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Different classes of topological materials are marked with 0, Z, Z2 in columns representing dimensions of these materials. What is the physical meaning of 0, Z, Z2 and what they represent?

Thanks

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I feel you are a bit confused.

The table gives you $0$, $\mathbb{Z}$ or $\mathbb{Z}/2\mathbb{Z}$ for each entry of the table, not "in the columns representing dimensions of these materials". Each entry of the table corresponds thus to both a particular choice of dimension and symmetry class. So the possibilities $0$, $\mathbb{Z}$ or $\mathbb{Z}/2\mathbb{Z}$ correspond to each such choice. What each of these possibilities mean is that $0$, $\mathbb{Z}$ or $\mathbb{Z}/2\mathbb{Z}$ is the set of path-connected components of Hamiltonians of systems in this dimension obeying this symmetry class.

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