Low-temperature vortex liquid in La _2-x Sr _x CuO ₄

In copper oxide superconductors, the lightly doped (small dopant concentration, x) region is of major interest because superconductivity, antiferromagnetism and the pseudogap state come together near a critical doping value, x _c . But the way in which superconductivity is destroyed as x is decreased at very low temperatures, T, is not clear. Does the pair condensate vanish abruptly at a critical value, x _c ? Or is phase coherence of the condensate destroyed by spontaneous vortices-as is the case at elevated T (refs-8, 9, 10)? So far, magnetization data at low T are very sparse in this region of the phase diagram. Here, we report torque magnetometry measurements on La _2x Sr _x CuO ₄ , which show that, in zero magnetic field, quantum phase fluctuations destroy superconductivity at x _c ≈ 0.055. The phase-disordered condensate survives to x=0.03. In finite field H, the vortex solid-to-liquid transition occurs at H lower than the depairing field, H _c2 . The resulting phase diagram reveals the large fraction of the x-H plane occupied by the quantum vortex liquid.