Theoretical Topics in Superconductivity and Graphene

超导体是带电流而不耗散的金属。对于制造用于医学成像的大型电磁铁来说，这是一个非常理想的特性。但是这种磁铁目前只能在低温下工作。因此它们需要冷藏。因此，寻找适合制造在室温下工作的磁铁的材料是非常重要的。每隔几年就会发现新的超导体。铜酸盐是一类重要的材料，它能保持临界温度值[Tc]，最高可达150开尔文。最近，铁基金属也被发现具有超导性，我们希望研究它们的性质，以期增加Tc的值。超导体并不是唯一在技术应用中具有重要意义的金属。电子工业也能从新的半导体材料中获益。2004年，单层石墨被剥离，这是一层单原子厚度的薄膜，具有意想不到的惊人特性。例如，石墨烯中载流子的运动是由相对论性狄拉克方程控制的。它们的移动性非常好，并且提出了许多新的应用，例如显示屏幕中的元素。我们正在研究石墨烯在磁场下的性质，以及它的性质如何依赖于电子之间的库仑相互作用。这对于理解石墨烯薄片中光与电荷振荡的相互作用是很重要的。还有其他新材料具有不同的和相当新的功能。其中包括单层MoS2，它是具有两个谷的直接间隙半导体。在这些材料中，有可能只从两个谷中的一个激发电子，而不影响其他谷。这在通信行业的应用中可能非常有用。我们计划研究它们的光学性质，目的是了解入射光如何在这些系统中转变为电荷电流。所有提出的研究都涉及理论研究，旨在更好地从微观上理解新发现材料的性质。

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.