Magnetic-field penetration depth and the lower critical field of the quasi-two-dimensional superconductor ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{\mathit{y}}$

The penetration depth λ and the lower critical field ${\mathit{H}}_{\mathit{c}1}$ were measured in single crystals of ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{\mathit{y}}$. In contrast to the case of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$, the temperature dependence of λ has a large ${\mathit{T}}^2$ term at low temperatures, where T is the temperature. The temperature dependence of ${\mathit{H}}_{\mathit{c}1}$ was found to be consistent with that of λ. These behaviors deviate from the standard BCS behavior. This strongly suggests the existence of low-energy excitation in the superconducting state. Possible origins, including the importance of the layered structure of the high-${\mathit{T}}_{\mathit{c}}$ cuprates, are discussed.