Order Parameter for Charge Confinement and Phase Structures in the Lattice U(1) Gauge-Higgs Model

In the lattice U</it>(1) gauge-Higgs model, we show the existence of mass gap by showing the exponential decay upper bound for the gauge-invariant two-point function. We construct the charged state as a non-localized (string-like) state and show its orthogonality to localized states in the QED phase.