# Research

**Nonequilibrium Phenomena in Topological Insulators**

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...

https://www.youtube.com/watch?v=hH405s2Yllo

**Analogues of Spintronics Phenomena in Superconductors**

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.

Nonequilibrium superconductivity matured a few decades before the advent of spintronics, partly due to the early success of the Bardeen-Cooper-Schrieffer (BCS) theory in modelling a wide array of superconductors. Approximate theoretical methods were developed in the 1960s and 1970s, which led to a reasonable understanding of the experimental observations. Currently, the field remains active due to prospects of designing and manipulating integrated circuits made from small superconducting circuits. These circuits are candidates for scalable quantum computation, but their functionality requires a good understanding of how the superconducting order parameter responds to external perturbations and how it relaxes back to equilibrium.

Although researchers working on superconductivity are faced with similar questions and challenges as those working on spintronics, the two fields have evolved independently and remain largely disconnected to this day. The main objetive of our research project is to create conceptual bridges between nonequilibrium magnetism and nonequilibrium superconductivity, and to search for a number of analogies that have remained unnoticed thus far.

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.