My interest in quantum phase transitions and quantum criticality
focuses on the study of two different systems:

1) Systems that simultaneously exhibit superconductivity and
ferromagnetism, such as UGe2.

In these systems, it is theoretically expected that a (triplet)
superconducting phase can exist both on the paramagnetic and
magnetically ordered side of the ferromagnetic (FM) transition
(experimentally, SC has so far only been observed in the FM phase).
I am interested in the nature of the SC transition (we recently
showed that a first order SC transition is possible), and how it
affects the quantum transition into the ferromagnetic state. In
those regions of the phase diagram where FM and SC coexist, I am
interested in the interplay between the SC d-vector and the
magnetization; and interplay that can give rise to interesting new
collective modes.


2) Nanoscale structures and Quantum Corrals.

We recently showed that quantum interference between impurities can
be used to tune a SC host system through a local quantum phase
transition. I am currently studying the interplay between ordered
nanostructures, such as triangular or elliptic quantum corrals, and
electronic structure of complex host systems, such as
superconductors, magnetic systems, semiconductors, etc. Of
particular interest for me is the question whether nanostructures
can be used to induce new types of quantum phase transitions and
created novel many-body states in these host systems. I believe that
nanostructures will provide a new venue to probe and gain insight
into the physics of many strongly correlated electron systems.