Superconductivity with a twist

Abstract

Superconductivity in high-Tc cuprates is one of the longer lasting mysteries in condensed- matter physics. Cuprates have a complicated chemical structure and display a variety of phenomena in their phase diagram. Because of this, it is not yet fully understood what is the mechanism that is responsible for superconductivity. Recently, supercon- ductivity has been found in twisted bilayer graphene (tBLG), which exhibits a similar phase diagram as high-Tc cuprates, but is purely carbon based. In addition, the doping concentration in tBLG can be varied by means of a gate voltage, which represents a huge advantage in comparison with high-Tc cuprates, for which a new sample must be prepared for each different doping concentration. Therefore, tBLG can possibly serve as a platform to investigate the superconducting mechanism that takes place in high-Tc cuprates. In this thesis, the electronic properties of graphene and bilayer graphene are addressed. Then, a description of superconductivity in relation to its macroscopic properties will be given via the Ginzburg-Landau formalism, and its microscopic prop- erties will be derived using the BCS theory. In the latter approach, the gap equation is derived for general dimensionality and dispersion. The geometry of tBLG will be discussed in relation to its Moiré pattern, after which its dispersion will be examined. Finally, a comparison between tBLG and high-Tc cuprates will be given.