Lattice-periodic plane wave ($e^{i\mathbf{k}\cdot \mathbf{R}}=1$)

A plane wave whose phase is unchanged by every direct lattice translation: $e^{i\mathbf{k}\cdot \mathbf{R}}=1$ for all $\mathbf{R}\in \Lambda$. Its wavevector is a reciprocal lattice vector. In one dimension $ka=2\pi m$.