Temperature dependence of the charge-density-wave energy gap onIn∕Cu(001)

A charge-density-wave (CDW) phase transition on $\mathrm{In}∕\mathrm{Cu}\left(001\right)$ with In coverage of 0.63 ML has been studied with angle-resolved photoelectron spectroscopy. Because of the quasi-two-dimensional electronic structure, the upper and lower bands of the CDW ground state were observed at a $k$ point slightly offset from $k_{\mathrm{F}}$ of the high-temperature phase. The two bands transformed to a metallic band at 405 K. Tracing the upper-band minimum and the lower-band maximum, we determined the temperature dependence of the CDW order parameter. The dependence indicates that the electronic entropy plays an important role in the transition. We discuss the enhanced contribution of electronic entropy to the free energy due to underlying bulk metallic states.