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People often think of physicists as reductionists who want to take apart the world to describe it bit by bit. Thankfully this is quite far from our pursuit, in both practice and ideology. In condensed matter physics, we're typically seeking to discover and understand emergent properties of materials--things which are not obvious given the individual particles but manifest as a collective behavior of the material. My interest is in quantum materials, compounds which often hold unexpected properties rooted in the well-known but counter-intuitive quantum theory.
Quantum mechanics is the most verified theory mankind has ever developed. Every material we've encountered so far obeys its laws, yet we understand the vast majority intuitively without invoking wave-functions, entanglement, superposition, or other quantum peculiarities. For the most part, quantum mechanics agrees with the classical physics of our intuition--you don't need to ask a quantum physicist to explain lumber before building a treehouse.
Yet, there do exist materials for which intuition fails. So-called ``quantum materials" are comprised of interacting (correlated) constituents forming an ensemble which behaves collectively, requiring a quantum mechanical description. Many of the great surprises of quantum matter are of broad interest because they exist at energy scales which are tangible. Basic research into these materials often reveals surprising emergent phenomena with great potential for immediate and transformative technologies. We don't need a mile-long particle accelerator to create a superconductor, and so we can put superconductors into commercial products such as MRI machines, ultra-sensitive magnetometers, and lossless electrical cable. The success of condensed matter is belied by its ubiquitousness in everyday life. We can hold in our pockets enormous feats of engineering made possible through achievements in basic research on condensed matter--the giant magnetoresistance effect which allowed us to reach gigabyte storage was a basic science discovery in just 1988. It is no exaggeration to say that the modern world is predicated on our ability to understand and manipulate material properties.
As we explore further exotic materials, careful and comprehensive scrutiny is crucial to understanding phenomena for which our common intuition fails. The discovery of topological materials is a dramatic and unexpected revelation which represents an entirely new avenue in materials classification with an untold future. Topological materials hold great potential for application, having novel magnetic and electronic properties which are robust against disorder. It is captivating to me that the basic phenomena we are seeking to understand could hold the key to technological advances in the short term as well as beyond the horizon.
Topology is a mathematical concept which gives insight as to why certain materials have novel properties unaffected by defects and disorder. Distinct topological classes have geometric properties which are unchanged by deformations. A classic example comparing a doughnut and a coffee cup: If you had a lump of clay in the shape of a donut, you could mold it into a coffee cup without poking additional holes or joining edges. In this example, the number of holes is preserved despite deformation of the clay. Similarly, some materials have an immutable characteristic akin to a “hole” which produces robust topological properties. A number of exotic phenomena related to putative topological properties have been identified, including effectively massless particles (Dirac Fermions), metallic surfaces surrounding an insulator (topological insulators), and electrons with magnetic components dictated by their motion (spin-locked momenta). Resilient and novel properties such as these are advantageous for bringing quantum materials into advanced stages of production.
With the basic ideas of topology established in condensed matter, extensive work is needed to design ideal topological materials and elucidate topology's further consequences. My work centers on strongly correlated topological materials in an effort to uncover the unexpected phenomena that arises when materials become more than the sum of their parts.