When certain metals are cooled to low temperatures, the electrons within form pairs that condense into a single quantum state. This superconducting phase exhibits a number of striking features, including electrical conduction without resistance and the expulsion of magnetic fields. Recently, a new class of superconductors has been predicted to exist with unique pairing symmetries. Astoundingly, these "topological" superconductors can potentially be harnessed to build a quantum computer that is immune to environmental noise. Towards this goal, our group is interested in discovering, characterizing, and engineering new unconventional superconductors.

# Research

Electrons confined within a material always interact through Coulomb's law. Sometimes this interaction is especially strong and the quantum wave function of the material develops correlations. When this happens, electrons can no longer be treated independently of each other. Strongly correlated electron systems give rise to some of the most interesting topics in quantum materials science, including high-temperature superconductivity, the fractional quantum Hall effect, quantum spin liquids, and the Kondo effect. Exploration of the emergent properties of correlated electron system is one of our primary goals.

Due to special relativity, the spin of an electron can couple to its motion. This effect occurs most strongly in materials with large atomic numbers, where the coupling often leads to qualitatively new phenomena such as band inversion in topological insulators and electronic order that spontaneously breaks spatial inversion symmetry. At present, it is unclear what new phases can emerge when spin-orbit coupling is combined with strong electron correlations. We are interested in pursuing this question from an experimental standpoint by investigating what consequences strong spin-orbit coupling imposes on correlated materials.

Interesting new phases of matter can emerge when an otherwise ordinary material is subjected to a strong periodic perturbation, for example from the oscillating optical field of a laser. Some predictions include "Floquet" topological insulators and light-induced superconductivity. Our goal is to push the experimental boundaries of this burgeoning field by generating and characterizing novel phases of matter through periodic driving.

When light of a fixed frequency illuminates a material, the nonlinear response of the material can produce reflected light at higher harmonics of the incident frequency. By measuring how this nonlinear harmonic generation depends on the angles of incidence and reflection of the light, one can determine the full nonlinear optical susceptibility tensor of the material, which encodes information about the symmetries of the material under study and the breaking of those symmetries at phase transitions.

In Einstein's photoelectric effect, the energy of a photon incident on a material is absorbed by an electron, which is subsequently excited and emitted from the material. In angle-resolved photoemission spectroscopy (ARPES), the energy and momentum of photoemitted electrons are measured, leading to a so-called "momentum space microscope." ARPES is a powerful tool for directly measuring the electronic structure of materials, including band dispersions, Fermi surfaces, and energy gaps.

Vortices and skyrmions are localized topological defects in superconductors and ferromagnets, respectively. These compact objects are accompanied by small magnetic dipole moments that can be imaged with a magneto-optical microscope. Such a microscope can also be used to manipulate vortices and skyrmions in order to study their properties and control their interactions.

In pump-probe reflectivity, two ultrafast laser pulses separated by a controlled time delay are directed onto a sample. The first pulse, the *pump*, transiently excites the material under study (in the same way a hammer excites a bell to ring). The second pulse, the *probe*, is then used to measure the reflectivity of the material. By recording how the reflectivity changes with time after the pump pulse (much like how our ears hear the tone of the bell diminish after it rings), one can learn about the dynamical properties of the material on femtosecond timescales.