Research
Machine learning for quantum matter
Machine learning (ML) is a transformative approach to computational problem solving, and applying it to quantum many-body physics is an exciting frontier. Decades of experiments have left behind an enormous record of quantum materials — crystal structures, transition temperatures, spectra — that no single theory has ever been able to digest as a whole. A data-driven approach learns from that record directly, and can therefore attack questions that first-principles theory still cannot answer. My guiding principle in this direction is interpretability: the goal is physical understanding, not black-box prediction. A model is valuable to me when I can read off from it which physical quantities control the answer, ideally with honest uncertainty attached. Superconductivity is a natural first target, since after a century of research we still cannot say, given a material, whether it will superconduct and at what critical temperature. Together with my collaborators I built an interpretable model based on descriptors that encode the local bonding geometry of a crystal, which predicts critical temperatures and singles out the distribution of electron affinity differences between neighboring atoms, a chemical control parameter that had been largely overlooked. It predicted a new superconductor, PtPb3Bi, which our collaborators then synthesized and confirmed in the lab. Materials data can also be organized with no labels at all: asking what the analogue of the periodic table is for compounds, we found that hundreds of thousands of inorganic materials are captured by just three latent coordinates, in which superconducting families cluster on their own. None of this machinery is specific to superconductivity, and as data on quantum materials keeps growing the same approach extends to magnetism, topological order, and other classes of materials. ML is also useful beyond materials data, as a computational tool for theory itself, for instance in computing topological invariants.
Topological and fractionalized phases of matter
Topology has become one of the cornerstones of modern condensed matter physics. Starting with the quantum Hall effect, where a perpendicular magnetic field induces a quantized response in a two-dimensional system, topological ideas have evolved into a major theme in the field. I am interested in the interplay between the topological properties of quantum systems, often described by the Berry curvature and quantum geometry, and factors like electron-electron interactions, disorder, and geometric confinement. The quantum geometry of the Bloch wavefunctions, for example, controls how far disorder-induced Andreev bound states spread, and can make a fully gapped superconductor respond as if it were nodal. Interactions make these systems even richer: electrons “fractionalize” and form entirely new types of order. Motivated by experiments on twisted transition metal dichalcogenides, I have been studying fractional quantum spin Hall insulators, constructing a trial wavefunction for a state with non-Abelian topological order by condensing an anyonic exciton, and mapping out where it is energetically favorable.
Superconductivity in novel mesoscale systems
Superconductivity is one of the most striking quantum many-body phenomena, showcasing quantum coherence in a very tangible way: when cooled below a certain temperature, many materials exhibit zero electrical resistance and perfect expulsion of magnetic fields. Investigating mesoscopic superconductors offers valuable new insights into the nature of superconductivity, and the rapid experimental progress in this area motivates theorists to think about novel settings where new physics can be uncovered. Much of my work has centered on topological superconductivity, a phase hosting non-Abelian excitations whose standard realizations require a magnetic field that suppresses the very superconductivity they rely on. I proposed an alternative in which the superconducting phase difference, a degree of freedom naturally available in any Josephson device, supplies the required symmetry breaking. This program has advanced from toy models to real devices in close collaboration with experimental groups, from planar Josephson junctions to Corbino-geometry junctions on topological insulators, which display reentrant superconductivity and a Josephson diode whose polarity reverses with the parity of the enclosed vortices. More broadly, I am interested in superconductors with non-trivial topology, disorder, unconventional pairing symmetry, or finite Cooper-pair momentum, including pair-density-wave states in rhombohedral graphene.
Physics of machine learning
Condensed matter physics applies the toolbox of statistical mechanics to the quantum world; the same methodology can be turned onto neural networks, the infrastructure behind modern AI, to understand why they work so well. My aim in this direction is a controlled analytical theory of deep learning, built the way physics builds theories: outward from solvable limits. One such limit is learning under severe data corruption, where wide networks turn out to implement a simple nearest-class-mean rule, universal across depths, activation functions, and noise distributions, and derivable in closed form. Phase transitions, among the most fascinating concepts in many-body physics, appear here too. Making the activation function a quenched random variable provides a controlled route between the universality classes of information propagation in deep networks, with a continuous transition at a critical mixing fraction that can be computed analytically and near which trained networks perform best. I am also generally interested in effective field theories and phase transitions in neural networks.