Theoretical Topics in Superconductivity and Graphene

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Superconductors are metals which carry a current without dissipation. This is a very desirable property for making large electromagnets used in medical imaging. But such magnets presently work only at low temperatures. Hence they require refrigeration. So finding materials suitable for the fabrication of magnets that would operate at room temperature is very important. New classes of superconductors are discovered every few years. An important class is the cuprates which are the materials that hold the record critical temperature value [Tc] up to about 150 Kelvin. More recently Fe-based metals have also been found to superconduct and we wish to study their properties with a view at increasing the value of Tc. Superconductors are not the only metals of importance in technological applications. The electronic industry can also benefit from new semiconducting materials. In 2004, a single sheet of graphite was exfoliated which is a membrane a single atom thick and has amazing unexpected properties. As an example, the motion of the charge carriers in graphene is governed by a relativistic Dirac equation. Their mobility is excellent and many novel applications have been suggested such as elements in display screens. We are studying the properties of graphene under magnetic field and how its properties depend on the coulomb interactions between the electrons. This is important in understanding the interaction of light with the charge oscillations in the graphene sheets. There are also other new materials with different and quite new functionalities. These include a single layer MoS2 which is a direct gap semiconductor with two valleys. It is possible in these materials to excite electrons exclusively from one of the two valleys leaving the others unaffected. This could be very useful in applications to the communication industry .We plan to study their optical properties with an aim at understanding how incident light can be change to a charge current in these systems. All the proposed research involves theoretical studies aimed at better microscopic understanding of the properties of recently discovered materials.