Berry Trashcan With Short Range Attraction: Exact $p_x+ip_y$ Superconductivity in Rhombohedral Graphene

Rhombohedral multilayer graphene ($n \ge 4$) under a displacement field develops a unique dispersion with a flat bottom and steep kinetic energy walls, a structure that we model as the "Berry Trashcan." This moiré-free model possesses uniform Berry curvature, and it is an ideal platform for studying interaction-driven physics. We show that the model's solvability for short-range attractive interactions stems from a restricted spectrum generating algebra (RSGA), a structure previously identified in quantum scars. This exactness allows us to demonstrate the emergence of analytic $p_x+ip_y$ superconducting ground states. While the RSGA framework permits the construction of other contrived exact models, we show the Berry Trashcan is a uniquely realistic point in its class to host this chiral state. The superconductivity exhibits several key features: a robust "ferromagnetic" coupling between the ground state's chirality and the system's Berry curvature, an unusual long-range pairing decaying as $\sim r^{-3/2}$, and excellent agreement between our analytically derived binding energies, excitation spectra, and off-diagonal long-range order (ODLRO) and numerical exact diagonalization. Our findings establish this system as a natural platform for chiral superconductivity, and position the Berry Trashcan model as a fundamental, analytically tractable building block for understanding interaction-driven physics in RnG.