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Graphene and topological insulator two-dimensional electron systems are described by massless Dirac equations. Although the two systems have similar Hamiltonians, they are polar opposites in terms of spin–orbit coupling strength. The status of efforts to achieve long spin-relaxation times in weakly spin–orbit-coupled graphene, and large current-induced spin-polarizations in strongly spin–orbit-coupled topological insulator surface states are reviewed in this Progress Article.
