From Fractionalization to Chiral Topological Superconductivity in a Flat Chern Band

Abstract

We show that interacting electrons in a flat Chern band can form, in addition to fractional Chern insulators, a chiral $f$-wave topological superconductor that hosts neutral Majorana fermion edge modes. Superconductivity emerges from an interaction-induced metallic state that exhibits anomalous Hall effect, as observed in rhombohedral graphene and near the $ν=\frac{2}{3}$ fractional Chern insulator in twisted transition metal dichalcogenides.

Figures (13)

• Figure 1: A schematic: electrons in twisted semiconductors in the absence of magnetic fields can be mapped to particles in a periodically varying magnetic field. Fractional Chern insulators (left) are favored when the emergent magnetic field is nearly uniform. On the other hand, the magnetic field inhomogeneity drives chiral topological superconductivity with Majorana fermion edge modes (right).
• Figure 2: (a-b) The quantum metric trace ${\rm Tr} g({\boldsymbol{k}})$ in units such that the average is unity for (a) $\mathcal{K} = 0.05$ and (b) $\mathcal{K} = 0.8$ (Eq. \ref{['eq:Kofr']}). (c-d) The many-body spectrum (in units of $V_1$) obtained from exact diagonalization as a function of the absolute value of the total momentum $|{\boldsymbol{k}}_{\rm cm}|$ for (c) $\mathcal{K} = 0.05$ and (d) $\mathcal{K} = 0.8$. Calculations were done on a 27 site cluster.
• Figure 3: (a) Interaction-induced dispersion $\epsilon({\boldsymbol{k}})$ (Eq. \ref{['Hamiltonian_PH']}) (in units of $V_1$) for $\mathcal{K} = 0.8$ plotted along a cut in the Brillouin zone. (b-d) Momentum occupation $n({\boldsymbol{k}}) = \langle c^{\dagger}_{{\boldsymbol{k}}} c_{{\boldsymbol{k}}} \rangle$ evaluated in the many-body ground state.
• Figure 4: (a)-(b) Total energy $E$ at $\mathcal{K} = 0.8$ as a function of the number of particles $N$ for $N_s = 27$ (a) and $N_s = 28$ (b) where $N_s$ denote the number of sites of the finite-size system. (c) Binding energy $E_b = E(N+2) + E(N) - 2 E(N+1)$ evaluated at $\mathcal{K} = 0.8$.
• Figure 5: Gap function $\Delta(\bm {k}) = \mel{\Psi_{N-2}}{c_{-\bm {k}} c_{\bm {k}}}{\Psi_{N}}$ for $\mathcal{K}$= 0.8 with $N = 20$ for $N_s = 27$ and $N = 21$ for $N_s = 28$. The size of the circle is proportional to $|\Delta({\boldsymbol{k}})|$ while the color denotes the phase.