Chiral Two-Body Bound States from Berry Curvature and Chiral Superconductivity

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 $2πm$ 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 surface area, $Φ= b k_F^2/2$. As $Φ$ increases, the system undergoes a sequence of first-order phase transitions between distinct chiral phases, occurring whenever $Φ$ crosses integer values. 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.

Figures (1)

• Figure 1: (a) Hierarchy of chiral pairing channels from the chiral two-body interaction, Eq. \ref{['eq:V12']}, controlled by commensurability of the Berry-curvature flux $\Phi$, Eq. \ref{['eq:Phi_FS']}, and the Fermi-surface area. Plotted are eigenvalues of the linearized gap equation, Eq. \ref{['eq:gap_equation']}, versus Berry curvature $b$ and carrier density $k_F^2/4\pi$, measured in units of $1/a$ and $a/2\pi$, respectively. The 3D surfaces show the leading (maximal) eigenvalues, labeled by angular-momentum quantum numbers $m = 1,3,5,7,\dots$. Phase boundaries $V_m = V_{m+2}$ between different $m$ are well approximated by the hyperbolae $b k_F^2/2 = \sqrt{(m+1)(m+2)}$. (b) The same phase boundaries $V_m = V_{m+2}$ in terms of flux $\Phi$, which occur near half-integer $\Phi$ at small $b$ and near integer $\Phi$ at large $b$.