Chiral superconductivity from parent Chern band and its non-Abelian generalization

TL;DR

This work develops a minimal projected model for spin-valley polarized electrons in rhombohedral tetralayer graphene, starting from a parent Chern band with quartic dispersion $\epsilon({\bm k})$ and exploring repulsive and attractive interactions. A Hartree–Fock analysis yields a phase diagram with a metallic region, an insulating anomalous Hall crystal ($C=1$), and a chiral $p+ip$ topological superconductor that undergoes a zero-temperature topological transition to a trivial gapped Bose–Einstein condensate as the chemical potential $\mu$ crosses zero. Extending to a composite-fermion field theory, the chiral superconducting state maps onto the non-Abelian Moore–Read quantum Hall phase, while a nearby confinement–deconfinement transition to a chiral spin liquid is predicted, highlighting rhombohedral multilayer graphene as a platform for rich correlated topological phenomena. Together, these results connect topological superconductivity, non-Abelian quantum Hall order, and potential spin-liquid physics in graphene-based systems, with experimentally accessible signatures in ARPES and transport.

Abstract

We propose a minimal model starting from a parent Chern band with quartic dispersion that can describe the spin-valley polarized electrons in rhombohedral tetralayer graphene. The interplay between repulsive and attractive interactions on top of that parent Chern band is studied. We conduct standard self-consistent mean-field calculations, and find a rich phase diagram that consists of metal, quantum anomalous Hall crystal, chiral topological superconductor, as well as trivial gapped Bose--Einstein condensate. In particular, there exists a topological phase transition from the chiral superconductor to the Bose--Einstein condensate at zero temperature. Motivated by the recent experimental and theoretical studies of composite Fermi liquid in rhombohedral stacked multilayer graphene, we further generalize the physical electron model to its composite fermion counterpart based on a field theory analysis. The chiral superconductor phase of the composite fermion becomes the nonabelian Moore--Read quantum Hall phase. We argue that a chiral (pseudo-)spin liquid phase can emerge in the vicinity of this Moore--Read quantum Hall phase. Our work suggests rhombohedral multilayer graphene as a potential platform for rich correlated topological phases.

Figures (3)

• Figure 1: (a) Phase diagram of Hamiltonian Eq. (\ref{['Eq:Hamiltonian']}) from self-consistent calculations. The gray region shows the (semi-)metallic phase. The yellow block stands for the AHC phase. The purple paddles denote the $(p+ip)$-wave TSC, and the blue block represents the trivial gapped BEC phase. The inset zooms in the left bottom corner of the phase diagram with higher resolution.
• Figure 2: Transition between the chiral TSC (purple region) and the trivial BEC phase (blue region), with $v = \epsilon_K$ and $0.7\epsilon_K\le u\le 1.2\epsilon_K$. One can see the chemical potential ($\mu$) drop as the increasing of the electron-phonon coupling strength $(u)$. The inset in TSC regime shows superconducting gap distribution with $u= 0.72 \epsilon_K$, $v = \epsilon_K$, where the real and imaginary part of $\Delta({\bm k})$ is shown in the left and right panel, clearly suggesting the feature of a $(p + ip)$-wave superconductor. The bottom insets illustrate the band structure of Bogoliubov quasiparticles. The band gap closes at the critical point $(u^*\approx 0.97 \epsilon_{K},~\mu = 0)$, indicating the topological phase transition from chiral TSC to trivial BEC phase.
• Figure S1: The phase diagrams with $0\le u\le 5\epsilon_K$ and $0\le v\le 10\epsilon_K$ for (a) $q_0=0.05|{\bm K}|$, (b) $q_0=0.3|{\bm K}|$, and (c) $q_0=20|{\bm K}|$. The insets zoom in the left bottom corners of the phase diagrams with higher numerical resolution.