In this work, we present a systematic investigation of the electronic structures, band topology, and intrinsic spin Hall effect (SHE) in the layered MAX carbides $M_{n+1}\mathrm{Al}{\mathrm{C}}_n (M=\mathrm{Nb},\mathrm{Ta};n=1,2,3)$ and explore the correlation effects on the SHE. Our results show that this family of materials exhibits Dirac-band-crossing features near the Fermi level $E_F$ and forms nodal lines in the absence of spin-orbit coupling (SOC). When the SOC is included, the Dirac band crossings are fully gapped, resulting in nontrivial $Z_2$ topological invariants (1;000) with a pair of surface states on the (001) plane. Notably, the multiple gapped Dirac points contribute to locally strong spin Berry curvatures, which lead to large spin Hall conductivities (SHCs) and spin Hall angles (0.02–0.62 at $E_F$) for $\mathrm{T}{\mathrm{a}}_{n+1}\mathrm{Al}{\mathrm{C}}_n$ ($n=1,2,3$). Moreover, we also elucidate the impact of the Hubbard $U$ correction on SHCs. Our findings suggest that $\mathrm{T}{\mathrm{a}}_{n+1}\mathrm{Al}{\mathrm{C}}_n$ ($n=1,2,3$) might represent intriguing layered $Z_2$ topological metals with superior charge-to-spin conversion efficiency.

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• Spin Hall effect
• MAX phase compounds
• Topological materials
• Density functional calculations