Zero-Magnetic-Field Phase-Decoherence Transition in Underdoped La$_{2-x}$Sr$_{x}$CuO$_{4}$

The two key prerequisites for superconductivity are electron pairing and phase coherence of the pair wave-function. We present an electrical transport study on underdoped La$_{2-x}$Sr$_{x}$CuO$_4$ (LSCO) films ($x=0.07$ and $0.08$) that suggests that, in zero magnetic field ($H=0$), superconductivity is destroyed by thermal unbinding of vortex-antivortex phase fluctuations at a temperature $T_{BKT}$. In particular, current-voltage ($I-V$) curves follow a power law $V \propto I^{\alpha(T)}$ with $\alpha (T) \geq 3$ for $T\leq T_{BKT}$. In addition, the contribution of the superconducting fluctuations to the conductivity, $\Delta\sigma_{SCF}(T,H=0)$, obtained by extrapolating the measured magnetoresistance from the normal state at high enough $H$ and $T$, increases monotonically with decreasing $T$ and diverges exponentially at $T_{BKT}$. These results suggest that the $H=0$ superconducting transition, where the Ohmic resistivity also vanishes, is due to the loss of phase coherence and manifests itself as a Berezinskii-Kosterlitz-Thouless transition. Our findings agree well with other experiments on LSCO with higher doping.