developments clearly show that these two approaches have created the strong modifications of their manners and techniques.