Superconductivity in doped planar Dirac insulators: A renormalization group study

TL;DR

This study uses a renormalization group approach to demonstrate that doped two-dimensional Dirac insulators with Fermi surfaces can host various superconducting states, including topological ones, arising purely from repulsive interactions.

Contribution

It provides a comprehensive analysis of how repulsive electron-electron interactions can lead to superconductivity, including topological phases, in doped Dirac insulators using an unbiased RG framework.

Findings

Superconductivity emerges from repulsive interactions in doped Dirac insulators.

Topological p-wave and conventional s-wave pairings are favored depending on the interaction details.

Superconducting states follow Clifford algebraic selection rules regardless of Fermi surface topology.

Abstract

From a leading-order unbiased renormalization group analysis we here showcase the emergence of superconductivity (including the topological ones) from purely repulsive electron-electron interactions in two-dimensional doped Dirac insulators, featuring a Fermi surface. In the absence of chemical doping, such systems describe quantum anomalous or spin Hall and normal insulators. Otherwise a simply connected Fermi surface becomes annular deep inside the topological regime. By considering all symmetry allowed repulsive local four-fermion interactions, we show that the nature of the resulting superconducting states at low temperature follows certain Clifford algebraic selection rules, irrespective of the underlying Fermi surface topology. Within the framework of a microscopic Hubbard model, on-site repulsion among fermions with opposite orbitals (spin projections) typically favors topological $p$-wave (conventional $s$-wave) pairing. Theoretically predicted superconductivity can in principle be observed in experiments once the promising candidate materials for quantum anomalous and spin Hall insulators are doped to foster Fermi surfaces.