Time-dependent bond-current functional theory for lattice Hamiltonians: Fundamental theorem and application to electron transport

► Time-dependent density functional theory (TDDFT) for lattice Hamiltonians is studied. ► Using Peierl's phases we prove the fundamental theorem of TDDFT on lattices. ► A lattice model for transport is studied with a discontinuous Kohn-Sham potential. ► The discontinuity is crucial in the Coulomb blockade regime. ► It may prevent the biased system from reaching a steady state.