Electronic Properties of “Graphene”

The discovery of two-dimensional (2D) materials has opened a new era of scientific research and industrial application. From the field effect transistor to the optoelectronic devices, 2D materials have surpassed their 3D counterparts in many ways. This all started with the successful exfoliation of the graphene from the bulk graphite sample by the Andre Geim group long back in 2004 Novoselov (2004). Soon after the discovery of graphene, a wide variety of 2D materials were discovered. These includes but not limited to semiconductors ( \({\text {MoSe}}_2, {\text {WSe}}_2, {\text {MoS}}_2, {\text {WS}}_{2}\) ), insulators (hBN), superconductors ( \({\text {NbSe}}_2, {\text {TaS}}_{2}\) ), ferromagnets ( \({\text {Cr}}_2{\text {Ge}}_2{\text {Te}}_6, {\text {FePS}}_3, {\text {CrI}}_3, {\text {MnPS}}_{3}\) ). In this chapter, we discuss the low-energy electronic properties of single-layer graphene. We further extend our discussion to bilayer and trilayer graphene. Next, we discuss the effect of the other substrate on graphene’s band structure. In particular, we will discuss the effect of moire potential imprinted due to rotational alignment between graphene and the hBN layer. All electronic properties studied in this chapter will be at zero magnetic fields. The zero magnetic field properties discussed in this chapter form the basis for understanding what happens in the finite magnetic field, which is discussed in Chap. 2 .