Two-dimensional Quantum Critical Point in Underdoped Bi₂ Sr ₂ CaCu ₂O₈+δ

Underdoped Bi ₂ Sr ₂ CaCu ₂ O₈ + δ films with Tc 's from 5 to 70 K are fabricated by sputtering and Pulsed Laser Deposition (PLD). Temperature dependences of superfluid densities are measured to study the superconductor-to-insulator quantum phase transition. Sputtered films, which tend have higher dopings, show superfluid densities that are weakly linear in T at low-T and drop dramatically where Kosterlitz-Thouless-Berezinski theory predicts, assuming that individual Cu O2 bilayers are uncoupled. However, our PLD films, which are more underdoped than the sputtered films, have superfluid densities that are roughly linear from low T to Tc . Also, There is no indication of thermal critical behavior near Tc . Underdoped YBCO crystals also lack critical behavior, even though critical behavior is strong in optimally doped and moderately underdoped samples. Near the superconductor-to-insulator phase transition, Tc and n s (0) have a linear relationship that mimics that of ultrathin, two-dimensional films of Ca-doped YBa 2 Cu ₃ O₇ - δ , thereby indicating a 2-D quantum critical point at low doping