Seminar By Thomas Scaffidi, University of California - Irvine

Title: Surprising Physics of 2D Fermions: From Repulsion-Driven Superconductivity in a Single Dirac Cone to Superdiffusive Hydrodynamics

Series: Condensed Matter Sciences Seminar

Host: Cyprian Lewandowski

Abstract: I will discuss two surprising phenomena of interacting fermions that rely crucially on being in two dimensions. In the first part, I ask when a single, doped Dirac cone can superconduct purely from short-range repulsive interactions via the Kohn–Luttinger mechanism. We show that an ideal, linear Dirac cone is immune to pairing at order 𝐔^𝟐; superconductivity instead emerges only through higher-order-in- corrections to the dispersion, which are unavoidable in any lattice realization and dictate the pairing symmetry. Thus, the structure of the order parameter directly reflects how the fundamental obstruction to realizing a single Dirac cone on a lattice is evaded. For a single Dirac cone realized in a chiral metal, we find a topological state with chirality opposite to that of the parent metal, while for a surface Dirac cone of a topological insulator we find highly anisotropic, near-nodal states arising from Fermi-surface warping. In the second part, I turn to transport and ask how electron–electron scattering relaxes spatially non-uniform currents in a perfectly clean 2D Fermi liquid. By numerically solving the kinetic Boltzmann equation and extracting the real-time current–current correlator, we uncover a rich hierarchy of anomalously slow relaxation timescales across ballistic, tomographic, and viscous regimes.