Recent advances in realizing optical frequency combs using nonlinear parametric processes in integrated photonic resonators have revolutionized on-chip optical clocks, spectroscopy, and multi-channel optical communications. At the same time, the introduction of topological physics in photonic systems has provided a new paradigm to engineer the flow of photons, and thereby, design photonic devices with novel functionalities and inherent robustness against fabrication disorders. Here, we use topological design principles to theoretically propose the generation of optical frequency combs and temporal Kerr solitons in a two-dimensional array of coupled ring resonators that creates a synthetic magnetic field for photons and exhibits topological edge states. We show that these topological edge states constitute a traveling-wave super-ring resonator that leads to the generation of coherent nested optical frequency combs, and self-formation of nested temporal solitons and Turing rolls that are remarkably phase-locked over >40 rings. In the nested soliton regime, our system operates as a pulsed optical frequency comb and achieves a mode efficiency of >50%, an order of magnitude higher than single ring frequency combs that are theoretically limited to only ~5%. Furthermore, we show that the topological nested solitons are robust against defects in the lattice. This topological frequency comb works in a parameter regime that can be readily accessed using existing low loss integrated photonic platforms like silicon-nitride. Our results could pave the way for efficient on-chip optical frequency combs, and investigations of various other soliton solutions in conjunction with synthetic gauge fields and topological phenomena in large arrays of coupled resonators.
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