# Research

Nonequilibrium Phenomena in Topological Insulators

The development of quantum physics in the beginning of the 20th century revolutionized people's understanding of materials. Based on the laws of quantum physics, solids were classified into insulators, semiconductors, metals, and superconductors. For decades, it was believed that all insulators were similar to one another when it came to their inability to conduct electricity, and that all superconductors were also similar to one another when it came to their extreme ability to carry electrical current.

Such belief was first shaken in 1980, and then shattered in 2005, when it became apparent that the behavior of electrons in solids can also be classified using a branch of mathematics known as topology. For example, according to the topological classification of solids, some insulators (dubbed "topological" insulators) conduct electricity on their surfaces whereas others (dubbed "non-topological" or "ordinary" insulators) do not. The metal at the surface of a topological insulator is quite special: electrons are weightless, their conduction of electricity is remarkably robust, and their magnetic properties peculiar.

Although the advent of topological materials and their technological promise have ignited a spark of research activity, most of the studies thus far have focused on equilibrium (time-independent) setups, as well as on situations in which electrons are isolated from their environments. Unfortunately, the assumption of equilibrium excludes a number of interesting technological applications, and the assumption of isolated electrons is often not realistic. Therefore, in order to develop useful topological devices that will benefit society, it is crucial to investigate how electrons in topological materials are affected by external perturbations and by their non-electronic environments. This investigation is a prime objective of my research program.

Here are a few representatives talk about my recent research:

http://www.birs.ca/events/2013/5-day-workshops/13w5158/videos/watch/2013...

Much of the current research in magnetism concentrates on ferromagnets that are perturbed away from equilibrium by external electric and magnetic fields. The blossoming of nonequilibrium magnetism has been stimulated by the advent of spintronics, a technology that exploits the spin of the electron in order to store and process information. In metals, the landmark spintronics phenomena arise from the quantum mechanical interplay between currents and magnetization. An iconic example of this interplay is the spin transfer torque (STT), which arises when a spin polarized current traverses a non-collinear magnetic configuration. There are two types of STT: the adiabatic'' STT is responsible for current-induced switching of magnetization, whereas the nonadiabatic'' STT is important for the current-driven motion of magnetic domain walls. Both STT are important for prototype magnetic memory devices.
The underlying mathematical connection between magnets and superconductors was first unveiled by P.W. Anderson, who realized that a superconductor is akin to a ferromagnet in the charge (instead of spin) space. In charge space, a spin-up'' (spin-down'') particle is an electron (hole).
It turns out that, in a superconductor, the majority of spins'' are oriented sideways''. Throughout the years, this insight has been fruitfully exploited in equilibrium (time-independent) situations. Our research will extend it into nonequilibrium scenarios, with the goal of transferring recent advances of spintronics to the field of superconductivity. In particular, we will be interested in finding the superconducting counterparts of spin transfer torques.