# Definition A topological surface state (TSS) is a [[surface state]] protected by the topology of the [[wavefunction]]. For example, in [[Time-Reversal Symmetric Topological Insulator|time-reversal symmetric topological insulators]], these states cannot be gapped as long as the bulk band gap is open and the $Z_2$ [[Z2 Topological Invariant|topological invariant]] remains nontrivial. Thus, unless we break time-reversal symmetry, the TSS remain and the surface of the TRS-TI stays conducting.