Bound States from Berry Curvature and Chiral Superconductivity

TL;DR

This paper explores how Berry curvature influences chiral superconductivity, revealing a cascade of topological phases with distinct angular momenta and oscillations in critical temperature, akin to the Little-Parks effect.

Contribution

It demonstrates that Berry curvature induces chiral, non-$s$-wave bound states and a sequence of topological superconducting phases with observable oscillations in $T_c$.

Findings

Identification of chiral bound states supported by Berry curvature.

Discovery of a cascade of chiral topological phases with different angular momenta.

Prediction of oscillations in $T_c$ analogous to the Little-Parks effect.

Abstract

Motivated by the discovery of exotic superconductivity in rhombohedral graphene, we study the two-body problem in electronic bands endowed with Berry curvature and show that it supports chiral, non-$s$-wave bound states with nonzero angular momentum. In the presence of a Fermi sea, these interactions give rise to a chiral pairing problem featuring multiple superconducting phases that break time-reversal symmetry. These phases form a cascade of chiral topological states with different angular momenta, where the order-parameter phase winds by $2\pi m$ around the Fermi surface, with $m = 1,3,5,\ldots$, and the succession of phases is governed by the Berry-curvature flux through the Fermi-sea area, $\Phi = b k_F^2/2$. As $\Phi$ increases, the system undergoes a sequence of first-order phase transitions between distinct chiral phases, occurring nearly periodically in $\Phi$ with period two. This realizes a quantum-geometry analog of the Little-Parks effect -- oscillations in $T_c$ that provide a clear and experimentally accessible hallmark of chiral superconducting order.