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Here, we report a hierarchical Co3ZnC/carbon nanotube-inserted nitrogen-doped carbon concave-polyhedrons synthesized by direct pyrolysis of bimetallic zeolitic imidazolate framework precursors under a flow of Ar/H2 and subsequent calcination for both high-performance rechargeable Li-ion and Na-ion batteries. In this structure, Co3ZnC nanoparticles were homogeneously distributed in in situ growth carbon nanotube-inserted nitrogen-doped carbon concave-polyhedrons. Such a hierarchical structure offers a synergistic effect to withstand the volume variation and inhibit the aggregation of Co3ZnC nanoparticles during long-term cycles. Meanwhile, the nitrogen-doped carbon and carbon nanotubes in the hierarchical Co3ZnC/carbon composite offer fast electron transportation to achieve excellent rate capability. As anode of Li-ion batteries, the electrode delivered a high reversible capacity (∼800 mA h/g at 0.5 A/g), outstanding high-rate capacity (408 mA h/g at 5.0 A/g), and long-term cycling performance (585 mA h/g ...