The word cloud summarizes some of my past and current research interests (from https://scimeter.org/). Please scroll below for a more detailed overview of some of our research interests. The research efforts in our group are funded by grants/awards from the following agencies: National Science Foundation, Alfred P. Sloan Foundation, U.S.-Israel Binational Science Foundation, and Cornell University.
Our group works on a variety of problems in theoretical condensed matter Physics. The concept of quasiparticles, the long-lived excitations above the ground state of a many-body system, which remain particle-like even in the presence of strong electron-electron interactions, has been immensely successful in describing the phenomenology of electronic systems. However, recent decades have seen an increasing number of challenges to these ideas, following the discovery of phenomena such as the fractional quantum Hall effect, "strange" metals and frustrated quantum magnetism. A central theme of our research is the Physics of such strongly correlated quantum systems, where the effects of interaction can lead to the emergence of dramatic new collective phenomena, not describable in terms of the standard quasiparticle-based framework. Many of these problems are inspired by our quest for understanding experiments on a variety of exotic materials, such as unconventional superconductors, quantum spin liquids and non-Fermi liquids, from a fundamental microscopic point of view.
UNIVERSAL PROPERTIES OF INCOHERENT METALS
There are a plethora of materials, such as the cuprates, the pnictides, the ruthenates, and more recently, twisted bilayers of graphene and transition metal dichalcogenides, that display a strong departure from conventional Fermi liquid behavior. This includes the mysterious observation of an electrical resistivity that scales linearly with temperature over a broad range of energy scales, and often down to shockingly low temperatures. One of the most remarkable empirical facts related to transport across these microscopically distinct systems is their apparent universality of (“Planckian”) scattering rates, controlled only by the ratio of kBT/h. Given the ubiquitous nature of these observations, the two fundamental questions that I am interested in are (i) what is the universal effective theory for a subset of these non-Fermi liquid metals, and (ii) what controls the emergent universality of the Planckian scattering rate?
SUPERCONDUCTIVITY AND QUANTUM CRITICALITY IN MOIRÉ MATERIALS
The discovery of superconductivity and other competing orders in twisted bilayer graphene has ushered a new era of studying correlated quantum phenomena in a highly tunable platform. The key question of interest across these materials is tied to the low-energy fate of electronic interactions projected to the “flat” bands. The problem is inherently non-perturbative, without any “small” parameter and requires the development of new theoretical tools. Additionally, the observation of continuous metal-insulator transitions and other correlated phenomena in moiré transition metal dichalcogenides allows us to revisit many classic unsolved problems in the field from a fresh perspective. Interestingly, understanding the experimental phenomenology across these platforms often involves analyzing the effects of interaction, disorder and topology in a highly non-trivial setting. The three questions that fascinate me are (i) Can we put universal constraints on the superconducting and transport properties of interacting flat-band systems in these highly non-perturbative regimes?, (ii) What is the correct theoretical formulation going beyond the traditional Landau-Ginzburg-Wilson paradigm for the experimentally observed quantum phase transitions between metals and correlated insulators?, and (iii) How should we design new experiments that can help probe the frequency and momentum-resolved correlation functions in these materials in the absence of many conventional scattering techniques?